

small (250x250 max)
medium (500x500 max)
Large
Extra Large
large ( > 500x500)
Full Resolution


AN EXAMINATION OF THE RELATIONSHIP BETWEEN CLASSROOM CLIMATE AND STUDENT MATH ACHIEVEMENT BELIZE DISTRICT HIGH SCHOOLS By LORNA MARIE MCKAY Bachelor of Science in Business Administration University of Belize Belize City, Belize 1997 Master of Education in Leadership University of North Florida Jacksonville, Florida 2003 Submitted to the Faculty of the Graduate College of the Oklahoma State University In partial fulfillment of the requirements for the Degree of DOCTOR OF EDUCATION July, 2012 iii AN EXAMINATION OF THE RELATIONSHIP BETWEEN CLASSROOM CLIMATE AND STUDENT MATH ACHIEVEMENT IN BELIZE DISTRICT HIGH SCHOOLS Dissertation Approved: Dr. Ed Harris Dissertation Adviser Dr. Bernita Krumm Dr. Steve Wanger Dr. Belinda Mccharen Dr. Sheryl A. Tucker Dean of the Graduate College iv PREFACE The purpose of the study was to examine the relationship that exist classroom climate and student math achievement. The study also sought to determine the classroom climate variables that affect student math achievement. The majority of learning environments assessments was based on students’ perceptions. Students’ and teacher perceptions of the learning environment could give valuable information to improve the quality of learning and can evaluate the innovation in education (Fraser, 1998). In the study the researcher concluded that: (1). the independent variable, school type was statistically significant to student math achievement scores; (2). the independent variable, gender was not statistically significant to student mathematics performance and, (3). the other climate variables contributed very little to influence students’ math scores on PSE. In the study, the sample consisted of 18 high schools and 477 students from ninth grade or first form who sat the BPSE in 2011. The population came from the Belize District schools of 2700 students that provided a randomly selected sample of 540 study participants. The researcher used a Learning Environment Inventory (LEI) by (Fraser, 1992) to collect data on classroom climate and the Belize Primary School Examination (BPSE) for 2011 in order to obtain students’ mathematics scores. The study was correlation. v TABLE OF CONTENTS Chapter Page I. INTRODUCTION…………………………………………………………………….1 The Importance of the Classroom Environment………………………………….....2 Problem Statement…………………………………………………………………..3 Purpose Statement……………………………………………………………….......4 Questions That Will Guide the Study…………………………………………….....4 Significance of Study………………………………………………………………..5 Definition of Terms……………………………………………………………….....6 Methodology…………………………………………………………………….......8 Epistemology Perspective……………………………………………………………9 Assumption…………………………………………………………………………10 Limitations of Study……………………………………………………………......10 Summary……………………………………………………………………….……11 II. REVIEW OF LITERATURE……………………………………………………….13 The Importance of Math…………………………………………………………….13 History of Math Educational Development…………………………………………14 History and Development of Instrument……………………………………………19 Importance of School Climate…………………………………………………........19 Significance of Classroom Climate…………………………………………….........20 Teacher Qualification and Student Achievement….………………………………..25 Teacher Attitude and Student Achievement..............................................................29 Teacher Effectiveness and Student Achievement…………………………………..30 Summary……………………………………………………………………………..35 III. METHODOLOGY…………………………………………………………………..37 Purpose Statement……………………………………………………………………37 Research Questions and Hypothesis……………………………………………….....37 Belize District High Schools……………………………………………………….....39 Participants…………………………………………………………………………....39 Description of Instrument…………………………………………………………….40 Reliability and Validity of Instrument………………………………………………..40 Description of Survey…………………………………………………………………41 Research Design and Procedure……………………………………………………....42 Ethical Consideration…………………………………………………………………44 Data Analysis………………………………………………………………………….45 Summary………………………………………………………………………………45 vi IV. FINDINGS……………………………………………………………….………….47 Population.............................................................................................................…...47 Purpose of the Study………………………………………...……………………….48 Design of Study………………………………………………………………….…...48 Assumptions of Oneway ANOVA………………………………………………….48 Research Question Three……………………………………………………………..49 Research Question Four…............................................................................................53 Results of Analysis of Oneway ANOVA…………………………………………...55 Pearson Product Moment Correlation…………………………………………...........59 Correlation Analysis…………………………………………………………………..61 Non Robust Inference Method………………………………………………………64 Model Summary………………………………………………………………………69 V. CONCLUSION………………………………………………………………………72 Summary of Study…………………………………………………………………….72 Null Hypotheses……………………………………………………………………….73 Summary of Findings………………………………………………………………….74 Limitation of Study………………………………………………………………........76 Conclusion……………………………………………………………………………..77 Implications for Research, Theory & Practice….………………………………...........78 Researcher’s Reflections………………………………………………………….........81 REFERENCES…………………………………………………………………………….83 APPENDICES………………………………………………………………………..........90 Learning Environment Inventory………………………………………………………90 Learning Environment Inventory Score Sheet…………………………………………92 Permission to Use Instrument………………………………………………………….94 IRB Approval Letter…………………………………………………………………...95 Managing Authority Letter SDA………………………………………………………97Managing Authority Letter BHS………………………………………………………98 Managing Authority Letter PHS………………………………………………………99 Managing Authority Letter SJC…………………………………………………........100 Managing Authority Letter NAZ……………………………………………………..101 Managing Authority Letter GS……………………………………………………….102 vii LIST OF TABLES Tables: Page 1. Normality PSE and Sex (Male)………………………………………………..........50 2. Homogeneity of Variances (Levene statistic)……………………………………….52 3. Descriptive Statistics on PSE Math Scores and Sex………………………………...52 4. School Type and PSE Math Score…………………………………………………..54 5. Homogeneity of Variance……………………………………………………….......55 6. Robust Test of Equality of Means…………………………………………………..55 7. Descriptive Statistic on PSE Scores and School Type…………………………........56 8. PSE Between and Within Group ANOVA…………………………………….........57 9. Multiple Comparisons of PSE Math Score & School Type…………………………59 10. Pearson Product Moment Correlations……………………………………………64 11. Heteroscedasticity – Consistent Model Summary……………………………………...66 12. Heteroscedasticity – Consistent Regression Coefficient Results………………………67 13. Regression and Residual ANOVA b………………………………………………........68 14. Regression Coefficients Model……………………………………………………........69 15. Model Summary a……………………………………………………………………….69 16. Model Summary b……………………………………………………………………….70 viii LIST OF FIGURES Figure Page 1.0 Normal QQ Plot Graph……………………………………………………………51 1.1 Means Plot Graph of PSE Math Scores and Sex (Male)……………………….......53 1.2 PSE Math Score and School Type Graph………………………………………….57 1 CHAPTER I INTRODUCTION Increasing math proficiency is a global agenda. Societies understand that to succeed in a global society, a person must master math skills, as well as, critical cultural and communications skills (World View, 2006). Every career uses some sort of math. More importantly, doing math helps the mind to reason and organize complicated situations or problems into clear, simple, and logical steps. The understanding of math is essential to gain a competitive edge in many fields in today’s global economy (Patton, 2010). Therefore, math is not only necessary in an increasing number of jobs, but also in any high paying job that requires the ability to do math. Students in classrooms today must be able to solve problems, think critically, interpret solutions, analyze data and formulate questions. Training in mathematics also helps students to reason logically and enable them to form clear models of problems. Math is a way to understand all sorts of things in the world (Arnold, 2003). In Belize, strong emphasis has being placed on math proficiency. However, every year a number of students do poorly on the math in the Belize Primary School Examination (BPSE). The BPSE is a standardized exam geared at testing students’ proficiency in four areas: social studies, mathematics, English, and science. Students’ performance on BPSE is calculated as a percentage score from the scores of three test scores. Data from the 2009 BPSE sitting indicate that math was the subject that many students performed poorly on with the math having a mean of 46.15 and a median of 49%. This indicated that more than 50% of the 6,858 students who sat the exam in 2009 scored below 49% in math (Guardian, 2009). In the 2009 sitting of BPSE the 2 schools that have better resources were the performing schools in all areas which included math. These included the top private and grantaided schools (Guardian, 2009). School has been and continues to be a major factor in a child’s education both in terms of number of hours spent and the quality of teaching (Eggen & Kauchak, 2003). Thus, teachers play an important role in promoting the required knowledge, skills and attitudes for active participation in society (Ministry of Education, 2005). At the high school level, only 31% of teachers are actually qualified by any teacher training standard (Education Statistical Digest of Belize, 20052006). There were cases of young, untrained teachers, deficient in content and pedagogy, often placed in the Belizean classrooms. This has created problems in specific content areas, such as mathematics, and is reflected in the country’s poor national performance in both national and regional examinations. Consequently, teachers need to ensure that students learn to apply their mathematical background and procedures to solve real life problems (DeVries & Zan, 1994). The Importance of the Classroom Environment Classroom environment, or climate as it is often called, is important in the learning process. Kowalski (1996) defined climate as “a comprehensive structure made up of culture, physical plant, organizational structure, social relationships, and individual behaviors” (p.16). This definition implies that climate is sporadic rather than static and was affected by constant changes in the environment or outside forces within the school system. Over the past years, the classroom learning environments have emerged as a thriving field of study (Deng, 1992; Edmonds & Frederiksen, 1979; Fisher & Fraser, 1981; Walberg, 1979). Climate can positively influence the wellbeing of the learning environment, or it can significantly impede learning (Freiberg, 1998). A growing body of research showed that an important key to preventing risks 3 and developing healthy schools where teaching and learning occurs in a positive school climate (Cohen, 2001). Considering the importance of climate and student learning, research in these areas in Belizean schools is of great important. Problem Statement In Belize, the BPSE has been used as a means to measure aptitude in math and other subjects, and concerted efforts have been made to improve math scores. Presently, efforts are being made by the Ministry of Education and Youth (MOEY) to develop teacher training and acquire the necessary resources for the improvement of schools in all areas and especially in mathematics. In a 2009 Teachers’ Day address, Belize’s Minister of Education, Patrick Faber, announced that $20 million from the Caribbean Development Bank (CDB) will be invested in teacher training. While many efforts have been made to improve math scores, math learning remained poor in some schools and in others there have been improvement. The BPSE results over the years consistently show math as the lowest performing subject area in the exam. Math continues to be the lowest performing subject (The Hemispheric Project for the Preparation of Policies and Strategies for the Prevention of School Failure, 2005). In Belize, performance is at a higher level on BPSE at the schools with more resources, such as private schools and grantaided schools, (Guardian, 2009). One possible explanation for this difference in math scores in the different schools was school climate. Positive classroom climate is important for learning to occur. Achievement is related to climate and student attitudes for primary school mathematics (Goh & Fraser, 1996). Classroom climate studies were common worldwide, but in Belize there was limited research in this area and no such data exist. In fact, there was limited research in the area of education and 4 other areas of research. Considering the data on BPSE math scores and the non existence of classroom climate data there was an important need for research in these areas. Thus, the purpose of the study was to investigate the relationship between classroom climate and math achievement of students in ninth grade Belize District High schools. Purpose Statement The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth grade. The dependent variable in the study was student achievement and the independent variable was classroom climate. Questions That Will Guide the Study The following research questions guided the study: 1. What is the relationship between students’ perceptions of classroom climate and mathematics achievement? 2. What is the relationship between students’ perceptions of specific classroom climate factors: personalization, involvement, cohesiveness, satisfaction, task orientation, innovation and individualization, and mathematics achievement? 3. Are there differences between student math achievement and school type? 4. Are there differences between student math achievement and gender? Null Hypotheses H1: There is no relationship between students’ perceptions of classroom climate and mathematics achievement. H2: There is no relationship between students’ perception of personalization in the classroom and mathematics achievement. 5 H3: There is no relationship between students’ perception of involvement in the classroom and mathematics achievement. H4: There is no relationship between students’ perception of cohesiveness and mathematics achievement. H5: There is no relationship between students’ perception of satisfaction in the classroom and mathematics achievement. H6: There is no relationship between students’ perception of task orientation in the classroom and mathematics achievement. H7: There is no relationship between students’ perception of innovation in the classroom and mathematics achievement. H8: There is no relationship between students’ perception of individualization in the classroom and mathematics achievement. H9: There is no difference between student math achievement and school type. H10: There is no difference between student math achievement and gender. Significance of the Study Many factors may be used to determine the success of student math achievement. Therefore, it was important to examine the various variables that may be significant to the learning environment. Learning environments not only have positive correlation with students’ outcomes, motivation, and attitudes, but also teachers’ motivation (Sinclair & Fraser, 2002). Therefore, this study has the following importance: a) It will add to the body of existing literature that relates to the classroom learning environment variables and student achievement globally; 6 b) Assist in the creation of much needed literature on classroom climate and student math achievement for Belize; c) Aid in providing crucial information to policymakers for the development of policies nationally in Belize; d) Can be used to assist policy makers to determine what changes, if any, could be made to achieve improved student math performance on the BPSE; and e) Can also heighten educators’ awareness on the importance of classroom climate and achievement in math in Belizean classrooms, as well as, determine and fill existing gaps on student math achievement. While there were several factors that influenced student achievement, studies indicated that the teacher and the classroom climate were two of the more important factors that determined student achievement. The teacher is in the unique position to have the largest impact on student achievement (Lasley, Siedentop & Yinger, 2006). Thus, it was in these contexts that the researcher sought to conduct the study so that an evaluation of the appropriateness of specific classroom climate factors and the influence on student math performance may be examined and ascertained. Definition of Terms In this study, the following terms needed to be defined: Achievement: For the purpose of this study, success in a subject area. Belize Primary School Examination or “BPSE” refers to a national examination that is administered by the Ministry of Education to students at the end of primary education to determine achievement in relation to the primary school curriculum (Belize Education Rules, 2000). 7 Classroom Climate: The mood or atmosphere created by a teacher in his or her classroom. Classroom Environment: Intellectual, social, physical, etc., conditions within or exogenous to a classroom that influence the learning situation. Governmentaided school: A school in receipt of a grantinaid from the Government in accordance with the provisions of the Act (Belize Education Rules, 2000). Government Schools in Belize: Schools maintained wholly from the General Revenue (Belize Education Rules, 2000). Mathematics Achievement: Level of attainment in any or all mathematics skills, usually estimated by performance on a test (Belize Glossary of Education, 2000). MOEY: Ministry of Education and Youth (Belize Education Rules, 2000). PISA: A triennial survey of the knowledge and skills of 15yearolds. It is the product of collaboration between participating countries and economies through the organization for Economic Cooperation and Development (OECD), and draws on leading international expertise to develop valid comparisons across countries and cultures. Private Schools  Schools which are neither a government school nor a governmentaided school (Belize Education Rules, 2000). School  An institution that provides preschool, primary or secondary education; an “institution” refers to educational institutions providing some form of schooling (Belize Education Rules, 2000). Speciallyassisted school: A school that is in receipt of aid from the Government of Belize in the form of teacher salary for one or two teachers. Teacher: A person appointed by the manager or managing authority of a school for the purpose of instructing students (Belize Education Rules, 2000). 8 TIMSS: Trends in Mathematics and Science Study. Methodology Description of Setting and Participants The population for the high schools in the Belize District consisted of various managing authorities. The selected schools fell into three main categories namely: governmentowned, grantaided and speciallyassisted schools. Government Schools are schools that are fully funded by the government; therefore, all expenditures such as teachers’ salaries, utilities and maintenance are paid for by the government. Grantaided schools are schools that were partially funded by the government. Therefore, the government paid 70% of the teachers’ salaries and gave a subsidy grant to the schools for students’ tuition. Speciallyassisted schools are schools that received a grant for the management to pay one or two teachers in the school. Schools were coded as Catholic, Government, Protestant and Private for analytical purposes. The target population comprised of 18 Belize District high schools, which represent a total population of 2700 male and female students collectively. From the 18 high schools selected for the sample, one was an all girl institution and one was an all boy institution. The remaining 14 schools were coeducational institutions. The population for this study represented only the first formers who took the Belize Primary School Examination in 2011. An average class size of 30 was used since this was an average of the number of students in Belize District classrooms. Also, there was an average of five (5) first forms in each of the schools with an average total of 180 students. Therefore, the researcher randomly selected the participants for the study by selecting every 6th person form each class to be a part of the survey. Therefore, each person had a fair chance of being selected to be a part of the study. The total sample 9 population was 540 students from the various high schools. In order to differentiate between the various types of schools, the schools were grouped into four categories: Catholic, Government, Protestant, and Private. There were eight (8) Government Schools, seven (7) Catholic, five (5) Protestant schools, and two (2) Speciallyassisted or Private schools. In the study the researcher compared students’ classroom climate scores with those of students’ BPSE math achievement scores, who sat the BPSE in 2011 and are presently in ninth grade in Belize District High Schools. Instrument Learning Environment Inventory (LEI) was the instrument used in the study. The instrument was first developed by Herbert Walberg (1968) and later modified by Barry Fraser (1992). It was used to examine students’ perception of the learning climate of the classroom as a part of the activities involving research and evaluation of the abovementioned Harvard Project Physics. Permission to use the instrument was obtained from Professor Barry Fraser of Curtin University in Australia. Epistemological Perspective In the study the positivist view was the epistemological perspective and behaviorism was the theory used by the researcher. Positivism refers a set of philosophies and perspectives that indicates the best approach to uncovering the processes by which both physical and human events occur (Watson, 1930). Behaviorism is a theory of learning based upon the idea that all behaviors are acquired through conditioning which is concerned mainly with the observable and measurable aspects of human behavior (Watson, 1930). In defining behavior, behaviorist learning emphasized changes in behavior that result from stimulusresponse associations made by the learner. 10 Behavior is directed by stimuli. An individual selects one response instead of another because of prior conditions and psychological drives present at the moment of the action (Parkay & Hass, 2000). The behaviorist theory (Skinner, 1950) emphasizes that only behaviors worthy of study are those that can be directly observed; thus, it is actions, rather than thoughts or emotions, which are the legitimate object of study. The behaviorist learning theory was not only important in achieving desired behavior in mainstream education, but also for special education teachers who have classroom behavior modification plans to implement for their students (Standridge, 2002). Since behaviorism was also based upon observable behaviors; the researcher felt that it would have been easier to collect and quantify data when conducting the research. Assumptions This study assumed that different classroom climate variables would have influenced student math achievement on BPSE. The study also assumed that students would have performed differently in different types of classroom climate settings. The study further assumed that the participants of the study will complete the questionnaire honestly and in a favorable school setting that would be free from distractions. Limitations The limitation of a study refers to factors that a researcher was unable to control or those factors that may impact the extent to which the findings can be effectively utilized (Gay, 2000). Correlation research merely demonstrates that a researcher can predict one variable from another variable and demonstrates that two variables were associated. Correlation research may also have limitations with respect to the generalizability of the findings. Thus, it may be uncertain whether the findings of this research may be generalized to other schools, students or situations. Therefore, there were limitations that encompassed the study. One limitation was that the study 11 was only being done in one area of Belize which was the Belize District. Therefore, high schools in the other five remaining districts were excluded from the study and the likelihood of important data could have been excluded. Another limitation was the fact that the sample of students in the study would not be a representative sample of the entire population of the ninth grade who sat the BPSE in 2011 in the entire country of Belize. Additionally, only the math scores were used in the study although science and social studies scores were also tested on the BPSE exam. Furthermore, only seven variables were examined, although there could be other variables that could affect student math achievement. Finally, surveys are selfreporting instrument and are subject to human error (Kaplan, 1996). Consequently, students may or may not have correctly stated a true view or perception of the nature of the classroom climate at the time that the exam was sat. Lastly, there was the time factor that may have affected the perception of the students who were answering the survey since these students were already in ninth grade when the study was conducted. However, it is worth noting that LEI has been tested consistently over the last several decades for its validity and reliability in a manner that was similar to this study. Summary The purpose of this study was to investigate the relationships between classroom climate and math achievement in ninth grade in Belize District High Schools. The study sought to determine if there was a relationship between classroom climate and student math achievement in grades on BPSE. Using a revised version of LEI by Fraser (1994), the researcher tried to determine the specific classroom climate variables that affect student math achievement. As was stated previously, there was no study of this nature that has been done in the country of Belize; therefore, information derived from this study is important to the development 12 of classroom climate studies and math achievement studies in Belize. Thus, there was a need for this study to be conducted in Belize. The subsequent chapters of this study include: Chapter Two Literature Review, Chapter Three  Methodology, Chapter Four Findings and Chapter Five Conclusions, Recommendations and Suggestions for further related research. 13 CHAPTER 11 LITERATURE REVIEW The purpose of this study was to investigate the relationship between classroom climate and math achievement in the Belize District. The study was done to find out if there was relationship between classroom climate variables and student math achievement on BPSE. The researcher, through an examination of related literature seeks to present an in depth understanding of classroom climate and student math achievement. The review of literature within this chapter encompasses the following areas: the importance of math, history of math educational development, history and development of the instrument, importance of school climate, teacher qualification and student achievement, teacher attitude and student achievement, teacher effectiveness and student achievement. Summary and conclusion close the section. The Importance of Math Mathematics is crucial not only for success in school, but also in becoming an informed citizen, being productive in one’s chosen career, and fulfilling personal something (Murnane & Levy, 1997). Learning mathematics gives the student the foundation to be successful in other content areas during a student’s educational experience. According to U.S. Department of Education’s white paper, Mathematics Equals Opportunity White Paper  October 1997, Murnane and Levy (1996), concluded that: Students who take a rigorous K12 mathematics sequence were more likely to go to college than those who do not. Students of all income levels who do very rigorous math courses in high school were more likely to go to college. 14 In the job market, students who have strong mathematics backgrounds were more likely to be employed and earn 38% more per hour that those with insufficient skills in algebra, geometry, measurement, and probability. In another study conducted at Londonderry High School in New Hampshire, there were several areas of focus. Findings from this study indicated that during the primary years of a student’ life the focus was on learning numbers and operation, basic measurement, and basic understanding of data. In the intermediate and middle school years, greater emphasis was placed on the practice and reinforcement of basic math facts and operations and increasing. Thus, the knowledge and understanding of skills in areas such as algebra and geometry were increased. At the high school level, the focus remained on improving the fundamental mathematical concepts and skills. The students were also taught new ways to analyze data and new perspectives in algebra and geometry. History of Math Educational Development Over several decades, many student achievement studies were conducted on math achievement. The extents of students’ opportunity to learn any content in mathematics lies heavily and bear much meaning on students’ mathematic achievement (Husen, 1967). The term opportunity to learn (OTL) refers to what was studied or embodied in the tasks that students perform. In math, OTL included the scope of the mathematics presented, how the mathematics was taught, and the match between the students’ entry skills and new material (Grouws & Cebulla, 1992). Grouws and Cebulla (2000) conducted a study where teachers were asked to rate the extent of student exposure to particular mathematical concepts and skills. The results of this study indicated that there were strong correlations between OTL scores and mean student 15 achievement scores, with high OTL scores associated with high achievement. Additionally, correlations were also found in subsequent studies, such as the Second International Mathematics Study, (McKnight, 1987) and the Third International Mathematics and Science Study, (Schmidt, McKnight, & Raizen, 1997). From these studies several classroom implications were apparent, which included the need to allocate sufficient time for math instruction at every grade level. Also, of notable importance was the fact that short class periods in math, whether instituted for whatever practical or philosophical reason, should be seriously questioned. These studies also highlighted the idea that there were special concerns for 3035 minute class periods for math that were being implemented in some middle schools during this period. Additionally, the findings pointed out that: (a) the use of textbooks that devoted major attention to review and that address little new content each year should be avoided or be heavily supplemented with other resources; (b) teachers should use textbooks as just one instructional tool among many others instead of being a slave to the textbook on a onesectionperday basis, and (c) wholeclass discussion which followed individual and group work improved student achievement. Wood (1999) also solidifies the fact that wholeclass discussion worked best when discussion expectations are clearly understood. Therefore, students in the classroom setting were expected to evaluate each other’s opinions and reasoning through ways that were not critical to the other students’ sharing. Findings from this study suggested that students were expected to be active listeners who participated in discussions and feel a sense of responsibility for each others’ grasp of the concept or concepts. Therefore, the class discussions must be a summary of individual work in which key ideas were brought to the surface. Thus, the use of wholeclass discussion could also be an effective diagnostic tool for determining the depth of students’ 16 understanding and identifying students’ misconceptions. The study further highlights the idea that teachers could identify areas of difficulty for particular students, as well as, ascertain areas of student success or progress. Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important (Wood, 1999). His study also indicated that number sense was related to having an intuitive feel for number size and combinations, and the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgments. In addition, number sense also involves mentally computing, estimating, sensing number magnitudes, moving between representation systems for numbers, and judging the reasonableness of numerical results. Markovits and Sowder (1994) studied seventhgrade classes where special units on number magnitude, mental computation and computational estimation were taught. From this study the researchers found that after this special instruction, students were more likely to use strategies that reflected sound number sense that was a longlasting change. In a similar study of second graders, Cobb (1991) concluded that a problemcentered curriculum that emphasizes student interaction and selfgenerated solution methods improved students’ number sense. The findings revealed that almost every student developed a variety of strategies to solve a wide range of problems. Therefore, students displayed increased determination in trying to solve the problems. Additionally, the results of the findings further highlighted the fact that in many classrooms efforts to reinforce the use of numbers is still not being given sufficient attention. The study recommends that as teachers develop strategies to teach the use of numbers, they should strongly consider moving beyond a unitskills approach (i.e. a focus on single skills in isolation) to a more integrated approach. The integrated approach encourages the development 17 of number use in all classroom activities from the development of computational procedures to mathematical problemsolving. History and Development of Instrument Initial development and validation of a preliminary version of Learning Environment Inventory (LEI) began in the late 1960’s in conjunction with the evaluation and research of a Harvard project Physics new course for high schools (Fraser, Anderson & Walberg 1982; Walberg & Anderson 1968). Continued efforts were made over several decades by Herbert Walberg and Rudolph Moos who also started separate research programs that began additional instrument development and validation on learning environments. It was during this process that Walberg (1968) developed LEI as a part of the activities involving research and evaluation of the abovementioned Harvard project physics. The rationale for developing the instrument consisted of three very important factors that included: (1) the prohibitive expense of classroom that caused the Harvard Project Physics evaluation group to seek a paper and pencil measure of classroom interaction that teachers could administer, (2) the traditional methods of observations that included mainly “ low inference” variables which bear little relationship to pupil learning in past research (Rosenshine, 1971), and (3) the pupils were considered to be in the best position to assess their own learning environment, particularly as observer ratings had failed to provide valid measures of “high inference” variables within the class. Moos (1979) and Moos and Trickett (1987) also became engaged in the development of the social climate scales, along with scales that were being used in psychiatric hospitals and correctional institutions. These scales were later known as the classroom environment scale (CES) by (Fisher & Fraser, 1983). The final version of the LEI instrument had a total of 105 items. In the instrument the respondents were asked to express various degrees of responses. The responses included four 18 response alternatives: (1) Strongly Disagree, (2) Disagree, (3) Agree, and (4) Strongly Agree. In the scoring procedure some of the items were reversed in the scoring direction (or polarity). An example of this was seen in one of the Cohesiveness scale item: All students know each other very well. This item was reversed in the Speed scale and was stated as the pace of the class is rushed. In the use of the instrument, the perceptions of students were examined comprehensively. LEI are an expansion and improvement of the Classroom Climate Questionnaire (CCQ) (Blank & Kershaw, 1998). The instrument is used to describe the nature of the interpersonal relationships in the class as well as the structural characteristics. The LEI instrument has two distinct uses: (1) to assess the perceptions of an individual student and (2) to gauge the learning environment of the class as a group. The researchers noted that if the instrument was used for the former purpose, then the normal research procedures would apply with one caution. Since individuals’ scores were measures of their perceptions of the group of which they were a part, the scores of different individuals within the class were not strictly independent. Therefore, since the scores of subjects within a class all relate to common class experiences, usually then it was the variance among scores rather than the scores themselves which were of educational and psychological interest. Additionally, since the class mean provided the best estimate of the collective student perceptions of the class, it should be used when a researcher was examining different conditions or treatments across classes. Therefore, if a study was addressing variables, such as curriculum or teacher characteristics, then the appropriate unit of analysis was the class mean. However, if a study was examining variables such as pupil sex, selfconcept, or personality, then individual scores will be required in this study. 19 As Fraser (2002) suggested, “There are six areas of research which apply to classroom environment assessments” (p. 8). These were: (1) the relationship between student outcomes and classroom environment, (2) evaluation of educational performance, (3) differences between students’ and teachers’ perceptions of the same classrooms, (4) determinants of classroom environment, (5) use qualitative research methods, and (6) crossnational studies. Learning environment questionnaires provide information on the measure of students’ learning outcomes, students’ perceptions of their learning environment indicates that “learning environment instruments essentially measure the meaningful environments for students to a given classroom” (Anderson, Hamilton, & Hatte, 2004, p. 212). This study underpins the main idea of the relationship between classroom climate and student achievement. Importance of School Climate Globally, research studies indicate that the culture of schools is one of the main indicators of an effective school (Deal & Peterson, 1993). School culture also affects the climate of a school and by extension, the classroom climate. Educators have also continuously forged towards developing positive school cultures and by extension positive classroom climates. School climate is the social, ethical, emotional and academic school life experiences of school personnel, students and parents of the institution (Berkowitz, 2005). A growing body of research that shows that an important key to preventing risks and developing healthy schools where teaching and learning occurs is a positive school climate (Cohen, 2001). Blum (2002) also discusses that a safe, caring responsive and participatory school climate usually encourages greater student attachment to the institution. Blum (2002) continues that school climate also assists in the development a foundation for holistic learning and is the hallmark of an effective school. 20 Van Houtte (2004) advocates for some clarity on the terms school culture and school climate and the role that both of them played in research based on school effectiveness. Van Houtte (2004) presents a theoretical framework with regards to school culture indicating that there is a specific branch of organizational culture that consisted of several dimensions and levels. Thus, school climate is referred to as the next level of school culture. This study indicates that a positive school climate is present in a school when students feel a sense of acceptance, security, comfort, caring, and trust. Furthermore, in schools where there is a positive school climate, there is also a sense of belonging. Consequently, this type of culture system also maintains a positive learning environment. The former study by (Van Houtte, 2005), on school culture suggest that educators need to persistently work in an effort to improve the culture and climate conditions of schools. These findings show that if a school has a positive climate, then the classroom climate will be more than likely positive. Significance of Classroom Climate Classroom environment or climate research has become a popular area of study. Relevant studies encompass several areas that include student behavior, student achievement, and students’ perspectives. The climate of the classroom is described as a system comprising four sets of variables: the physical involvement, the organizational objectives, and characteristics of teachers and students (Schmidt & Cagran, 2006). Classroom climate is considered to be very important since it is a determinant of quality education in schools. There is a significant relationship between classroom climate and factors such as achievement, student engagement, behavior, selfefficacy, social and emotional development, principal leadership style, stages of educational reform, teacher burnout, and the overall quality of school life (Fraser, 1998 & 21 Freiberg, 1999). Therefore, the need for teachers to maintain positive climates or environments in the classrooms has been continuously emphasized in schools. There are three types of classroom climate that the teacher can use in different situations (Borich, 1996). These types include the competitive, cooperative and individualistic. In competitive classrooms, students compete with one another and are usually led by the teacher with little autonomy for students. Although competition can be motivating to students; classrooms that are led by teachers have been found to enhance student achievement. Cooperative classrooms emphasized students’ cooperation along with the teacher’s timely intervention to guide the students towards learning goals. These types of classrooms are also effective in the development of crucial cooperative learning skills that can enhance student achievement. Individual classrooms emphasize students’ individual work with little intervention by the teacher. This type of classroom could help in the student with the development of independent learning skills. In this study, the real possibility of access to participation in the classroom is one of the most important indicators of classroom climate. The voluntary participation in the classroom is much related to the climate of it (Okolo, 2007). Learning environment assessment not only provides information on how to measure students’ performance, but also information on the teachers’ competences to create positive learning outcomes. The majority of learning environments assessments is based on students’ perceptions. Fraser (1998) states, “students’ and teacher perceptions of the learning environment could give valuable information to improve the quality of learning and can evaluate the innovation in education” (p. 122). Therefore, the learning environment assessments could measure aspects in the classrooms such as teacher, students, teaching, and the learning process. PattersonRowlett (2000) conducted a study on school effects and school climate research that 22 revealed that school environment affects academic achievement. Rowlett found that an important aspect of the school environment is classroom climate which has been found to influence achievement, attitude, behavior, selfconcept, and future aspirations. Brown and Campione (1996) stated that “a learning environment should be managed so that students are encouraged to set personal goals, actively gather meaningful information, monitor and evaluate their own learning and reflect personal learning experiences in different authentic environments and social contexts” (p. 439). A further study by Brown and Campione (1996) showed that teachers play an important role in creating constructive learning environments which could help students achieve best performances and meaningful learning experiences. Positive classroom climate could motivate both students and teacher to learn and teach effectively. Thus a teacher who creates a positive classroom climate such as having a good relationship with students helps students to achieve their learning outcomes (Jarvela, 1998). For example, the teacher who knows how to attract students’ attention by using varied and interesting teaching strategies, humor, and positive reinforcements. In this type of classroom climate the students would enjoy their learning and express their ideas and opinions. Davis (2007) conducted a study using one hundred three ninth and tenth grade algebra students who completed selfreports of motivation, classroom climate, and learning styles preferences. A nonverbal measure of aptitude and algebra pretest was administered at the beginning of the academic year (August, 2007) and an algebra post test was administered at the midpoint of the academic year (February, 2007). Results indicated that selfreported levels of motivation were not significant predictors for achievement in algebra classes. In the case of classroom climate, students with lower ratings for classroom involvement and higher ratings of task orientation demonstrated higher increases in achievement than students with higher ratings 23 of involvement and lower ratings of task orientation. Conversely, in this study a student who displayed a thinking preference achieved high scores than student with demonstrating a feeling preference. Results show that students whose perceptions and preferences are more consistent with instructional style demonstrate higher short term gains in math than students with less congruent preferences and perceptions. The creation of a positive classroom climate in schools require a specific focus on (1) ensuring that the curriculum promotes academic, social and emotional learning, (2) improving the quality of the classroom for both teachers and students, (3) enabling intrinsic motivation that will encourage classroom teaching and learning, and (4) supporting and enabling teachers to be effective with a wide range of students (Davis, 2007). Therefore, several factors are important to create and maintain a positive classroom climate which include: (a) the meaningful participation for staff and students in the decision making processes of the school, (b) social support mechanisms for both staff and students in the institution and a welcoming, caring and hopeful atmosphere, and (c) a variety of options for pursuing and reaching goals. In another study, Guo (2004) examined the effects of classroom climate on the relations of children's social behaviors to school adjustment. This study was among the first to make contributions to the literature by exploring the effects of such classroom climate as teacher warmth, teacher admonishment, student relationship, class order and rule clarity, respectively, on the relations of prosocial, aggressive, victimized, delinquent and withdrawn behaviors to children's school adjustment in a sample of rural Chinese school children. Participants in the study included 3059 middle school students from 37 classes of a rural area in northern China. Peer nominations were used to measure children's prosocial, aggressive, withdrawn, victimized, delinquent behaviors and peers acceptance. Classroom climate factors used included teacher 24 warmth, teacher admonishment, student relationship, and class order and rule clarity. These were measured by student selfreports that were aggregated into classroom variables. Student academic achievement consisted of final exam scores for Chinese, mathematics, and English. Multilevel path analyses were used to explore the effects of classroom climate on the relations between children's social behaviors, their academic achievement and peer acceptance. The results of this study showed that children's prosocial behavior positively predicted students’ academic achievement and peer acceptance, whereas aggression, withdrawal, victimization and delinquency negatively predicted these two school adjustment variables. Except for prosocial behavior, the relations of different social behaviors to school adjustment varied significantly across classes. Multilevel results showed that teacher warmth negatively predicted aggression, withdrawn, victimization and delinquency. Teacher admonishment reduced the negative relation between aggression, withdrawn, victimization, delinquency, respectively, to school adjustment variables. Student relationship reinforced the negative relations of aggression, withdrawn, victimization, delinquency, respectively to school adjustment variables. Classroom order and rule clarity also enhanced the negative relation between aggression, withdrawn, victimization, delinquency, respectively, to school adjustment. This study also proved that classroom climate variables had little effect on prosocial behavior and its relations to school adjustment variables. The results provided different understandings of children's school adjustment that is subject to the influence of children's social behaviors and peer relationship but also to the classroom climate and cultures. Therefore, teachers and researchers need to consider classroom cultures when studying and defining desirable versus undesirable social behaviors and how these behaviors contribute to successful versus unsuccessful school adjustment of the children perceived to be similarly supportive for 25 both technical and university path students. The study concludes that the possible influence by teachers, schools, race, age, and grade should be viewed with caution due to some limitations within the study. Teacher Qualification and Student Achievement In any education system, the need for trained teachers cannot be overemphasized. Greenwald, Hedges, and Laine (1996) found through a metaanalysis of previous studies that educational resources had a major effect on student achievement and one of the most crucial variables was teacher quality. The research shows that the more experienced the teacher, the more resilient and successful are the students (Borman & Overman, 2004; Okpala, Smith, Jones, and Ellis (2000); Tajalli & Opheim, 2004). The study also found that although teacher quality issues may vary from study to study, it is important to note that there is usually the teacher certification status variable. Ferguson (1991) concluded from a research in Texas and elsewhere that, "Good teachers have distinguishable impacts on student exam scores (p. 465). Sanders (1998) stated that “the single largest factor affecting academic growth of populations of students is differences in effectiveness of individual classroom teachers” (p. 27). Associated with this growing consensus that highly skilled teachers are the key to improving student achievement is the realization that a substantial number of teachers appear to be under qualified for their current teaching positions (Ingersoll, 1999). One strategy supported by the U.S. Department of Education is to allow individuals enrolled in alternative certification programs to be designated. In general, researchers have found that possessing a major or minor in mathematics or science is related to increased student achievement in these subject areas. Goldhaber and Brewer (2000) found that students with teachers with degrees in mathematics had greater gains in achievement than students with teachers with non mathematics degrees, but researchers found no such results 26 for science. In a previous study, Goldhaber and Brewer (1996) also found that subject specific training in mathematics and science has a significant and positive impact on student achievement in these areas. This suggests that greater subjectmatter knowledge is associated with gains in student achievement, albeit only in the areas of mathematics and science. Conclusive in this study is the fact that students perform better in Mathematics when the teachers are qualified. Wenglinsky (2002) identified the positive outcome of learned teacher classroom practices on student achievement. Wenglinsky used the data from a 1996 National Assessment of Educational Progress (NAEP) in mathematics and found that the effects of teacher classroom practices, in union with other teacher characteristics, were as significant to student achievement in mathematics as a student’s background. The study found that the degree of certain classroom practices reported by teachers had an impact on students’ mathematics achievement. These practices included individualized instruction, handson learning and higherorder thinking skills. Additionally, Wenglinsky (2002) found that mathematics and science teachers with an undergraduate minor or major in their field elicited greater gains in student performance. In fact, Wenglinsky noted that “students whose teachers majored or minored in the subject area that they are teaching outperform their peers by about 40% of a grade level in both math and science” (p. 45). A more recent analysis by Wenglinsky (2000), who used multilevel structural equation modeling to analyze data from the NAEP, found that teachers with a major or minor in the subject area that they are assigned to teach produce greater gains in student achievement in both mathematics and science. The overall findings from these studies suggest that teacher subjectmatter knowledge positively influences student achievement. This effect seems to be more pronounced for the upper grades than the lower grades. DarlingHammond (2000) found that the 27 percentage of teachers with both a subject matter major and full state certification was positively associated with a state’s reading and mathematics scores on the National Assessment of Educational Progress (NAEP). Goldhaber and Brewer (2000) also concluded that twelvegrade students taught by teachers certified in mathematics had greater gains on a mathematics assessment than students taught by either uncertified teachers or teachers certified in non mathematics subject areas. Improperly certified teachers produced lower gains in student achievement than properly certified teachers. On the other hand, there were no differences in the gains in student achievement on a science assessment between students taught by teachers certified in science and students taught by either uncertified or improperly certified teachers. In another study, Chiang, Miller and Rowan (1997) found that students taught by teachers with mathematics major had greater gains in student achievement, although the effect on student achievement was rather small. Also a recent study by LaczkoKerr and Berliner (2002) directly addressed the issue of the effect of teacher certification on student achievement. The researchers created matched pairs of certified and uncertified teachers. Teachers were matched based on their certification status (an uncertified teacher was matched with a certified teacher) and were matched with teachers (a) within the same school, (b) within the same district, or (c) within similar districts. This matching procedure was adopted to “minimize exogenous variables associated with student achievement scores” (LaczkoKerr & Berliner, (2002. p. 24). Based on their analysis of the gain scores of 109 matched pairs of teachers, the authors found that students in classrooms of under certified teachers would have made 20% more growth had they been assigned to certified teachers classrooms. Research on teacher qualification and student achievement suggests that both subjectmatter knowledge and pedagogical knowledge are 28 positively related to student achievement. Results in a study by Alexander and Fuller (2004) showed that the estimates for the 1999 Texas state achievement exam scores for students who had certified teachers compared to noncertified teachers were statistically significant. On average, students who had a certified teacher had greater gains on the mathematics exam than students who had noncertified teachers, after controlling for several variables. Monk (1994) found that, in many cases, undergraduate coursework in mathematics pedagogy contributed more to gains in student achievement than did undergraduate coursework in mathematics. He also found that undergraduate coursework in science pedagogy was positively associated with student achievement for students in Grade 11 and that graduate coursework in science pedagogy was positively associated with student performance in Grade 10. Ferguson and Womack (1993), measuring teacher effectiveness through supervisor evaluations, realized that education coursework explained a greater proportion of the variation in evaluations than did content knowledge as measured by standardized test scores. Education coursework explained 16% of the variance in the evaluations. Thus, Monk (1994) stated that, “It would appear that a good grasp of one’s subject area is necessary but not a sufficient condition for effective teaching” (p. 142). These studies are further reinforced through a Secretary of Education’s report (USDOE, 2002) which states: Research emphasizes the importance of recruiting teachers with solid content knowledge and verbal ability, but today’s certification system seems to work against the recruitment of these individuals. Of course, many teachers are smart and know their subjects well, but our system allows too many talented candidates (p. 12). 29 These studies succinctly summarize the importance and effect of teacher qualification on student achievement. Thus the need for qualified teachers in the education system cannot be ignored by the policymakers. Teacher Attitude and Student Achievement Teachers’ attitudes are an important factor in determining the success of students (Grosin, 1995). Unsuitable physical environment and teacher’s personality characteristics lead to student indiscipline in classrooms (Patankar & Northam, 2003). Effective teaching requires that the teacher gives the student plenty of opportunities to contribute and elaborate on their own ideas, and that he or she genuinely listens to students say and attempts to consider this from other students’ perspectives. In addition, it is important that students know that there is comfort in the classrooms and that they will be treated humanely when they do contribute. Wrong answers should not provoke negative reactions on the part of the teacher, but needs to be perceived as part of the students’ learning process (Patankar & Northam, 2003). In order to provide the atmosphere for optimum learning, the teacher must have the class well organized or disciplined. Classroom guidelines are needed for routine activities and general classroom behaviors. Lin (2002) investigated teachers' perspectives on teacher value and the relationship between teacher value and classroom climate. The research questions guiding this study were concerned with (1) identification of values important to teachers; (2) the importance of teacher value on teachers' curriculum, teaching strategy, assessment, relationship with students, and classroom climate; (3) students' evaluations of classroom climate; and (4) the correlation between teachers' perceptions and students' evaluations. The study examined the school character (public or private), as well as the teachers' gender, country, age and number of years of teaching experience. Sixteen teachers completed a survey with questions that were designed for 30 the purposes of this study, and 459 students completed the College and University Classroom Environment Inventory developed by Fraser and Treagust in 1986. The researcher collected teachers' responses and implemented the investigations with students in the classroom on a specific day. The data was analyzed using the Statistical Package for the Social Science (SPSS) Version 10.0 for Microsoft Windows. Descriptive statistics were used to summarize demographic information and teachers' perspectives on teacher value. Pearson's correlation coefficient was also used to analyze the relationship between each teacher's perceptions and students' evaluations. Descriptive statistics were used to summarize demographic information and teachers' perspectives on teacher value. Pearson's correlation coefficient was also used to analyze the relationship between each teacher's perceptions and students' evaluations. Descriptive statistics were used to summarize demographic information and teachers' perspectives on teacher value. Pearson's correlation coefficient was also used to analyze the relationship between each teacher's perceptions and students' evaluations. This study concludes that teacher value is related to positive classroom climate. Teacher Effectiveness and Student Achievement Teaching and learning are complex tasks. In order for students to learn effectively, they must participate fully in the learning process. Students must be encouraged to ask and answer questions, attempt new approaches, make mistakes, and ask for assistance. The effect on student learning of changing a single teaching practice may be difficult to discern because of the simultaneous effects of both other teaching activities that surround it and the context in which the teaching takes place (Grouws & Cebulla, 2000). The number of research studies conducted in mathematics education over the past three decades has increased dramatically (Kilpatrick, 1992). In these studies there are a wide variety 31 of areas which include research methodologies, content and grade levels. Results from these studies, together with relevant findings from research in other areas of studies that include studies on cognitive psychology, are being used to identify successful teaching practices and strategies. Furthermore, the results of studies that have been conducted indicates that teachers who seek to improve the effectiveness of their teaching must be careful to study the context in which the delivery is done and the types of students that they teach. Wright (2005) conducted a study on the social network analysis of middle school classrooms. In studying student teacher relations, Wright (2005) conducted direct observations in classrooms over a year, interviewed teachers and students, and collected questionnaire data from teachers and students. By utilizing network tools, a comparison and contrast on the structural composition of classrooms and studentteacher relations was done. This systematic structured observations of classrooms over extended periods of time provided data on studentteacher social interaction that are impossible to gather using selfreport studies alone. Direct observation also offers insight into the social structural mechanisms through which student productivity is constrained or enabled in the classroom. This study was one of the first of its kind to utilize formal social network theory and methods to characterize classroom social structure. The development of this study offered a new set of variables  social networks for policy makers and educators to access in order to enhance student productivity and teacher effectiveness in the classroom. Heilman (1999) conducted a study to investigate the combined impact of reform efforts, content coverage, the importance of grades, honor roll, and nonschool interests of students’ pressure for teachers to replace strategies that motivate students with strategies that promote efficiency and competition. The study examined how teachers emphasized learning or 32 competitive goals and regulate the purpose of the class in response to the huge number of influences that determined the classroom climate. A researcherdeveloped survey instrument was used to collect data from a random cluster sample of 412 students in eighteen classrooms to determine the relationship between student effort and selfperceptions of ability to theories of motivation. Scales used in the survey instrument were teacher support, teacher control, organization and rules, and task orientation; task value and selfperceptions of ability; masteryorientation and performanceorientation; mastery evaluation and performance evaluation. Independent samples t tests were done which indicated that masteryoriented experiences of students are related to higher levels of selfperceptions of ability, effort, support, task value, organization and rules, and promotion of selfregulation than performanceoriented class experiences (p < .05). A series of analyses of variance in this study found that effort levels (high, middle, and low effort) were related to selfperceptions of ability, task value, teacher support, teacher control, task orientation, organization and rules, masteryorientation, promotion of selfregulation, and grades ( p < .05). Competitive classroom experiences were found to have no significant relationship to student effort. Grade level and gender were significantly related to climate variables. It also reported that ninth grade students worked significantly harder than seniors (p < .05) while the upperclassmen results showed higher levels of teacher support, organization and rules, and mastery orientation (p < .05). The study indicates that females worked harder than males and received higher levels of teacher support (p < .05). Another study by Olina and Sullivan (2002) investigated the effects of teacher evaluation and the combination of teacher evaluation and student selfevaluation on student performance and attitudes. Participants in the study were 189 Latvian high school students and their six 33 teachers. The six teachers were assigned to one of three treatment conditions: (a) no evaluation, (b) teacher evaluation, and (c) selfevaluation plus teacher evaluation. All groups completed a 12lesson instructional program on how to conduct experiments and produce research reports. Students in the teacherevaluation group received teacher evaluation on their initial research reports. Students in a selfplusteacher evaluation group selfevaluated their reports and received teacher evaluation on them. The noevaluation group received no formal evaluation instructions. Results of this study indicated that students in the teacherevaluation and the selfplus teacher evaluation groups received significantly higher ratings on their final projects than those in the noevaluation group. However, the noevaluation group had more favorable attitudes toward the program than the other two groups, while the selfplusteacher evaluation group was significantly more confident of their ability to independently conduct future research experiments. Participants in the study were 189 Latvian high school students and their six teachers. The six teachers were assigned to one of three treatment conditions: (a) no evaluation, (b) teacher evaluation, and (c) selfevaluation plus teacher evaluation. All groups completed a 12lesson instructional program on how to conduct experiments and produce research reports. Students in the teacherevaluation group received teacher evaluation on their initial research reports. Students in a selfplusteacher evaluation group selfevaluated their reports and received teacher evaluation on them. The noevaluation group received no formal evaluation instructions. Results of this study indicated that students in the teacherevaluation and the selfplus teacher evaluation groups received significantly higher ratings on their final projects than those in the noevaluation group. However, the noevaluation group had more favourable attitudes toward the program than the other two groups, while the selfplusteacher evaluation group was 34 significantly more confident of their ability to independently conduct future research experiments. Therefore, short class periods in mathematics whether instituted for whatever practical or philosophical reason, should be seriously questioned. These studies highlighted the fact that there was special concern for 3035 minute class periods for math which was being implemented in some middle schools during this period. Additional findings of the study showed that the use of textbooks that devote major attention to review and that address little new content each year should be avoided or be heavily supplemented with other resources. The findings also suggest that teachers should use textbooks as just one instructional tool among many instead of being a slave to textbooks on a onesectionperday basis. Wholeclass discussion following individual and group work improves student achievement. Research in student math achievement also suggest that the use of whole class discussion can be effective if it is used for explaining and sharing the many ways by which individual students arrive at solutions for math problems. This kind of interaction allows students to view the various ways of examining a situation and the diversity acceptable solutions to specific problems. Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important. Number sense relates to having an intuitive feel for number size and combinations, and the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgments. It involves mentally computing, estimating, sensing number magnitudes, moving between representation systems for numbers, and judging the reasonableness of numerical results. Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view 35 mathematics as a discipline in which thinking is important. Number sense relates to having an intuitive feel for number size and combinations, and the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgments. It involves mentally computing, estimating, sensing number magnitudes, moving between representation systems for numbers, and judging the reasonableness of numerical results. Markovits and Sowder (1994) studied seventhgrade classes where special units on number magnitude, mental computation and computational estimation were taught. Through this study it was found that after this special instruction, students were more likely to use strategies that reflected sound number sense, and that this was a longlasting change. Results showed that almost every student developed a variety of strategies to solve a wide range of problems. Students also displayed increased determination in trying to solve the problems. However, the findings also highlighted the fact that in many classrooms efforts to reinforce the use of numbers are still not given sufficient attention. Therefore, the study recommended that teachers develop strategies to teach the use of numbers, they should strongly consider moving beyond a unitskills approach (i.e. a focus on single skills in isolation) to a more integrated approach that encourages the development of number use in all classroom activities, from the development of computational procedures to mathematical problemsolving. Summary This review of the literature on classroom climate and student math achievement indicates that there is a unified trend towards the promotion of the creation of suitable classroom climate for students that will influence student achievement in content areas. Classroom climate plays a vital role in the student achievement. The literature also points to the fact that the classroom climate factors such as school climate, teacher and student attitude and teacher 36 qualification are part of the many areas that affect student achievement in schools. This review highlighted several studies that clarify the vital role that the teacher plays in fostering a positive classroom climate along with student success and achievement in schools. However, while there is also a great deal of agreement that classroom climate is important for achievement; there are still other areas to be investigated. Unsuitable physical environment and teacher’s personality characteristics lead to student indiscipline in classrooms (Patnakar, 2007). The review of literature has also underscored the need for LEI to be used in this study. This research was an effort to determine the relationship between classroom climate and student achievement and has, no doubt, created literature on classroom climate for Belize and added to the body of research that exist globally. 37 CHAPTER 111 METHODOLOGY This chapter gives a description of a proposed study design that will seek to determine if a relationship exists between classroom climate and student math achievement along with the variables that affect such relationship. The following sections are included in this chapter: purpose statement, the questions and hypotheses, a description of high schools in Belize, participants and sample size, a description of the instrument, and the research design and procedures. An explanation on ethical considerations and a summary are also included in this chapter. Purpose Statement The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth grade in Belize District high schools. The study also sought to determine the classroom climate factors that influence student math achievement of in ninth grade in Belize District High Schools. The dependent variable in the study is student achievement and the independent variable is classroom climate. Research Questions and Hypotheses The following research questions will guide the study: 1. What is the relationship between students’ perceptions of the classroom climate and mathematics achievement? 2. What is the relationship between students’ perceptions of specific classroom climate factors and mathematics achievement? 3. Are there differences between students’ PSE Mathematics scores and gender? 4. Are there differences between students’ PSE Mathematics scores and school type? 38 H1: There is no difference between students’ perceptions of classroom climate and math achievement. H2: There is no difference between students’ perceptions of specific classroom climate factors and mathematics achievement. H3: There is no difference students’ perception of personalization and mathematics achievement. H 4: There is no difference students’ perception of involvement and mathematics achievement. H5: There is no difference between students’ perception of cohesiveness and mathematics achievement. H6: There is no difference between students’ perception of satisfaction and mathematics achievement. H7: There is no difference between students’ perception of task orientation and mathematics achievement. H8: There is no difference between students’ perception of innovation and mathematics achievement. H9: There is no difference between students’ perception of individualization and mathematics achievement. H10: There is no difference between PSE Math Achievement Scores and gender. H 11: There is no difference between students’ PSE Math Achievement Scores and school type. 39 Belize District High Schools High schools are located throughout the country of Belize and vary in location, population and managing authorities. Presently there are 49 high schools in the country of Belize. According to the Education Statistical Digest of Belize (2005 06) the total number of secondary schools increased by 13 schools from 36 in 200102 to 49 in 200506. These 49 schools are a reflection of the entire high school population in the six districts of Belize namely: Orange Walk and Corozal Districts in the north, Stann Creek and Toledo Districts in the south, Cayo District in the west, and Belize District in the east. The Belize District is also inclusive of the Caye – San Pedro and Caye Caulker. However, it must be noted that two recently opened high schools are not accounted for in the previous data which brings the total to 18 high schools. The high school populations range from 90 students in one school to over 800 students in others. Students from these various high schools also come from various ethnic groups and backgrounds. Besides location and population, high schools in country of Belize also differ in the type of managing authorities which include the government, churches, and private entities. For the purpose of this study, only the 18 high schools in the Belize District were used. A total of 13 of these high schools are located in the urban portion of the district, three in the rural area, one San Pedro, and one in Caye Caulker. Participants The target population that was studied includes 18 Belize District High Schools which represent a total population of 2700 male and female students collectively. Students were from various socioeconomic backgrounds across the country in Belize also represent a wide cross section of the various ethnic groups in Belize. These included the Creole, Mestizo, Garifuna, 40 East Indian and Maya. Two of the proposed institutions that were selected for the sample were all girl institutions and one was an all boy institution with the other 15 being coeducational institutions. The number of high school in the Belize District is small; therefore, the researcher used all of the 18 high schools to obtain a random sample. This sample was indicative of the students to whom the survey instrument was distributed. For the study 540 questionnaires were issued and 477 were received. A response rate of 88% was received. Description of Instrument In the study a customized version of The Learning Environment Inventory (LEI) first developed by Herbert Walberg (1968) and later modified by Barry Fraser (1992) to examine students’ perception of the learning climate of the classroom was used. The quantitative instrument was tested and used in several classroom climate studies in the past. The participants were students who sat the BPSE in 2011 at the grade eight levels and are presently in grades nine at high school. However, the same seven classroom climate variables personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation and individualization were used in the study. Reliability and Validity Several studies have been done to test and retest the instrument that was used in this study. These studies include The Harvard Project Physics (1962 72) that required the development of an instrument to assess learning environments in physics classrooms. This instrument was the start of the initial development and testing of Learning Environment Inventory (LEI) (Walberg, 1968), where students were asked to report their perceptions of the wholeclass environment. Moos and Trickett (1974) later developed a series of environment measures which concluded with the Classroom Environment Scale (CES). CES was also used to 41 ask students for their perceptions of the learning environment of classrooms. Two questionnaires provided considerable milestone for the study of classroom learning environments, were used extensively for a variety of research purposes, and provided models for the development of a range of instruments over the next two decades. This set of studies also influenced Fraser, Giddings and McRobbie (1992) to propose a different form of a learning environment instrument to investigate students’ personal perception of their role in the environment of the classroom rather than students’ perception of the learning environment in the class as a whole. These two forms are the personal form and the class form. Later, there was the development of Classroom Climate Inventory (1986) and subsequently Learning Climate Inventory (1992) by Barry Fraser. Wong & Fraser (1996) further validated the instrument by administering the Personal Form to 1,592 grade 10 chemistry students in 56 classes in Singapore. Therefore, since the LEI was validated and proven reliable over several years of testing, the researcher used the instrument in its original form. Thus, the researcher did not alter the instrument in anyway. This guaranteed the validity and the reliability of the instrument in the conducting of the research. Description of Survey The Learning Climate Inventory survey is comprised of 49 items for the participants to answer. The survey has a range of four answers which include the following: SA = Strongly Agree, A = Agree, D = Disagree and SD = Strongly Disagree. A score sheet accompanies the survey that divides the required item into seven categories that are clearly defined. These categories include the following: 1. Personalization emphasizes opportunities for students to interact with the instructor and the instructor's concern for student' personal welfare; 42 2. Involvement  assesses extent to which students participate actively and attentively in class discussions and activities; 3. Student Cohesiveness looks at the extent to which students know, help and are friendly toward each other; 4. Satisfaction measures the degree of enjoyment of classes; 5. Task Orientation considers the extent to which class activities are clear and well organized; 6. Innovation is the extent to which the instructor plans new and unusual class activities, teaching techniques, and assignments; and 7. Individualization is the extent to which students are allowed to make decisions and are treated differently according to ability, interest and rate of working. The score sheet also had some underlined items that were calculated from the responses of the participants using a specific formula for each range. This survey was appropriate for this study since it specifically addressed the classroom climate variables that the researcher examined. Research Design and Procedure Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. 43 The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth graders who were eight graders when they sat the BPSE. The dependent variable in the study was student math achievement and the independent variable was classroom climate. Data for this study was gathered using the seven independent variables of LEI (personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation, and individualization) and the dependent variable (BPSE math score). Existing data from the 2011 BPSE sitting was used to correlate with the data gathered from the instrument. In this study, data on gender and school type was also collected due to the coding of the high schools. High Schools Selection In this study, the researcher used only 18 high schools in the Belize District. The Belize District has the largest high school population of the 49 high schools across the entire country. The sample was drawn from all of the high schools that fell within the Belize District. Managements for the high schools ranged from grant aided/ church state to government and privately owned status. Three of the proposed high schools are situated in the rural section of the Belize District, two are in the Cayes, and the other 14 are in Belize City. Participants Selection The researcher proposes to use a sample of 540 Belize District High School students from the total target population of (N= 2700) students. The sample was drawn from the total list of high schools in the Belize District. This was done so that the researcher can get a narrow, homogeneous or uniform sample that will make data collection and data analysis easy and simple. Once the sample was drawn, a random selection was done. Every participant was given a fair and equal chance to participate in the study. At the high school 30 surveys were 44 distributed to the participants through the principals at the school. A consent form was placed with each survey for each participant to take home in order for the participants to obtain permission from the parent or guardian to voluntarily participate in the study. The students were given LEI survey to answer. The surveys were collected one week after distribution. An appropriate day and date was arranged with the principals of the 18 high schools to collect the surveys from the institution in order to have started the data analysis process. The LEI has been used in this manner several times over the past two decades (Fraser, 1989; Fraser, 1987; Moos & Trickett, 1987 and Walberg, 1968). Therefore, the time frame for the data to be collected was suitable for the study. Ethical Considerations The researcher also ensured the adherence to the ethical standards and guidelines concerning the involvement of human subjects. Permission was obtained from Human Subject Research Board (HSRB) from Oklahoma State University to guarantee that the process of data collection was valid. Protecting participants’ information was also required, hence personal data was kept confidential and their identities remained anonymous. The researcher ensured that the participants knew that any information given was kept confidential and that their participation would have been voluntary. Thus, the participants could have chosen to discontinue their participation at any time during the data collection process if they so desired. The safety of the participants was of utmost importance so that any intention of harm and maliciousness against the participants was prevented. Additionally, the names of participating institutions were kept anonymous through the use of a coding system. Gay and Airsaian (2000) indicate that the use of descriptive designs in a study involving human subjects in real life situations, where events have already occurred, 45 reduce the chance of the researcher to influence the participants because the researcher will not be in direct contact with the participants of the study. Lack of the direct contact led to more credible data collection and the increased validity of the data on classroom climate and student achievement. Data Analysis The data in this study was analyzed using descriptive statistics. The Pearson product moment correlations, multiple regression analysis, and analysis of variance (ANOVA) tests were used in the data analysis. These tests were used in order to investigate the relationships between classroom climate perceptions and learning outcomes using LEI and the mathematics scores from the 2011 (PSE). Several steps were employed. First, the ANOVA test was performed to determine if there is a significant difference between levels of means of the independent variables. Next, a Pearson productmoment correlation between the classroom climate variables studied and the PSE math achievement scores was obtained. Therefore, the means of the LEI scores, which include personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation and individualization, were compared to the total means of the overall students’ BPSE math scores. Finally, a multiple regression analysis was done in order to verify whether a combination of classroom climate variables determined the predictive power of BPSE math achievement. Summary The purpose of the study was to investigate the relationships between classroom climate and students’ math achievement in 18 high schools in the Belize District. A random sample was drawn from the target population (N=2700). The total number of proposed participants was 540 students. The researcher used a tested instrument, the LEI, which aided in the collection of valid, reliable and necessary data for the analysis. The study was aimed at looking at correlation to 46 determine whether a relationship, if any, between the classroom climate variables and student math achievement existed. The data informed the development of graphs and tables to explain findings and solidify the study. The Statistical Package for the Social Sciences (SPSS) 19.0 by Nie (1968) was used to represent the statistical data in a form of graphs and tables for this proposed study. 47 CHAPTER 1V FINDINGS Chapter four discusses the results of the study on classroom climate and student math achievement. The purpose of study, sample population, design and findings are discussed. Population The population for the high schools in the Belize District consisted of various managing authorities. The selected schools fell into three main categories namely: governmentowned, grantaided and speciallyassisted schools. Government Schools are schools that are fully funded by the government; therefore, all expenditures such as teachers’ salaries, utilities and maintenance are paid for by the government. Grantaided schools are schools that were partially funded by the government. Therefore, the government paid 70% of the teachers’ salaries and gave a subsidy grant to the schools for students’ tuition. Speciallyassisted schools are schools that received a grant for the management to pay one or two teachers in the school. Schools were coded as Catholic, Government, Protestant and Private for analytical purposes. The target population comprised of 18 Belize District high schools, which represent a total population of 2700 male and female students collectively. From the 18 high schools selected for the sample, one was an all girl institution and one was an all boy institution. The remaining 14 schools were coeducational institutions. The population for this study represented only the first formers who took the Belize Primary School Examination in 2011. An average class size of 30 was used since this was an average of the number of students in Belize District classrooms. The sample for this study was purposive and random. Therefore, the sample from the population was a total of 540 students from the various high schools. A total of 30 students 48 were sampled from each high school. In order to differentiate between the various types of schools, the schools were grouped into four categories: Catholic, Government, Protestant, and Private. There were eight (8) Government Schools, seven (7) Catholic, five (5) Protestant schools, and two (2) Speciallyassisted or Private schools. In the study the researcher compared students’ classroom climate scores with those of students’ BPSE math achievement scores, who sat the BPSE in 2011 and are presently in ninth grade in Belize District High Schools. Purpose of the Study The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth grade. The dependent variable in the study was student achievement and the independent variable was classroom climate. Design of Study Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. Assumptions of Oneway ANOVA The following are the assumptions of a oneway ANOVA that was first used to analyze the data: 1) An independent variable consists of two or more categorical independent groups. In this study the independent variable was sex and this had two groups namely: male and female; 49 2) A dependent variable is either interval or ratio (continuous). The PSE math achievement was the dependent variable and is a ratio or continuous variable; and 3) a dependent variable is approximately normally distributed for each category of the independent variable. An assessment of the normality of data is a prerequisite for many statistical tests as normal data is an underlying assumption in parametric testing. There are two main methods of assessing normality  graphically and numerically. The following methods were used to determine whether the data was normal and if this assumption was met in the data for the statistical tests. The approaches were divided into two main themes: relying on statistical tests or visual inspection. Statistical tests have the advantage of making an objective judgment of normality, but are disadvantaged by not being sensitive enough at low sample sizes or overly sensitive to large sample sizes. As such, some statisticians prefer to use their experience to make a subjective judgment about the data from plots/graphs. Thus, graphical interpretation has the advantage of allowing good judgment to assess normality in situations when numerical tests might be over or under sensitive. However, graphical methods may also lack objectivity. Conversely, since the researcher did not have a great deal of experience interpreting normality through graphs, the best option was to use the numerical methods. Research Question 3 Are there differences between student math achievement and school type? Table 1 below presents the results from two wellknown tests of normality, namely the KolmogorovSmirnov Test (1967) and the ShapiroWilk Test (1965). The researcher used both the ShapiroWilk Test and the KolmogorovSmirnov Test as the numerical means of assessing normality. 50 Table1. Test of Normality Statistic df Sig. Statistic df Sig. PSE Math Score Male .100 222 .000 .954 222 .000 Female .097 255 .000 .961 255 .000 Sex KolmogorovSmirnova ShapiroWilk Tests of Normality The table above shows that the PSE math achievement scores for each male and female group were not normally distributed. If the significance value of the ShapiroWilk test (Shapiro & Wilk, 1965) or the KolmogorovSmirnov test (Chakravarti, Laha & Roy, 1967) is greater than 0.05, then the data is normal for each category. If it was below 0.05, then the data significantly would deviate from a normal distribution. Normal QQ Plot In order to determine normality graphically, the researcher used the output of a normal QQ Plot. In the Q Q Plot, if the data were normally distributed, then the data points will be close to the diagonal line. Conversely, if the data points stray from the line in an obvious nonlinear fashion, then the data are not normally distributed. In the Q Q Plot below the data is not normally distributed. This is easily seen by using the numerical methods since the normality of data based on plots is difficult to determine 51 Figure1.0. Normal QQ Plot of PSE Math Score The oneway ANOVA is considered to be a robust test against the normal assumption. This means that it tolerates violations to its normality assumption rather well. In regards to the normality of group data, the oneway ANOVA can tolerate data that is nonnormal (skewed or kurtotic distributions) with only a small affect on the Type I error rate. Equality of variances between the independent groups (homogeneity of variances). One of the assumptions of the oneway ANOVA is that the compared variances of the groups are similar. Table 2 Test of Homogeneity of Variances shows the result of Levene's test of homogeneity of variance, which tested for similar variances. It is noteworthy that if the significance value is greater than 0.05 (found in the significance column), then there is homogeneity of variances. Because Levene's F statistic had a significance value of 0.094 (which is more than 0.05), the assumption of Homogeneity of Variance was met. 52 Table 2.Test of Homogeneity of Variances Results and Analysis of Oneway ANOVA The descriptive table (see Table 3 below) provides some very useful descriptive statistics including the mean, standard deviation and 95% confidence intervals for the dependent variable (PSE math achievement scores) for each separate group (male and female) as well as, when all groups are combined (total). These figures are useful for the researcher to describe the data. Table3. Descriptive Statistics on PSE Math Scores and Sex Lower Bound Upper Bound 222 48.6 22.290 1.496 45.6 51.5 12.0 92.0 255 50.1 21.985 1.377 47.4 52.8 11.0 95.0 477 49.4 22.117 1.013 47.4 51.4 11.0 95.0 Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Descriptive Statistics on PSE Math Scores and Sex Male Female Total PSE Math Score Content Area N Mean The Descriptive Statistics table above (Table 3) and the Means Plot Graph (Figure: 1.1) below showed that female students reported higher mean in PSE math achievement scores compared to male students. Levene Statistic df1 df2 Sig. 16.878 3 473 0.094 Test of Homogeneity of Variances PSE Math Score 53 Figure1.1. Means Plot of PSE Math Scores and Sex Results of the ANOVA The oneway between subjects ANOVA tests were conducted to examine whether there were significant differences in the mean PSE math achievement scores in sex (male and female) group means. These tests proved that there was no significant difference in the PSE math achievement scores between male (M = 48.6, SD = 22.290) and female (M = 50.1, SD = 21.985) Sex group; F (1, 475) = 0.560, p = 0.455. These results suggested that male students have PSE Math Achievement Scores that were not significantly different from female students. Research Question 4 Are there differences in PSE math achievement scores between school types in schools? The assumptions of a oneway ANOVA in this question indicate that: 1) The independent variable consists of two or more categorical independent groups. Independent variable is school type and this has 4 groups namely Catholic, Government, Pentecostal and Private Schools; 54 2) The dependent variable is either interval or ratio (continuous). PSE Math Achievement Scores is the dependent variable and is a ratio or a continuous variable; and 3) Dependent variable is approximately normally distributed for each category of the independent variables. Table 4. Tests of Normality for School Type and PSE Score Statistic df Sig. Statistic df Sig. Catholic .106 86 .018 .960 86 .009 Government .162 224 .000 .904 224 .000 Pentecostal .076 136 .052 .985 136 .134 Private .120 31 .200 .952 31 .183 a. Lilliefors Significance Correction This is a lower bound of the true significance. Tests of Normality School Type KolmogorovSmirnova ShapiroWilk PSE Math Score Table 4 shows that the PSE math achievement scores for each group of school type was not normally distributed. How do we know this? If the significance of the ShapiroWilk test or the KolmogorovSmirnov test is greater the 0.05, then the data is normal for each category. If it is below 0.05 then the data significantly deviates from the normal distribution. In this case, Catholic and Government school type groups were not normally distributed; hence the assumption of normality was not met. However, the oneway ANOVA is considered a robust Test against the normality assumption. This means that it tolerates violations to its normality assumption rather well and, thus the reason why the researcher used this test. Equality of Variances between the Independent Groups (homogeneity of variances) One of the assumptions of the oneway ANOVA is that the variances of the groups that are being compared are similar. Table 5 below shows the test of homogeneity of variances 55 shows the result of Levene's test of homogeneity of variance, which tests for similar variances. If the significance value is greater than 0.05 (found in the Sig. column below), then there is homogeneity of variances. In the test, in Table 5, the Levene's F statistic had a significance value that was less than 0.001 and, therefore, the assumption of homogeneity of variance was met. Table 5. Test of Homogeneity of Variance Robust Tests of Equality of Means Table Even though there was a violation of the assumption of homogeneity of variances, the researcher used the traditional ANOVA by using the Welch test (Shapiro & Wilk, 1965). This was done in order to determine whether there were significant differences between the groups. Like the ANOVA test, if the significance value is less than 0.05, then there are statistically significant differences between groups. Hence, then there were statistically significant differences between school type groups since the p value in the Welch test was less than 0.05 (p <0.001). Levene Statistic df1 df2 Sig. 16.878 3 473 0.094 Test of Homogeneity of Variances PSE Math Score 56 Table 6. Robust Tests of Equality of Means Statistica df1 df2 Sig. Welch 125.811 3 151.155 .000 a. Asymptotically F distributed. Robust Tests of Equality of Means PSE Math Score Independence of cases – This assumption is that data from different subjects are independent, which means that the behavior of one participant does not influence the behavior of another. Results and Analysis of Oneway ANOVA Descriptive Statistics The descriptive statistics table (see Table 7 below) provided some very useful descriptive statistics including the mean, standard deviation and 95% confidence intervals for the dependent variable PSE math achievement scores for each separate group of School Type (Catholic, Government, Pentecostal and Private Schools) as well as, when all groups were combined. Table 7. Descriptive Statistics on PSE Math Scores and School Type Lower Bound Upper Bound Catholic 86 64.3 19.749 2.130 60.10 68.57 16 95 Government 224 40.6 21.136 1.412 37.79 43.36 11 87 Pentecostal 136 47.8 16.109 1.381 45.08 50.55 12 92 Private 31 78.3 8.537 1.533 75.16 81.42 60 91 Total 477 49.4 22.117 1.013 47.39 51.37 11 95 95% Confidence Interval for Mean Minimu m Maximum Descriptive Statistics on PSE Math Scores and School Type PSE Math Scores School Type N Mean Std. Deviation Std. Error The descriptive statistics table above and the means plot below showed that students from private schools reported higher mean of math achievement scores than students from Catholic, 57 Pentecostal and Government Schools. Students from Catholic Schools reported higher mean of PSE math achievement scores than students from Pentecostal and Government Schools. Students from Pentecostal Schools reported higher mean of PSE math achievement scores than students from Government Schools. Figure1.2. Graph of Mean of PSE Math Scores and School Type Table 8. PSE Math Score between Groups and Within Groups ANOVA Sum of Squares df Mean Square F Sig. Between Groups 62845.106 3 20948.369 58.288 .000 Within Groups 169992.722 473 359.393 Total 232837.828 476 ANOVA PSE Math Score 58 The ANOVA table above shows the output of the ANOVA analysis and tells if there was a statistically significant difference in the PSE achievement math scores among school type (Catholic, Government, Pentecostal and Private Schools) group means. In this table the significance level is 0.000 (i.e. p < 0.001), which is less than 0.05 and, therefore, there is a statistically significant difference in the PSE achievement scores among school type groups. Multiple/ PairWise Comparisons From the previous results there were significant differences in PSE math achievement scores from different school type groups as a whole. Table 9 below, Multiple Comparisons, shows which groups significantly differed from each other. The Games Howell test (Keppel & Wickens, 2004) is a generally preferred test for conducting posthoc tests in a oneway ANOVA when the assumption of homogeneity of variance has been violated. The table below indicates that there is a significant difference in PSE math achievement scores between Catholic and Government Schools, Catholic and Pentecostal Schools (p < 0.001), Catholic (p < 0.001) and Private Schools (p < 0.001), Government and Pentecostal Schools (p=0.002 < 0.05), Government and Private Schools (p < 0.001) and Pentecostal and Private Schools (p < 0.001). 59 Table 9. Multiple Comparisons of PSE Math Score and School Type Lower Bound Upper Bound Government 23.761* 2.555 .000 17.13 30.39 Pentecostal 16.521* 2.538 .000 9.93 23.11 Private 13.953* 2.624 .000 20.80 7.11 Catholic 23.761* 2.555 .000 30.39 17.13 Pentecostal 7.240* 1.975 .002 12.34 2.14 Private 37.714* 2.085 .000 43.17 32.26 Catholic 16.521* 2.538 .000 23.11 9.93 Government 7.240* 1.975 .002 2.14 12.34 Private 30.474* 2.064 .000 35.88 25.07 Catholic 13.953* 2.624 .000 7.11 20.80 Government 37.714* 2.085 .000 32.26 43.17 Pentecostal 30.474* 2.064 .000 25.07 35.88 *. The mean difference is significant at the 0.05 level. Std. Error Sig. 95% Confidence Interval Catholic Government Pentecostal Private Multiple Comparisons PSE Math ScorGe amesHowell (I) School Type (J) School Type Mean Difference (IJ) Results of the ANOVA The oneway ANOVA test was conducted to examine whether there were statistically significant differences among students in different school types in relation to their PSE math achievement scores. There was at least one statistically significant difference between groups as determined by oneway ANOVA (F (3, 473) = 58.288, p < 0.001). A Games Howell posthoc test (Keppel & Wickens, 2004) revealed that there were statistically significant differences between students PSE math achievement scores from Catholic (M = 64.3, SD = 19.749) (p < 0.001) and those Government Schools (M = 40.6, SD = 21.136) (p < 0.001), Catholic (M = 64.3, SD = 19.749) and Pentecostal Schools (M = 47.8, SD = 16.109) (p < 0.001), Catholic (M = 64.3, SD = 19.749) and Private Schools (M = 78.3, SD = 8.537) (p < 0.001), Government (M = 40.6, SD = 21.136) and Pentecostal Schools (M = 47.8, SD = 16.109) (p < 0.001), Government (M = 60 40.6, SD = 21.136) and Private Schools (M = 78.3, SD = 8.537) (p < 0.001) and Pentecostal (M = 8.1, SD = 2.040) and Private Schools (M = 78.3, SD = 8.537) (p < 0.001). From the results of the data the researcher concluded that the students from Private Schools reported significantly higher PSE math. Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. Students from Private schools reported significantly higher math achievement scores than students from Catholic, Pentecostal and Government, Schools. In addition students from Catholic Schools reported significantly higher math achievement scores than students from Pentecostal and Government Schools. Furthermore, students from Pentecostal Schools reported significantly higher math achievement scores than students from Government Schools. Pearson Product Moment Correlation In this section of the analysis, the bivariate analysis first looked at bivariate relationships between the dependent variable, PSE math achievement scores and each independent variables (i.e. personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation, individualization, school type and sex) using Pearson productmoment correlation, point biserial correlation and eta correlation ( Rosenthal, Rosnow & Rubin, 2000). These 61 coefficients were selected because the data were quantitative (continuous) and quantitative (categorical). The Pearson productmoment correlation coefficient measured the degree (strength of the relationship – i.e. weak, moderate, strong or independent [i.e. no relationships]) to which two continuous variables vary (direction of the relationship) together (i.e. direct or positive relationship) or oppositely (inverse or negative relationship). Pearson Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. The research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. The productmoment correlation coefficient was chosen as a correlation coefficient because it was suitable for variables that were continuous (i.e. interval or ratio type). Additionally, pointbiserial correlation coefficient measured the degree to which two variables 62 vary together and are used when one of the two variables is truly dichotomous (Rosenthal, Rosnow, & Rubin, 2000). A truly dichotomous variable is a categorical variable with two (2) levels and there is no underlying continuum between the categories (e.g. sex). Thus, the pointbiserial correlation coefficient is related to a Pearson productmoment correlation coefficient since pointbiserial correlation coefficient is equal to the Pearson productmoment correlation coefficient when the dichotomous variable was coded with different values. Eta is a coefficient of nonlinear association correlation coefficient measures of the strength of a relationship between a continuous dependent variable and a categorical (nominal, ordinal, or grouped interval) independent variable. Like the pointbiserial correlation coefficient, the eta correlation coefficient is related to the Pearson productmoment correlation coefficient because for linear relationships, eta equals the Pearson productmoment correlation coefficient. After computing the correlation coefficients for each pair of variables, the bivariate analysis then examined the coefficient of determination, which is the square of each of the correlation coefficients used in this study (i.e. Pearson productmoment correlation, pointbiserial research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. 63 The coefficient of determination indicated how much variance PSE math achievement scores and each independent variable share (i.e. it described the proportion of variance in common between the two variables). Correlation Analysis A Pearson productmoment correlation coefficient was computed to assess the relationship between PSE math achievement scores and continuous independent variables (i.e. personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation, and individualization). The results revealed that there were weak positive correlations between the PSE math achievement scores and student cohesiveness (r = 0.219, n = 477, p < 0.001), task orientation (r = 0.149, n = 477, p = 0.001), personalization (r = 0.146, n = 477, p = 0.001), involvement (r = 0.139, n = 477, p = 0.002), and satisfaction (r = 0.016, n = 477, p = 0.720) (see Table 10 below). Also there were weak negative correlations between the PSE math achievement scores and innovation (r = 0.035, n = 477, p = 0.451), and individualization (r = 0.016, n = 477, p = 0.720). The weak correlations between PSE and aforementioned continuous independent variables, implied that increases or decreases in PSE math achievement scores did not relate (or relate weakly) to increases or decreases in each of the continuous independent variables. That is, PSE math achievement scores and each continuous independent variable vary separately or independently. Hence, when the magnitudes of PSE math Achievement Scores were high, the magnitudes of the continuous independent variables were sometimes high and sometimes low. 64 Table10. Pearson Product Moment Correlation PSE Math Score Personalizatio n Involvemen t Student Cohesiveness Satisfaction Task Orientatio Innovation Individualizatio n Pearson Correlation 1 0.146** 0.139** 0.219** .016 0.149** .035 .016 Sig. (2tailed) .001 .002 .000 .720 .001 .451 .720 N 477 477 477 477 477 477 477 477 Coefficient of Determination 100.00 2.13 1.93 4.80 0.03 2.22 0.12 0.03 *. Correlation is significant at the 0.05 level (2tailed). Pearson ProductMoment Correlations Between PSE Math Score, Personalization, Involvement, Student Cohesiveness, Satisfaction, Task Orientation, Innovation, and Individualization PSE Math Score **. Correlation is significant at the 0.01 level (2tailed). The independent variable School Type was then recoded into two (2) levels (Private and Non Private [i.e. Government and Churches]) to correct this Multicollinearity problem and hence this School Type variable with two levels was used in the regression analysis. To correct for the violations of the regression assumptions for Homoscedasticity and normality of errors, transformations of the continuous variables were computed and subsequent regression analyses were conducted using transformed and nontransformed continuous variables. In regression, transformation means that one changes the scale on which the variables are measured. The results of the regression analyses with transformed variables revealed that the transformation did not fix the Homoscedasticity and normality of errors violations of the regression assumptions problem. The violations of these assumptions invalidate statistical inferences such as those made using a hypothesis test (e.g. tests of significance on the multiple correlation coefficient, R), deriving the p value for the ratio of the sample estimate of the regression coefficient of interest to an estimate of the standard error of the estimate, or by using the estimated standard error to derive a confidence interval. 65 Thus, since the transformation technique did not allow for valid regression analyses to be conducted, HeteroscedasticityRobust Inference Method using a HeteroscedasticityConsistent Standard Error Estimator (Hinckley, 1977; Long & Ervin, 2000; MacKinnon & White, 1985; White, 1980) was employed in this study. This technique uses Ordinary Least Squares to estimate the regression model as is with the NonRobust Inference Method (i.e. the standard or usual Regression Method) aforementioned, however, the difference was that the standard errors were estimated using another method that does not require the Homoscedasticity assumption to be met. The Heteroscedasticity Robust Inference Method using a HeteroscedasticityConsistent Standard Error Estimator was selected since it reduced the effects of Heteroscedasticity on inferences and yet it did not require 1) the use of transformations of the independent, and/or dependent variable(s), and 2) rigorous computer simulation programs. Thus, the researcher had to look at the results of Regression using the HeteroscedasticityRobust Inference Method and the Non HeteroscedasticityRobust Inference Method. HeteroscedasticityRobust Inference Regression Method (Using a HeteroscedasticityConsistent Standard Error Estimator) The Simultaneous Method, where all predictor variables aforementioned are entered at once in the model, was used for selecting the model since the researcher: specified the set of predictor variables that make up the model, had no prior ideas of the order of entry of which independent variables, and which independent variables will contribute significantly to the model. Using the Simultaneous Method (with the HeteroscedasticityRobust Inference Method), a significant model emerged where p < 0.001 and F (9, 467) = 38.60, (see Table 11 below). Please note that this does not support the null hypothesis so we reject the null hypothesis that there is no relationship between PSE Math achievement scores and Personalization, Involvement, 66 Student Cohesiveness, Satisfaction, Task Orientation, Innovation, Individualization, School Type and Sex. Table11. Heteroscedasticity Consistent Model Summary HeteroscedasticityConsistent Model Summaryc Model R Square Adjusted R Square F df1 df2 p Full 0.166a 0.164 38.597 9 467 0.000 Parsimonious 0.150b 0.149 153.951 2 474 0.000 a  Predictors: (Constant), School Type, Individualization, Male, Task Orientation, Innovation, Student Cohesiveness, Involvement, Personalization, and Satisfaction c  Dependent Variable: PSE Math Score b  Predictors: (Constant), School Type and Student Cohesiveness Summary The Adjusted R Square value was 0.164 (see Table 12 below). This indicates that 16.4% of the variance in PSE Math Achievement Scores was explained by the model. This table also indicates a low or weak positive correlation between the combination of all independent variables and PSE Math Achievement Scores. Next to find out which of the independent variables have a significant linear relationship with PSE Math achievement scores the researcher looked at the p values in the Regression Coefficients Table. Results of the regression analysis (without the HeteroscedasticityRobust Inference Method) provided partial confirmation for the research hypothesis since the combination of variables that significantly predicted PSE Math Achievement Scores or had a significant relationship with PSE Math Achievement Scores were only with School Type (p < 0.001), and Student Cohesiveness (p = 0.003) in Table12 below). The Beta (B) weights (or coefficients), presented in Table 13 tells us the individual contribution of each independent 67 variable to the model as well as the relationship between PSE Math Achievement Scores and each independent variable. School Type was the independent variable that contributed most to this model (i.e. strongest predictor of PSE Math Achievement Scores) since it had the largest B value of 13.253 or the smallest p value. To determine the most parsimonious model for the HeteroscedasticityRobust Inference Method, a backward stepwise model was employed. In this method, all independent variables were initially entered into the regression model and they were deleted if they made insignificant contribution to the model. Hence, the outcome will be a regression model with only significant independent variables. In this study, all independent variables were removed from the regression model except for School Type and Student Cohesiveness. The parsimonious model with only School Type and Student Cohesiveness independent variables was significant (i.e. p < 0.001 and F(9, 467) = 38.60) and had an adjusted R2 value of 14.9% indicating that 14.9% of the variability in PSE Math achievement scores is explained by these independent variables (see Table 13 below ). Table12. Heteroscedasticity Consistent Regression Coefficients Results HeteroscedasticityConsistent Regression Coefficients Results Beta Coefficient SE(HC) t P>t Constant 13.253 10.851 1.221 0.223 Personalization 1.269 2.138 0.594 0.553 Involvement 2.872 2.208 1.301 0.194 Student Cohesiveness 5.078 1.670 3.040 0.003 Satisfaction 2.176 1.546 1.408 0.160 Task Orientation 4.288 2.253 1.903 0.058 Innovation 0.667 1.824 0.366 0.715 Individualization 1.272 1.914 0.665 0.506 Male 1.321 1.908 0.692 0.489 School Type 27.253 2.176 12.526 0.000 NonRobust Inference Method (Standard OLS Regression Method) 68 The Simultaneous Method (using the Standard NonRobust Inference Method), where all independent variables are entered at once in the model produced a significant model (F (9, 467) = 10.342, p < 0.001 (see Table13 below) like the results of the Heteroscedasticity Robust Inference Method. This does not support the null hypothesis so we reject the null hypothesis that there is no relationship between PSE Math achievement scores and Personalization, Involvement, Student Cohesiveness, Satisfaction, Task Orientation, Innovation, Individualization, School Type and Sex. Table13. Regression and Residual ANOVA b Sum of Squares df Mean Square F Sig. Regression 38694.931 9 4299.437 10.342 0.000a Residual 194142.897 467 415.724 Total 232837.828 476 b  Dependent Variable: PSE Math Score a  Predictors: (Constant), School Type, Individualization, Male, Task Orientation, Innovation, Student Cohesiveness, Involvement, Personalization, and Satisfaction ANOVAb Model 1 To find out which of the independent variables have a significant linear relationship with PSE Math achievement scores we will look at the p values in the Regression Coefficients Table. Results of the regression analysis provided partial confirmation for the research hypothesis since the variables that had a significant relationship with PSE Math Achievement Scores were only with School Type, Student Cohesiveness and Task Orientation. The Beta weights or coefficients, presented in Table13 below, suggest that Student Type contributed most to this model followed by Student Cohesiveness and Task Orientation. This is similar to the HeteroscedasticityRobust Inference Method which had only School Type and Student Cohesiveness significantly contributing to the model. 69 Table 14. Regression Coefficients Model Standardized Coefficients B Std. Error Beta Tolerance VIF (Constant) 13.253 10.598 1.251 0.212 Personalization 1.269 2.087 0.031 .608 0.543 0.703 1.422 Involvement 2.872 1.974 0.071 1.455 0.146 0.740 1.352 Student Cohesiveness 5.078 1.598 0.146 3.177 0.002 0.847 1.180 Satisfaction 2.176 1.535 0.074 1.417 0.157 0.652 1.535 Task Orientation 4.288 2.177 0.095 1.970 0.049 0.773 1.293 Innovation 0.667 1.809 0.016 .369 0.713 0.896 1.116 Individualization 1.272 1.856 0.030 .685 0.493 0.937 1.067 Male 1.321 1.902 0.030 .694 0.488 0.968 1.033 School Type 27.253 3.919 0.304 6.955 0.000 0.934 1.071 a  Dependent Variable: PSE Math Score 1 Regression Coefficientsa Model Unstandardized Coefficients t Sig. Collinearity Statistics The Adjusted R Square value for the full model was 0.150 (see Table14 below). This indicates that 15.0% of the variance in PSE Math Achievement Scores was explained by the model with all the independent variables. This table also indicates a low or weak positive correlation between the combination of all independent variables and PSE Math Achievement Scores. Table 15. Model Summary a Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.408a 0.166 0.150 20.389 a  Predictors: (Constant), School Type, Individualization, Male, Task Orientation, Innovation, Student Cohesiveness, Involvement, Personalization, and Satisfaction Model Summary 70 The coefficient of variation (Standard Error of the Estimate/Mean of PSE Math Achievement Scores) is 0.413 which is greater than 10% indicating that our prediction intervals of this model will be wide. Hence, this model would not be useful for prediction purposes. To determine the most parsimonious model a backward stepwise model was employed. All independent variables were removed from the regression model except for School Type, Student Cohesiveness and Task Orientation. The parsimonious model with only School Type, Student Cohesiveness and Task Orientation independent variables had an adjusted R2 value of 15.2% indicating that 15.2% of the variability in PSE Math achievement scores is explained by these independent variables (see Table15 below). Table 16. Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.397a 0.158 0.152 20.362 Model Summaryb a  Predictors: (Constant), School Type, Task Orientation, Student Cohesiveness b  Dependent Variable: PSE Math Score It is worthy to note that the full model with all independent variables yielded an adjusted R2 value that is less than the model with just three independent variables (School Type, Student Cohesiveness and Task Orientation). This should not be the case and is a direct consequence of the violation of the Homoscedasticity and normality assumptions in the regression. 71 CHAPTER V CONCLUSIONS, IMPLICATIONS AND REFLECTIONS The purpose of the study was to examine the relationship that exist classroom climate and student math achievement. The study also sought to determine the classroom climate variables that affect student math achievement. In this study, students’ perception of classroom climate was determined by using Learning Climate Inventory (LEI) and its seven subscales of personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation and individualization. The dependent variable used was the PSE mathemat
Click tabs to swap between content that is broken into logical sections.
Rating  
Title  Examination of the Relationship Between Classroom Climate and Student Math Achievement 
Date  20120701 
Author  McKay, Lorna Marie 
Keywords  Achievement, Classroom Climate, High School, Mathematics, Primary School Examination, Relationship 
Department  Education (all programs) 
Document Type  
Full Text Type  Open Access 
Abstract  The purpose of the study was to examine the relationship that exist classroom climate and student math achievement. The study also sought to determine the classroom climate variables that affect student math achievement. The majority of learning environments assessments was based on students' perceptions. Students' and teacher perceptions of the learning environment could give valuable information to improve the quality of learning and can evaluate the innovation in education (Fraser, 1998). In the study the researcher concluded that: (1). the independent variable, school type was statistically significant to student math achievement scores; (2). the independent variable, gender was not statistically significant to student mathematics performance and, (3). the other climate variables contributed very little to influence students' math scores on PSE. In the study, the sample consisted of 18 high schools and 477 students from ninth grade or first form who sat the BPSE in 2011. The population came from the Belize District schools of 2700 students that provided a randomly selected sample of 540 study participants. The researcher used a Learning Environment Inventory (LEI) by (Fraser, 1992) to collect data on classroom climate and the Belize Primary School Examination (BPSE) for 2011 in order to obtain students' mathematics scores. The study was correlation. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  AN EXAMINATION OF THE RELATIONSHIP BETWEEN CLASSROOM CLIMATE AND STUDENT MATH ACHIEVEMENT BELIZE DISTRICT HIGH SCHOOLS By LORNA MARIE MCKAY Bachelor of Science in Business Administration University of Belize Belize City, Belize 1997 Master of Education in Leadership University of North Florida Jacksonville, Florida 2003 Submitted to the Faculty of the Graduate College of the Oklahoma State University In partial fulfillment of the requirements for the Degree of DOCTOR OF EDUCATION July, 2012 iii AN EXAMINATION OF THE RELATIONSHIP BETWEEN CLASSROOM CLIMATE AND STUDENT MATH ACHIEVEMENT IN BELIZE DISTRICT HIGH SCHOOLS Dissertation Approved: Dr. Ed Harris Dissertation Adviser Dr. Bernita Krumm Dr. Steve Wanger Dr. Belinda Mccharen Dr. Sheryl A. Tucker Dean of the Graduate College iv PREFACE The purpose of the study was to examine the relationship that exist classroom climate and student math achievement. The study also sought to determine the classroom climate variables that affect student math achievement. The majority of learning environments assessments was based on students’ perceptions. Students’ and teacher perceptions of the learning environment could give valuable information to improve the quality of learning and can evaluate the innovation in education (Fraser, 1998). In the study the researcher concluded that: (1). the independent variable, school type was statistically significant to student math achievement scores; (2). the independent variable, gender was not statistically significant to student mathematics performance and, (3). the other climate variables contributed very little to influence students’ math scores on PSE. In the study, the sample consisted of 18 high schools and 477 students from ninth grade or first form who sat the BPSE in 2011. The population came from the Belize District schools of 2700 students that provided a randomly selected sample of 540 study participants. The researcher used a Learning Environment Inventory (LEI) by (Fraser, 1992) to collect data on classroom climate and the Belize Primary School Examination (BPSE) for 2011 in order to obtain students’ mathematics scores. The study was correlation. v TABLE OF CONTENTS Chapter Page I. INTRODUCTION…………………………………………………………………….1 The Importance of the Classroom Environment………………………………….....2 Problem Statement…………………………………………………………………..3 Purpose Statement……………………………………………………………….......4 Questions That Will Guide the Study…………………………………………….....4 Significance of Study………………………………………………………………..5 Definition of Terms……………………………………………………………….....6 Methodology…………………………………………………………………….......8 Epistemology Perspective……………………………………………………………9 Assumption…………………………………………………………………………10 Limitations of Study……………………………………………………………......10 Summary……………………………………………………………………….……11 II. REVIEW OF LITERATURE……………………………………………………….13 The Importance of Math…………………………………………………………….13 History of Math Educational Development…………………………………………14 History and Development of Instrument……………………………………………19 Importance of School Climate…………………………………………………........19 Significance of Classroom Climate…………………………………………….........20 Teacher Qualification and Student Achievement….………………………………..25 Teacher Attitude and Student Achievement..............................................................29 Teacher Effectiveness and Student Achievement…………………………………..30 Summary……………………………………………………………………………..35 III. METHODOLOGY…………………………………………………………………..37 Purpose Statement……………………………………………………………………37 Research Questions and Hypothesis……………………………………………….....37 Belize District High Schools……………………………………………………….....39 Participants…………………………………………………………………………....39 Description of Instrument…………………………………………………………….40 Reliability and Validity of Instrument………………………………………………..40 Description of Survey…………………………………………………………………41 Research Design and Procedure……………………………………………………....42 Ethical Consideration…………………………………………………………………44 Data Analysis………………………………………………………………………….45 Summary………………………………………………………………………………45 vi IV. FINDINGS……………………………………………………………….………….47 Population.............................................................................................................…...47 Purpose of the Study………………………………………...……………………….48 Design of Study………………………………………………………………….…...48 Assumptions of Oneway ANOVA………………………………………………….48 Research Question Three……………………………………………………………..49 Research Question Four…............................................................................................53 Results of Analysis of Oneway ANOVA…………………………………………...55 Pearson Product Moment Correlation…………………………………………...........59 Correlation Analysis…………………………………………………………………..61 Non Robust Inference Method………………………………………………………64 Model Summary………………………………………………………………………69 V. CONCLUSION………………………………………………………………………72 Summary of Study…………………………………………………………………….72 Null Hypotheses……………………………………………………………………….73 Summary of Findings………………………………………………………………….74 Limitation of Study………………………………………………………………........76 Conclusion……………………………………………………………………………..77 Implications for Research, Theory & Practice….………………………………...........78 Researcher’s Reflections………………………………………………………….........81 REFERENCES…………………………………………………………………………….83 APPENDICES………………………………………………………………………..........90 Learning Environment Inventory………………………………………………………90 Learning Environment Inventory Score Sheet…………………………………………92 Permission to Use Instrument………………………………………………………….94 IRB Approval Letter…………………………………………………………………...95 Managing Authority Letter SDA………………………………………………………97Managing Authority Letter BHS………………………………………………………98 Managing Authority Letter PHS………………………………………………………99 Managing Authority Letter SJC…………………………………………………........100 Managing Authority Letter NAZ……………………………………………………..101 Managing Authority Letter GS……………………………………………………….102 vii LIST OF TABLES Tables: Page 1. Normality PSE and Sex (Male)………………………………………………..........50 2. Homogeneity of Variances (Levene statistic)……………………………………….52 3. Descriptive Statistics on PSE Math Scores and Sex………………………………...52 4. School Type and PSE Math Score…………………………………………………..54 5. Homogeneity of Variance……………………………………………………….......55 6. Robust Test of Equality of Means…………………………………………………..55 7. Descriptive Statistic on PSE Scores and School Type…………………………........56 8. PSE Between and Within Group ANOVA…………………………………….........57 9. Multiple Comparisons of PSE Math Score & School Type…………………………59 10. Pearson Product Moment Correlations……………………………………………64 11. Heteroscedasticity – Consistent Model Summary……………………………………...66 12. Heteroscedasticity – Consistent Regression Coefficient Results………………………67 13. Regression and Residual ANOVA b………………………………………………........68 14. Regression Coefficients Model……………………………………………………........69 15. Model Summary a……………………………………………………………………….69 16. Model Summary b……………………………………………………………………….70 viii LIST OF FIGURES Figure Page 1.0 Normal QQ Plot Graph……………………………………………………………51 1.1 Means Plot Graph of PSE Math Scores and Sex (Male)……………………….......53 1.2 PSE Math Score and School Type Graph………………………………………….57 1 CHAPTER I INTRODUCTION Increasing math proficiency is a global agenda. Societies understand that to succeed in a global society, a person must master math skills, as well as, critical cultural and communications skills (World View, 2006). Every career uses some sort of math. More importantly, doing math helps the mind to reason and organize complicated situations or problems into clear, simple, and logical steps. The understanding of math is essential to gain a competitive edge in many fields in today’s global economy (Patton, 2010). Therefore, math is not only necessary in an increasing number of jobs, but also in any high paying job that requires the ability to do math. Students in classrooms today must be able to solve problems, think critically, interpret solutions, analyze data and formulate questions. Training in mathematics also helps students to reason logically and enable them to form clear models of problems. Math is a way to understand all sorts of things in the world (Arnold, 2003). In Belize, strong emphasis has being placed on math proficiency. However, every year a number of students do poorly on the math in the Belize Primary School Examination (BPSE). The BPSE is a standardized exam geared at testing students’ proficiency in four areas: social studies, mathematics, English, and science. Students’ performance on BPSE is calculated as a percentage score from the scores of three test scores. Data from the 2009 BPSE sitting indicate that math was the subject that many students performed poorly on with the math having a mean of 46.15 and a median of 49%. This indicated that more than 50% of the 6,858 students who sat the exam in 2009 scored below 49% in math (Guardian, 2009). In the 2009 sitting of BPSE the 2 schools that have better resources were the performing schools in all areas which included math. These included the top private and grantaided schools (Guardian, 2009). School has been and continues to be a major factor in a child’s education both in terms of number of hours spent and the quality of teaching (Eggen & Kauchak, 2003). Thus, teachers play an important role in promoting the required knowledge, skills and attitudes for active participation in society (Ministry of Education, 2005). At the high school level, only 31% of teachers are actually qualified by any teacher training standard (Education Statistical Digest of Belize, 20052006). There were cases of young, untrained teachers, deficient in content and pedagogy, often placed in the Belizean classrooms. This has created problems in specific content areas, such as mathematics, and is reflected in the country’s poor national performance in both national and regional examinations. Consequently, teachers need to ensure that students learn to apply their mathematical background and procedures to solve real life problems (DeVries & Zan, 1994). The Importance of the Classroom Environment Classroom environment, or climate as it is often called, is important in the learning process. Kowalski (1996) defined climate as “a comprehensive structure made up of culture, physical plant, organizational structure, social relationships, and individual behaviors” (p.16). This definition implies that climate is sporadic rather than static and was affected by constant changes in the environment or outside forces within the school system. Over the past years, the classroom learning environments have emerged as a thriving field of study (Deng, 1992; Edmonds & Frederiksen, 1979; Fisher & Fraser, 1981; Walberg, 1979). Climate can positively influence the wellbeing of the learning environment, or it can significantly impede learning (Freiberg, 1998). A growing body of research showed that an important key to preventing risks 3 and developing healthy schools where teaching and learning occurs in a positive school climate (Cohen, 2001). Considering the importance of climate and student learning, research in these areas in Belizean schools is of great important. Problem Statement In Belize, the BPSE has been used as a means to measure aptitude in math and other subjects, and concerted efforts have been made to improve math scores. Presently, efforts are being made by the Ministry of Education and Youth (MOEY) to develop teacher training and acquire the necessary resources for the improvement of schools in all areas and especially in mathematics. In a 2009 Teachers’ Day address, Belize’s Minister of Education, Patrick Faber, announced that $20 million from the Caribbean Development Bank (CDB) will be invested in teacher training. While many efforts have been made to improve math scores, math learning remained poor in some schools and in others there have been improvement. The BPSE results over the years consistently show math as the lowest performing subject area in the exam. Math continues to be the lowest performing subject (The Hemispheric Project for the Preparation of Policies and Strategies for the Prevention of School Failure, 2005). In Belize, performance is at a higher level on BPSE at the schools with more resources, such as private schools and grantaided schools, (Guardian, 2009). One possible explanation for this difference in math scores in the different schools was school climate. Positive classroom climate is important for learning to occur. Achievement is related to climate and student attitudes for primary school mathematics (Goh & Fraser, 1996). Classroom climate studies were common worldwide, but in Belize there was limited research in this area and no such data exist. In fact, there was limited research in the area of education and 4 other areas of research. Considering the data on BPSE math scores and the non existence of classroom climate data there was an important need for research in these areas. Thus, the purpose of the study was to investigate the relationship between classroom climate and math achievement of students in ninth grade Belize District High schools. Purpose Statement The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth grade. The dependent variable in the study was student achievement and the independent variable was classroom climate. Questions That Will Guide the Study The following research questions guided the study: 1. What is the relationship between students’ perceptions of classroom climate and mathematics achievement? 2. What is the relationship between students’ perceptions of specific classroom climate factors: personalization, involvement, cohesiveness, satisfaction, task orientation, innovation and individualization, and mathematics achievement? 3. Are there differences between student math achievement and school type? 4. Are there differences between student math achievement and gender? Null Hypotheses H1: There is no relationship between students’ perceptions of classroom climate and mathematics achievement. H2: There is no relationship between students’ perception of personalization in the classroom and mathematics achievement. 5 H3: There is no relationship between students’ perception of involvement in the classroom and mathematics achievement. H4: There is no relationship between students’ perception of cohesiveness and mathematics achievement. H5: There is no relationship between students’ perception of satisfaction in the classroom and mathematics achievement. H6: There is no relationship between students’ perception of task orientation in the classroom and mathematics achievement. H7: There is no relationship between students’ perception of innovation in the classroom and mathematics achievement. H8: There is no relationship between students’ perception of individualization in the classroom and mathematics achievement. H9: There is no difference between student math achievement and school type. H10: There is no difference between student math achievement and gender. Significance of the Study Many factors may be used to determine the success of student math achievement. Therefore, it was important to examine the various variables that may be significant to the learning environment. Learning environments not only have positive correlation with students’ outcomes, motivation, and attitudes, but also teachers’ motivation (Sinclair & Fraser, 2002). Therefore, this study has the following importance: a) It will add to the body of existing literature that relates to the classroom learning environment variables and student achievement globally; 6 b) Assist in the creation of much needed literature on classroom climate and student math achievement for Belize; c) Aid in providing crucial information to policymakers for the development of policies nationally in Belize; d) Can be used to assist policy makers to determine what changes, if any, could be made to achieve improved student math performance on the BPSE; and e) Can also heighten educators’ awareness on the importance of classroom climate and achievement in math in Belizean classrooms, as well as, determine and fill existing gaps on student math achievement. While there were several factors that influenced student achievement, studies indicated that the teacher and the classroom climate were two of the more important factors that determined student achievement. The teacher is in the unique position to have the largest impact on student achievement (Lasley, Siedentop & Yinger, 2006). Thus, it was in these contexts that the researcher sought to conduct the study so that an evaluation of the appropriateness of specific classroom climate factors and the influence on student math performance may be examined and ascertained. Definition of Terms In this study, the following terms needed to be defined: Achievement: For the purpose of this study, success in a subject area. Belize Primary School Examination or “BPSE” refers to a national examination that is administered by the Ministry of Education to students at the end of primary education to determine achievement in relation to the primary school curriculum (Belize Education Rules, 2000). 7 Classroom Climate: The mood or atmosphere created by a teacher in his or her classroom. Classroom Environment: Intellectual, social, physical, etc., conditions within or exogenous to a classroom that influence the learning situation. Governmentaided school: A school in receipt of a grantinaid from the Government in accordance with the provisions of the Act (Belize Education Rules, 2000). Government Schools in Belize: Schools maintained wholly from the General Revenue (Belize Education Rules, 2000). Mathematics Achievement: Level of attainment in any or all mathematics skills, usually estimated by performance on a test (Belize Glossary of Education, 2000). MOEY: Ministry of Education and Youth (Belize Education Rules, 2000). PISA: A triennial survey of the knowledge and skills of 15yearolds. It is the product of collaboration between participating countries and economies through the organization for Economic Cooperation and Development (OECD), and draws on leading international expertise to develop valid comparisons across countries and cultures. Private Schools  Schools which are neither a government school nor a governmentaided school (Belize Education Rules, 2000). School  An institution that provides preschool, primary or secondary education; an “institution” refers to educational institutions providing some form of schooling (Belize Education Rules, 2000). Speciallyassisted school: A school that is in receipt of aid from the Government of Belize in the form of teacher salary for one or two teachers. Teacher: A person appointed by the manager or managing authority of a school for the purpose of instructing students (Belize Education Rules, 2000). 8 TIMSS: Trends in Mathematics and Science Study. Methodology Description of Setting and Participants The population for the high schools in the Belize District consisted of various managing authorities. The selected schools fell into three main categories namely: governmentowned, grantaided and speciallyassisted schools. Government Schools are schools that are fully funded by the government; therefore, all expenditures such as teachers’ salaries, utilities and maintenance are paid for by the government. Grantaided schools are schools that were partially funded by the government. Therefore, the government paid 70% of the teachers’ salaries and gave a subsidy grant to the schools for students’ tuition. Speciallyassisted schools are schools that received a grant for the management to pay one or two teachers in the school. Schools were coded as Catholic, Government, Protestant and Private for analytical purposes. The target population comprised of 18 Belize District high schools, which represent a total population of 2700 male and female students collectively. From the 18 high schools selected for the sample, one was an all girl institution and one was an all boy institution. The remaining 14 schools were coeducational institutions. The population for this study represented only the first formers who took the Belize Primary School Examination in 2011. An average class size of 30 was used since this was an average of the number of students in Belize District classrooms. Also, there was an average of five (5) first forms in each of the schools with an average total of 180 students. Therefore, the researcher randomly selected the participants for the study by selecting every 6th person form each class to be a part of the survey. Therefore, each person had a fair chance of being selected to be a part of the study. The total sample 9 population was 540 students from the various high schools. In order to differentiate between the various types of schools, the schools were grouped into four categories: Catholic, Government, Protestant, and Private. There were eight (8) Government Schools, seven (7) Catholic, five (5) Protestant schools, and two (2) Speciallyassisted or Private schools. In the study the researcher compared students’ classroom climate scores with those of students’ BPSE math achievement scores, who sat the BPSE in 2011 and are presently in ninth grade in Belize District High Schools. Instrument Learning Environment Inventory (LEI) was the instrument used in the study. The instrument was first developed by Herbert Walberg (1968) and later modified by Barry Fraser (1992). It was used to examine students’ perception of the learning climate of the classroom as a part of the activities involving research and evaluation of the abovementioned Harvard Project Physics. Permission to use the instrument was obtained from Professor Barry Fraser of Curtin University in Australia. Epistemological Perspective In the study the positivist view was the epistemological perspective and behaviorism was the theory used by the researcher. Positivism refers a set of philosophies and perspectives that indicates the best approach to uncovering the processes by which both physical and human events occur (Watson, 1930). Behaviorism is a theory of learning based upon the idea that all behaviors are acquired through conditioning which is concerned mainly with the observable and measurable aspects of human behavior (Watson, 1930). In defining behavior, behaviorist learning emphasized changes in behavior that result from stimulusresponse associations made by the learner. 10 Behavior is directed by stimuli. An individual selects one response instead of another because of prior conditions and psychological drives present at the moment of the action (Parkay & Hass, 2000). The behaviorist theory (Skinner, 1950) emphasizes that only behaviors worthy of study are those that can be directly observed; thus, it is actions, rather than thoughts or emotions, which are the legitimate object of study. The behaviorist learning theory was not only important in achieving desired behavior in mainstream education, but also for special education teachers who have classroom behavior modification plans to implement for their students (Standridge, 2002). Since behaviorism was also based upon observable behaviors; the researcher felt that it would have been easier to collect and quantify data when conducting the research. Assumptions This study assumed that different classroom climate variables would have influenced student math achievement on BPSE. The study also assumed that students would have performed differently in different types of classroom climate settings. The study further assumed that the participants of the study will complete the questionnaire honestly and in a favorable school setting that would be free from distractions. Limitations The limitation of a study refers to factors that a researcher was unable to control or those factors that may impact the extent to which the findings can be effectively utilized (Gay, 2000). Correlation research merely demonstrates that a researcher can predict one variable from another variable and demonstrates that two variables were associated. Correlation research may also have limitations with respect to the generalizability of the findings. Thus, it may be uncertain whether the findings of this research may be generalized to other schools, students or situations. Therefore, there were limitations that encompassed the study. One limitation was that the study 11 was only being done in one area of Belize which was the Belize District. Therefore, high schools in the other five remaining districts were excluded from the study and the likelihood of important data could have been excluded. Another limitation was the fact that the sample of students in the study would not be a representative sample of the entire population of the ninth grade who sat the BPSE in 2011 in the entire country of Belize. Additionally, only the math scores were used in the study although science and social studies scores were also tested on the BPSE exam. Furthermore, only seven variables were examined, although there could be other variables that could affect student math achievement. Finally, surveys are selfreporting instrument and are subject to human error (Kaplan, 1996). Consequently, students may or may not have correctly stated a true view or perception of the nature of the classroom climate at the time that the exam was sat. Lastly, there was the time factor that may have affected the perception of the students who were answering the survey since these students were already in ninth grade when the study was conducted. However, it is worth noting that LEI has been tested consistently over the last several decades for its validity and reliability in a manner that was similar to this study. Summary The purpose of this study was to investigate the relationships between classroom climate and math achievement in ninth grade in Belize District High Schools. The study sought to determine if there was a relationship between classroom climate and student math achievement in grades on BPSE. Using a revised version of LEI by Fraser (1994), the researcher tried to determine the specific classroom climate variables that affect student math achievement. As was stated previously, there was no study of this nature that has been done in the country of Belize; therefore, information derived from this study is important to the development 12 of classroom climate studies and math achievement studies in Belize. Thus, there was a need for this study to be conducted in Belize. The subsequent chapters of this study include: Chapter Two Literature Review, Chapter Three  Methodology, Chapter Four Findings and Chapter Five Conclusions, Recommendations and Suggestions for further related research. 13 CHAPTER 11 LITERATURE REVIEW The purpose of this study was to investigate the relationship between classroom climate and math achievement in the Belize District. The study was done to find out if there was relationship between classroom climate variables and student math achievement on BPSE. The researcher, through an examination of related literature seeks to present an in depth understanding of classroom climate and student math achievement. The review of literature within this chapter encompasses the following areas: the importance of math, history of math educational development, history and development of the instrument, importance of school climate, teacher qualification and student achievement, teacher attitude and student achievement, teacher effectiveness and student achievement. Summary and conclusion close the section. The Importance of Math Mathematics is crucial not only for success in school, but also in becoming an informed citizen, being productive in one’s chosen career, and fulfilling personal something (Murnane & Levy, 1997). Learning mathematics gives the student the foundation to be successful in other content areas during a student’s educational experience. According to U.S. Department of Education’s white paper, Mathematics Equals Opportunity White Paper  October 1997, Murnane and Levy (1996), concluded that: Students who take a rigorous K12 mathematics sequence were more likely to go to college than those who do not. Students of all income levels who do very rigorous math courses in high school were more likely to go to college. 14 In the job market, students who have strong mathematics backgrounds were more likely to be employed and earn 38% more per hour that those with insufficient skills in algebra, geometry, measurement, and probability. In another study conducted at Londonderry High School in New Hampshire, there were several areas of focus. Findings from this study indicated that during the primary years of a student’ life the focus was on learning numbers and operation, basic measurement, and basic understanding of data. In the intermediate and middle school years, greater emphasis was placed on the practice and reinforcement of basic math facts and operations and increasing. Thus, the knowledge and understanding of skills in areas such as algebra and geometry were increased. At the high school level, the focus remained on improving the fundamental mathematical concepts and skills. The students were also taught new ways to analyze data and new perspectives in algebra and geometry. History of Math Educational Development Over several decades, many student achievement studies were conducted on math achievement. The extents of students’ opportunity to learn any content in mathematics lies heavily and bear much meaning on students’ mathematic achievement (Husen, 1967). The term opportunity to learn (OTL) refers to what was studied or embodied in the tasks that students perform. In math, OTL included the scope of the mathematics presented, how the mathematics was taught, and the match between the students’ entry skills and new material (Grouws & Cebulla, 1992). Grouws and Cebulla (2000) conducted a study where teachers were asked to rate the extent of student exposure to particular mathematical concepts and skills. The results of this study indicated that there were strong correlations between OTL scores and mean student 15 achievement scores, with high OTL scores associated with high achievement. Additionally, correlations were also found in subsequent studies, such as the Second International Mathematics Study, (McKnight, 1987) and the Third International Mathematics and Science Study, (Schmidt, McKnight, & Raizen, 1997). From these studies several classroom implications were apparent, which included the need to allocate sufficient time for math instruction at every grade level. Also, of notable importance was the fact that short class periods in math, whether instituted for whatever practical or philosophical reason, should be seriously questioned. These studies also highlighted the idea that there were special concerns for 3035 minute class periods for math that were being implemented in some middle schools during this period. Additionally, the findings pointed out that: (a) the use of textbooks that devoted major attention to review and that address little new content each year should be avoided or be heavily supplemented with other resources; (b) teachers should use textbooks as just one instructional tool among many others instead of being a slave to the textbook on a onesectionperday basis, and (c) wholeclass discussion which followed individual and group work improved student achievement. Wood (1999) also solidifies the fact that wholeclass discussion worked best when discussion expectations are clearly understood. Therefore, students in the classroom setting were expected to evaluate each other’s opinions and reasoning through ways that were not critical to the other students’ sharing. Findings from this study suggested that students were expected to be active listeners who participated in discussions and feel a sense of responsibility for each others’ grasp of the concept or concepts. Therefore, the class discussions must be a summary of individual work in which key ideas were brought to the surface. Thus, the use of wholeclass discussion could also be an effective diagnostic tool for determining the depth of students’ 16 understanding and identifying students’ misconceptions. The study further highlights the idea that teachers could identify areas of difficulty for particular students, as well as, ascertain areas of student success or progress. Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important (Wood, 1999). His study also indicated that number sense was related to having an intuitive feel for number size and combinations, and the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgments. In addition, number sense also involves mentally computing, estimating, sensing number magnitudes, moving between representation systems for numbers, and judging the reasonableness of numerical results. Markovits and Sowder (1994) studied seventhgrade classes where special units on number magnitude, mental computation and computational estimation were taught. From this study the researchers found that after this special instruction, students were more likely to use strategies that reflected sound number sense that was a longlasting change. In a similar study of second graders, Cobb (1991) concluded that a problemcentered curriculum that emphasizes student interaction and selfgenerated solution methods improved students’ number sense. The findings revealed that almost every student developed a variety of strategies to solve a wide range of problems. Therefore, students displayed increased determination in trying to solve the problems. Additionally, the results of the findings further highlighted the fact that in many classrooms efforts to reinforce the use of numbers is still not being given sufficient attention. The study recommends that as teachers develop strategies to teach the use of numbers, they should strongly consider moving beyond a unitskills approach (i.e. a focus on single skills in isolation) to a more integrated approach. The integrated approach encourages the development 17 of number use in all classroom activities from the development of computational procedures to mathematical problemsolving. History and Development of Instrument Initial development and validation of a preliminary version of Learning Environment Inventory (LEI) began in the late 1960’s in conjunction with the evaluation and research of a Harvard project Physics new course for high schools (Fraser, Anderson & Walberg 1982; Walberg & Anderson 1968). Continued efforts were made over several decades by Herbert Walberg and Rudolph Moos who also started separate research programs that began additional instrument development and validation on learning environments. It was during this process that Walberg (1968) developed LEI as a part of the activities involving research and evaluation of the abovementioned Harvard project physics. The rationale for developing the instrument consisted of three very important factors that included: (1) the prohibitive expense of classroom that caused the Harvard Project Physics evaluation group to seek a paper and pencil measure of classroom interaction that teachers could administer, (2) the traditional methods of observations that included mainly “ low inference” variables which bear little relationship to pupil learning in past research (Rosenshine, 1971), and (3) the pupils were considered to be in the best position to assess their own learning environment, particularly as observer ratings had failed to provide valid measures of “high inference” variables within the class. Moos (1979) and Moos and Trickett (1987) also became engaged in the development of the social climate scales, along with scales that were being used in psychiatric hospitals and correctional institutions. These scales were later known as the classroom environment scale (CES) by (Fisher & Fraser, 1983). The final version of the LEI instrument had a total of 105 items. In the instrument the respondents were asked to express various degrees of responses. The responses included four 18 response alternatives: (1) Strongly Disagree, (2) Disagree, (3) Agree, and (4) Strongly Agree. In the scoring procedure some of the items were reversed in the scoring direction (or polarity). An example of this was seen in one of the Cohesiveness scale item: All students know each other very well. This item was reversed in the Speed scale and was stated as the pace of the class is rushed. In the use of the instrument, the perceptions of students were examined comprehensively. LEI are an expansion and improvement of the Classroom Climate Questionnaire (CCQ) (Blank & Kershaw, 1998). The instrument is used to describe the nature of the interpersonal relationships in the class as well as the structural characteristics. The LEI instrument has two distinct uses: (1) to assess the perceptions of an individual student and (2) to gauge the learning environment of the class as a group. The researchers noted that if the instrument was used for the former purpose, then the normal research procedures would apply with one caution. Since individuals’ scores were measures of their perceptions of the group of which they were a part, the scores of different individuals within the class were not strictly independent. Therefore, since the scores of subjects within a class all relate to common class experiences, usually then it was the variance among scores rather than the scores themselves which were of educational and psychological interest. Additionally, since the class mean provided the best estimate of the collective student perceptions of the class, it should be used when a researcher was examining different conditions or treatments across classes. Therefore, if a study was addressing variables, such as curriculum or teacher characteristics, then the appropriate unit of analysis was the class mean. However, if a study was examining variables such as pupil sex, selfconcept, or personality, then individual scores will be required in this study. 19 As Fraser (2002) suggested, “There are six areas of research which apply to classroom environment assessments” (p. 8). These were: (1) the relationship between student outcomes and classroom environment, (2) evaluation of educational performance, (3) differences between students’ and teachers’ perceptions of the same classrooms, (4) determinants of classroom environment, (5) use qualitative research methods, and (6) crossnational studies. Learning environment questionnaires provide information on the measure of students’ learning outcomes, students’ perceptions of their learning environment indicates that “learning environment instruments essentially measure the meaningful environments for students to a given classroom” (Anderson, Hamilton, & Hatte, 2004, p. 212). This study underpins the main idea of the relationship between classroom climate and student achievement. Importance of School Climate Globally, research studies indicate that the culture of schools is one of the main indicators of an effective school (Deal & Peterson, 1993). School culture also affects the climate of a school and by extension, the classroom climate. Educators have also continuously forged towards developing positive school cultures and by extension positive classroom climates. School climate is the social, ethical, emotional and academic school life experiences of school personnel, students and parents of the institution (Berkowitz, 2005). A growing body of research that shows that an important key to preventing risks and developing healthy schools where teaching and learning occurs is a positive school climate (Cohen, 2001). Blum (2002) also discusses that a safe, caring responsive and participatory school climate usually encourages greater student attachment to the institution. Blum (2002) continues that school climate also assists in the development a foundation for holistic learning and is the hallmark of an effective school. 20 Van Houtte (2004) advocates for some clarity on the terms school culture and school climate and the role that both of them played in research based on school effectiveness. Van Houtte (2004) presents a theoretical framework with regards to school culture indicating that there is a specific branch of organizational culture that consisted of several dimensions and levels. Thus, school climate is referred to as the next level of school culture. This study indicates that a positive school climate is present in a school when students feel a sense of acceptance, security, comfort, caring, and trust. Furthermore, in schools where there is a positive school climate, there is also a sense of belonging. Consequently, this type of culture system also maintains a positive learning environment. The former study by (Van Houtte, 2005), on school culture suggest that educators need to persistently work in an effort to improve the culture and climate conditions of schools. These findings show that if a school has a positive climate, then the classroom climate will be more than likely positive. Significance of Classroom Climate Classroom environment or climate research has become a popular area of study. Relevant studies encompass several areas that include student behavior, student achievement, and students’ perspectives. The climate of the classroom is described as a system comprising four sets of variables: the physical involvement, the organizational objectives, and characteristics of teachers and students (Schmidt & Cagran, 2006). Classroom climate is considered to be very important since it is a determinant of quality education in schools. There is a significant relationship between classroom climate and factors such as achievement, student engagement, behavior, selfefficacy, social and emotional development, principal leadership style, stages of educational reform, teacher burnout, and the overall quality of school life (Fraser, 1998 & 21 Freiberg, 1999). Therefore, the need for teachers to maintain positive climates or environments in the classrooms has been continuously emphasized in schools. There are three types of classroom climate that the teacher can use in different situations (Borich, 1996). These types include the competitive, cooperative and individualistic. In competitive classrooms, students compete with one another and are usually led by the teacher with little autonomy for students. Although competition can be motivating to students; classrooms that are led by teachers have been found to enhance student achievement. Cooperative classrooms emphasized students’ cooperation along with the teacher’s timely intervention to guide the students towards learning goals. These types of classrooms are also effective in the development of crucial cooperative learning skills that can enhance student achievement. Individual classrooms emphasize students’ individual work with little intervention by the teacher. This type of classroom could help in the student with the development of independent learning skills. In this study, the real possibility of access to participation in the classroom is one of the most important indicators of classroom climate. The voluntary participation in the classroom is much related to the climate of it (Okolo, 2007). Learning environment assessment not only provides information on how to measure students’ performance, but also information on the teachers’ competences to create positive learning outcomes. The majority of learning environments assessments is based on students’ perceptions. Fraser (1998) states, “students’ and teacher perceptions of the learning environment could give valuable information to improve the quality of learning and can evaluate the innovation in education” (p. 122). Therefore, the learning environment assessments could measure aspects in the classrooms such as teacher, students, teaching, and the learning process. PattersonRowlett (2000) conducted a study on school effects and school climate research that 22 revealed that school environment affects academic achievement. Rowlett found that an important aspect of the school environment is classroom climate which has been found to influence achievement, attitude, behavior, selfconcept, and future aspirations. Brown and Campione (1996) stated that “a learning environment should be managed so that students are encouraged to set personal goals, actively gather meaningful information, monitor and evaluate their own learning and reflect personal learning experiences in different authentic environments and social contexts” (p. 439). A further study by Brown and Campione (1996) showed that teachers play an important role in creating constructive learning environments which could help students achieve best performances and meaningful learning experiences. Positive classroom climate could motivate both students and teacher to learn and teach effectively. Thus a teacher who creates a positive classroom climate such as having a good relationship with students helps students to achieve their learning outcomes (Jarvela, 1998). For example, the teacher who knows how to attract students’ attention by using varied and interesting teaching strategies, humor, and positive reinforcements. In this type of classroom climate the students would enjoy their learning and express their ideas and opinions. Davis (2007) conducted a study using one hundred three ninth and tenth grade algebra students who completed selfreports of motivation, classroom climate, and learning styles preferences. A nonverbal measure of aptitude and algebra pretest was administered at the beginning of the academic year (August, 2007) and an algebra post test was administered at the midpoint of the academic year (February, 2007). Results indicated that selfreported levels of motivation were not significant predictors for achievement in algebra classes. In the case of classroom climate, students with lower ratings for classroom involvement and higher ratings of task orientation demonstrated higher increases in achievement than students with higher ratings 23 of involvement and lower ratings of task orientation. Conversely, in this study a student who displayed a thinking preference achieved high scores than student with demonstrating a feeling preference. Results show that students whose perceptions and preferences are more consistent with instructional style demonstrate higher short term gains in math than students with less congruent preferences and perceptions. The creation of a positive classroom climate in schools require a specific focus on (1) ensuring that the curriculum promotes academic, social and emotional learning, (2) improving the quality of the classroom for both teachers and students, (3) enabling intrinsic motivation that will encourage classroom teaching and learning, and (4) supporting and enabling teachers to be effective with a wide range of students (Davis, 2007). Therefore, several factors are important to create and maintain a positive classroom climate which include: (a) the meaningful participation for staff and students in the decision making processes of the school, (b) social support mechanisms for both staff and students in the institution and a welcoming, caring and hopeful atmosphere, and (c) a variety of options for pursuing and reaching goals. In another study, Guo (2004) examined the effects of classroom climate on the relations of children's social behaviors to school adjustment. This study was among the first to make contributions to the literature by exploring the effects of such classroom climate as teacher warmth, teacher admonishment, student relationship, class order and rule clarity, respectively, on the relations of prosocial, aggressive, victimized, delinquent and withdrawn behaviors to children's school adjustment in a sample of rural Chinese school children. Participants in the study included 3059 middle school students from 37 classes of a rural area in northern China. Peer nominations were used to measure children's prosocial, aggressive, withdrawn, victimized, delinquent behaviors and peers acceptance. Classroom climate factors used included teacher 24 warmth, teacher admonishment, student relationship, and class order and rule clarity. These were measured by student selfreports that were aggregated into classroom variables. Student academic achievement consisted of final exam scores for Chinese, mathematics, and English. Multilevel path analyses were used to explore the effects of classroom climate on the relations between children's social behaviors, their academic achievement and peer acceptance. The results of this study showed that children's prosocial behavior positively predicted students’ academic achievement and peer acceptance, whereas aggression, withdrawal, victimization and delinquency negatively predicted these two school adjustment variables. Except for prosocial behavior, the relations of different social behaviors to school adjustment varied significantly across classes. Multilevel results showed that teacher warmth negatively predicted aggression, withdrawn, victimization and delinquency. Teacher admonishment reduced the negative relation between aggression, withdrawn, victimization, delinquency, respectively, to school adjustment variables. Student relationship reinforced the negative relations of aggression, withdrawn, victimization, delinquency, respectively to school adjustment variables. Classroom order and rule clarity also enhanced the negative relation between aggression, withdrawn, victimization, delinquency, respectively, to school adjustment. This study also proved that classroom climate variables had little effect on prosocial behavior and its relations to school adjustment variables. The results provided different understandings of children's school adjustment that is subject to the influence of children's social behaviors and peer relationship but also to the classroom climate and cultures. Therefore, teachers and researchers need to consider classroom cultures when studying and defining desirable versus undesirable social behaviors and how these behaviors contribute to successful versus unsuccessful school adjustment of the children perceived to be similarly supportive for 25 both technical and university path students. The study concludes that the possible influence by teachers, schools, race, age, and grade should be viewed with caution due to some limitations within the study. Teacher Qualification and Student Achievement In any education system, the need for trained teachers cannot be overemphasized. Greenwald, Hedges, and Laine (1996) found through a metaanalysis of previous studies that educational resources had a major effect on student achievement and one of the most crucial variables was teacher quality. The research shows that the more experienced the teacher, the more resilient and successful are the students (Borman & Overman, 2004; Okpala, Smith, Jones, and Ellis (2000); Tajalli & Opheim, 2004). The study also found that although teacher quality issues may vary from study to study, it is important to note that there is usually the teacher certification status variable. Ferguson (1991) concluded from a research in Texas and elsewhere that, "Good teachers have distinguishable impacts on student exam scores (p. 465). Sanders (1998) stated that “the single largest factor affecting academic growth of populations of students is differences in effectiveness of individual classroom teachers” (p. 27). Associated with this growing consensus that highly skilled teachers are the key to improving student achievement is the realization that a substantial number of teachers appear to be under qualified for their current teaching positions (Ingersoll, 1999). One strategy supported by the U.S. Department of Education is to allow individuals enrolled in alternative certification programs to be designated. In general, researchers have found that possessing a major or minor in mathematics or science is related to increased student achievement in these subject areas. Goldhaber and Brewer (2000) found that students with teachers with degrees in mathematics had greater gains in achievement than students with teachers with non mathematics degrees, but researchers found no such results 26 for science. In a previous study, Goldhaber and Brewer (1996) also found that subject specific training in mathematics and science has a significant and positive impact on student achievement in these areas. This suggests that greater subjectmatter knowledge is associated with gains in student achievement, albeit only in the areas of mathematics and science. Conclusive in this study is the fact that students perform better in Mathematics when the teachers are qualified. Wenglinsky (2002) identified the positive outcome of learned teacher classroom practices on student achievement. Wenglinsky used the data from a 1996 National Assessment of Educational Progress (NAEP) in mathematics and found that the effects of teacher classroom practices, in union with other teacher characteristics, were as significant to student achievement in mathematics as a student’s background. The study found that the degree of certain classroom practices reported by teachers had an impact on students’ mathematics achievement. These practices included individualized instruction, handson learning and higherorder thinking skills. Additionally, Wenglinsky (2002) found that mathematics and science teachers with an undergraduate minor or major in their field elicited greater gains in student performance. In fact, Wenglinsky noted that “students whose teachers majored or minored in the subject area that they are teaching outperform their peers by about 40% of a grade level in both math and science” (p. 45). A more recent analysis by Wenglinsky (2000), who used multilevel structural equation modeling to analyze data from the NAEP, found that teachers with a major or minor in the subject area that they are assigned to teach produce greater gains in student achievement in both mathematics and science. The overall findings from these studies suggest that teacher subjectmatter knowledge positively influences student achievement. This effect seems to be more pronounced for the upper grades than the lower grades. DarlingHammond (2000) found that the 27 percentage of teachers with both a subject matter major and full state certification was positively associated with a state’s reading and mathematics scores on the National Assessment of Educational Progress (NAEP). Goldhaber and Brewer (2000) also concluded that twelvegrade students taught by teachers certified in mathematics had greater gains on a mathematics assessment than students taught by either uncertified teachers or teachers certified in non mathematics subject areas. Improperly certified teachers produced lower gains in student achievement than properly certified teachers. On the other hand, there were no differences in the gains in student achievement on a science assessment between students taught by teachers certified in science and students taught by either uncertified or improperly certified teachers. In another study, Chiang, Miller and Rowan (1997) found that students taught by teachers with mathematics major had greater gains in student achievement, although the effect on student achievement was rather small. Also a recent study by LaczkoKerr and Berliner (2002) directly addressed the issue of the effect of teacher certification on student achievement. The researchers created matched pairs of certified and uncertified teachers. Teachers were matched based on their certification status (an uncertified teacher was matched with a certified teacher) and were matched with teachers (a) within the same school, (b) within the same district, or (c) within similar districts. This matching procedure was adopted to “minimize exogenous variables associated with student achievement scores” (LaczkoKerr & Berliner, (2002. p. 24). Based on their analysis of the gain scores of 109 matched pairs of teachers, the authors found that students in classrooms of under certified teachers would have made 20% more growth had they been assigned to certified teachers classrooms. Research on teacher qualification and student achievement suggests that both subjectmatter knowledge and pedagogical knowledge are 28 positively related to student achievement. Results in a study by Alexander and Fuller (2004) showed that the estimates for the 1999 Texas state achievement exam scores for students who had certified teachers compared to noncertified teachers were statistically significant. On average, students who had a certified teacher had greater gains on the mathematics exam than students who had noncertified teachers, after controlling for several variables. Monk (1994) found that, in many cases, undergraduate coursework in mathematics pedagogy contributed more to gains in student achievement than did undergraduate coursework in mathematics. He also found that undergraduate coursework in science pedagogy was positively associated with student achievement for students in Grade 11 and that graduate coursework in science pedagogy was positively associated with student performance in Grade 10. Ferguson and Womack (1993), measuring teacher effectiveness through supervisor evaluations, realized that education coursework explained a greater proportion of the variation in evaluations than did content knowledge as measured by standardized test scores. Education coursework explained 16% of the variance in the evaluations. Thus, Monk (1994) stated that, “It would appear that a good grasp of one’s subject area is necessary but not a sufficient condition for effective teaching” (p. 142). These studies are further reinforced through a Secretary of Education’s report (USDOE, 2002) which states: Research emphasizes the importance of recruiting teachers with solid content knowledge and verbal ability, but today’s certification system seems to work against the recruitment of these individuals. Of course, many teachers are smart and know their subjects well, but our system allows too many talented candidates (p. 12). 29 These studies succinctly summarize the importance and effect of teacher qualification on student achievement. Thus the need for qualified teachers in the education system cannot be ignored by the policymakers. Teacher Attitude and Student Achievement Teachers’ attitudes are an important factor in determining the success of students (Grosin, 1995). Unsuitable physical environment and teacher’s personality characteristics lead to student indiscipline in classrooms (Patankar & Northam, 2003). Effective teaching requires that the teacher gives the student plenty of opportunities to contribute and elaborate on their own ideas, and that he or she genuinely listens to students say and attempts to consider this from other students’ perspectives. In addition, it is important that students know that there is comfort in the classrooms and that they will be treated humanely when they do contribute. Wrong answers should not provoke negative reactions on the part of the teacher, but needs to be perceived as part of the students’ learning process (Patankar & Northam, 2003). In order to provide the atmosphere for optimum learning, the teacher must have the class well organized or disciplined. Classroom guidelines are needed for routine activities and general classroom behaviors. Lin (2002) investigated teachers' perspectives on teacher value and the relationship between teacher value and classroom climate. The research questions guiding this study were concerned with (1) identification of values important to teachers; (2) the importance of teacher value on teachers' curriculum, teaching strategy, assessment, relationship with students, and classroom climate; (3) students' evaluations of classroom climate; and (4) the correlation between teachers' perceptions and students' evaluations. The study examined the school character (public or private), as well as the teachers' gender, country, age and number of years of teaching experience. Sixteen teachers completed a survey with questions that were designed for 30 the purposes of this study, and 459 students completed the College and University Classroom Environment Inventory developed by Fraser and Treagust in 1986. The researcher collected teachers' responses and implemented the investigations with students in the classroom on a specific day. The data was analyzed using the Statistical Package for the Social Science (SPSS) Version 10.0 for Microsoft Windows. Descriptive statistics were used to summarize demographic information and teachers' perspectives on teacher value. Pearson's correlation coefficient was also used to analyze the relationship between each teacher's perceptions and students' evaluations. Descriptive statistics were used to summarize demographic information and teachers' perspectives on teacher value. Pearson's correlation coefficient was also used to analyze the relationship between each teacher's perceptions and students' evaluations. Descriptive statistics were used to summarize demographic information and teachers' perspectives on teacher value. Pearson's correlation coefficient was also used to analyze the relationship between each teacher's perceptions and students' evaluations. This study concludes that teacher value is related to positive classroom climate. Teacher Effectiveness and Student Achievement Teaching and learning are complex tasks. In order for students to learn effectively, they must participate fully in the learning process. Students must be encouraged to ask and answer questions, attempt new approaches, make mistakes, and ask for assistance. The effect on student learning of changing a single teaching practice may be difficult to discern because of the simultaneous effects of both other teaching activities that surround it and the context in which the teaching takes place (Grouws & Cebulla, 2000). The number of research studies conducted in mathematics education over the past three decades has increased dramatically (Kilpatrick, 1992). In these studies there are a wide variety 31 of areas which include research methodologies, content and grade levels. Results from these studies, together with relevant findings from research in other areas of studies that include studies on cognitive psychology, are being used to identify successful teaching practices and strategies. Furthermore, the results of studies that have been conducted indicates that teachers who seek to improve the effectiveness of their teaching must be careful to study the context in which the delivery is done and the types of students that they teach. Wright (2005) conducted a study on the social network analysis of middle school classrooms. In studying student teacher relations, Wright (2005) conducted direct observations in classrooms over a year, interviewed teachers and students, and collected questionnaire data from teachers and students. By utilizing network tools, a comparison and contrast on the structural composition of classrooms and studentteacher relations was done. This systematic structured observations of classrooms over extended periods of time provided data on studentteacher social interaction that are impossible to gather using selfreport studies alone. Direct observation also offers insight into the social structural mechanisms through which student productivity is constrained or enabled in the classroom. This study was one of the first of its kind to utilize formal social network theory and methods to characterize classroom social structure. The development of this study offered a new set of variables  social networks for policy makers and educators to access in order to enhance student productivity and teacher effectiveness in the classroom. Heilman (1999) conducted a study to investigate the combined impact of reform efforts, content coverage, the importance of grades, honor roll, and nonschool interests of students’ pressure for teachers to replace strategies that motivate students with strategies that promote efficiency and competition. The study examined how teachers emphasized learning or 32 competitive goals and regulate the purpose of the class in response to the huge number of influences that determined the classroom climate. A researcherdeveloped survey instrument was used to collect data from a random cluster sample of 412 students in eighteen classrooms to determine the relationship between student effort and selfperceptions of ability to theories of motivation. Scales used in the survey instrument were teacher support, teacher control, organization and rules, and task orientation; task value and selfperceptions of ability; masteryorientation and performanceorientation; mastery evaluation and performance evaluation. Independent samples t tests were done which indicated that masteryoriented experiences of students are related to higher levels of selfperceptions of ability, effort, support, task value, organization and rules, and promotion of selfregulation than performanceoriented class experiences (p < .05). A series of analyses of variance in this study found that effort levels (high, middle, and low effort) were related to selfperceptions of ability, task value, teacher support, teacher control, task orientation, organization and rules, masteryorientation, promotion of selfregulation, and grades ( p < .05). Competitive classroom experiences were found to have no significant relationship to student effort. Grade level and gender were significantly related to climate variables. It also reported that ninth grade students worked significantly harder than seniors (p < .05) while the upperclassmen results showed higher levels of teacher support, organization and rules, and mastery orientation (p < .05). The study indicates that females worked harder than males and received higher levels of teacher support (p < .05). Another study by Olina and Sullivan (2002) investigated the effects of teacher evaluation and the combination of teacher evaluation and student selfevaluation on student performance and attitudes. Participants in the study were 189 Latvian high school students and their six 33 teachers. The six teachers were assigned to one of three treatment conditions: (a) no evaluation, (b) teacher evaluation, and (c) selfevaluation plus teacher evaluation. All groups completed a 12lesson instructional program on how to conduct experiments and produce research reports. Students in the teacherevaluation group received teacher evaluation on their initial research reports. Students in a selfplusteacher evaluation group selfevaluated their reports and received teacher evaluation on them. The noevaluation group received no formal evaluation instructions. Results of this study indicated that students in the teacherevaluation and the selfplus teacher evaluation groups received significantly higher ratings on their final projects than those in the noevaluation group. However, the noevaluation group had more favorable attitudes toward the program than the other two groups, while the selfplusteacher evaluation group was significantly more confident of their ability to independently conduct future research experiments. Participants in the study were 189 Latvian high school students and their six teachers. The six teachers were assigned to one of three treatment conditions: (a) no evaluation, (b) teacher evaluation, and (c) selfevaluation plus teacher evaluation. All groups completed a 12lesson instructional program on how to conduct experiments and produce research reports. Students in the teacherevaluation group received teacher evaluation on their initial research reports. Students in a selfplusteacher evaluation group selfevaluated their reports and received teacher evaluation on them. The noevaluation group received no formal evaluation instructions. Results of this study indicated that students in the teacherevaluation and the selfplus teacher evaluation groups received significantly higher ratings on their final projects than those in the noevaluation group. However, the noevaluation group had more favourable attitudes toward the program than the other two groups, while the selfplusteacher evaluation group was 34 significantly more confident of their ability to independently conduct future research experiments. Therefore, short class periods in mathematics whether instituted for whatever practical or philosophical reason, should be seriously questioned. These studies highlighted the fact that there was special concern for 3035 minute class periods for math which was being implemented in some middle schools during this period. Additional findings of the study showed that the use of textbooks that devote major attention to review and that address little new content each year should be avoided or be heavily supplemented with other resources. The findings also suggest that teachers should use textbooks as just one instructional tool among many instead of being a slave to textbooks on a onesectionperday basis. Wholeclass discussion following individual and group work improves student achievement. Research in student math achievement also suggest that the use of whole class discussion can be effective if it is used for explaining and sharing the many ways by which individual students arrive at solutions for math problems. This kind of interaction allows students to view the various ways of examining a situation and the diversity acceptable solutions to specific problems. Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view mathematics as a discipline in which thinking is important. Number sense relates to having an intuitive feel for number size and combinations, and the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgments. It involves mentally computing, estimating, sensing number magnitudes, moving between representation systems for numbers, and judging the reasonableness of numerical results. Teaching mathematics with a focus on number sense encourages students to become problem solvers in a wide variety of situations and to view 35 mathematics as a discipline in which thinking is important. Number sense relates to having an intuitive feel for number size and combinations, and the ability to work flexibly with numbers in problem situations in order to make sound decisions and reasonable judgments. It involves mentally computing, estimating, sensing number magnitudes, moving between representation systems for numbers, and judging the reasonableness of numerical results. Markovits and Sowder (1994) studied seventhgrade classes where special units on number magnitude, mental computation and computational estimation were taught. Through this study it was found that after this special instruction, students were more likely to use strategies that reflected sound number sense, and that this was a longlasting change. Results showed that almost every student developed a variety of strategies to solve a wide range of problems. Students also displayed increased determination in trying to solve the problems. However, the findings also highlighted the fact that in many classrooms efforts to reinforce the use of numbers are still not given sufficient attention. Therefore, the study recommended that teachers develop strategies to teach the use of numbers, they should strongly consider moving beyond a unitskills approach (i.e. a focus on single skills in isolation) to a more integrated approach that encourages the development of number use in all classroom activities, from the development of computational procedures to mathematical problemsolving. Summary This review of the literature on classroom climate and student math achievement indicates that there is a unified trend towards the promotion of the creation of suitable classroom climate for students that will influence student achievement in content areas. Classroom climate plays a vital role in the student achievement. The literature also points to the fact that the classroom climate factors such as school climate, teacher and student attitude and teacher 36 qualification are part of the many areas that affect student achievement in schools. This review highlighted several studies that clarify the vital role that the teacher plays in fostering a positive classroom climate along with student success and achievement in schools. However, while there is also a great deal of agreement that classroom climate is important for achievement; there are still other areas to be investigated. Unsuitable physical environment and teacher’s personality characteristics lead to student indiscipline in classrooms (Patnakar, 2007). The review of literature has also underscored the need for LEI to be used in this study. This research was an effort to determine the relationship between classroom climate and student achievement and has, no doubt, created literature on classroom climate for Belize and added to the body of research that exist globally. 37 CHAPTER 111 METHODOLOGY This chapter gives a description of a proposed study design that will seek to determine if a relationship exists between classroom climate and student math achievement along with the variables that affect such relationship. The following sections are included in this chapter: purpose statement, the questions and hypotheses, a description of high schools in Belize, participants and sample size, a description of the instrument, and the research design and procedures. An explanation on ethical considerations and a summary are also included in this chapter. Purpose Statement The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth grade in Belize District high schools. The study also sought to determine the classroom climate factors that influence student math achievement of in ninth grade in Belize District High Schools. The dependent variable in the study is student achievement and the independent variable is classroom climate. Research Questions and Hypotheses The following research questions will guide the study: 1. What is the relationship between students’ perceptions of the classroom climate and mathematics achievement? 2. What is the relationship between students’ perceptions of specific classroom climate factors and mathematics achievement? 3. Are there differences between students’ PSE Mathematics scores and gender? 4. Are there differences between students’ PSE Mathematics scores and school type? 38 H1: There is no difference between students’ perceptions of classroom climate and math achievement. H2: There is no difference between students’ perceptions of specific classroom climate factors and mathematics achievement. H3: There is no difference students’ perception of personalization and mathematics achievement. H 4: There is no difference students’ perception of involvement and mathematics achievement. H5: There is no difference between students’ perception of cohesiveness and mathematics achievement. H6: There is no difference between students’ perception of satisfaction and mathematics achievement. H7: There is no difference between students’ perception of task orientation and mathematics achievement. H8: There is no difference between students’ perception of innovation and mathematics achievement. H9: There is no difference between students’ perception of individualization and mathematics achievement. H10: There is no difference between PSE Math Achievement Scores and gender. H 11: There is no difference between students’ PSE Math Achievement Scores and school type. 39 Belize District High Schools High schools are located throughout the country of Belize and vary in location, population and managing authorities. Presently there are 49 high schools in the country of Belize. According to the Education Statistical Digest of Belize (2005 06) the total number of secondary schools increased by 13 schools from 36 in 200102 to 49 in 200506. These 49 schools are a reflection of the entire high school population in the six districts of Belize namely: Orange Walk and Corozal Districts in the north, Stann Creek and Toledo Districts in the south, Cayo District in the west, and Belize District in the east. The Belize District is also inclusive of the Caye – San Pedro and Caye Caulker. However, it must be noted that two recently opened high schools are not accounted for in the previous data which brings the total to 18 high schools. The high school populations range from 90 students in one school to over 800 students in others. Students from these various high schools also come from various ethnic groups and backgrounds. Besides location and population, high schools in country of Belize also differ in the type of managing authorities which include the government, churches, and private entities. For the purpose of this study, only the 18 high schools in the Belize District were used. A total of 13 of these high schools are located in the urban portion of the district, three in the rural area, one San Pedro, and one in Caye Caulker. Participants The target population that was studied includes 18 Belize District High Schools which represent a total population of 2700 male and female students collectively. Students were from various socioeconomic backgrounds across the country in Belize also represent a wide cross section of the various ethnic groups in Belize. These included the Creole, Mestizo, Garifuna, 40 East Indian and Maya. Two of the proposed institutions that were selected for the sample were all girl institutions and one was an all boy institution with the other 15 being coeducational institutions. The number of high school in the Belize District is small; therefore, the researcher used all of the 18 high schools to obtain a random sample. This sample was indicative of the students to whom the survey instrument was distributed. For the study 540 questionnaires were issued and 477 were received. A response rate of 88% was received. Description of Instrument In the study a customized version of The Learning Environment Inventory (LEI) first developed by Herbert Walberg (1968) and later modified by Barry Fraser (1992) to examine students’ perception of the learning climate of the classroom was used. The quantitative instrument was tested and used in several classroom climate studies in the past. The participants were students who sat the BPSE in 2011 at the grade eight levels and are presently in grades nine at high school. However, the same seven classroom climate variables personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation and individualization were used in the study. Reliability and Validity Several studies have been done to test and retest the instrument that was used in this study. These studies include The Harvard Project Physics (1962 72) that required the development of an instrument to assess learning environments in physics classrooms. This instrument was the start of the initial development and testing of Learning Environment Inventory (LEI) (Walberg, 1968), where students were asked to report their perceptions of the wholeclass environment. Moos and Trickett (1974) later developed a series of environment measures which concluded with the Classroom Environment Scale (CES). CES was also used to 41 ask students for their perceptions of the learning environment of classrooms. Two questionnaires provided considerable milestone for the study of classroom learning environments, were used extensively for a variety of research purposes, and provided models for the development of a range of instruments over the next two decades. This set of studies also influenced Fraser, Giddings and McRobbie (1992) to propose a different form of a learning environment instrument to investigate students’ personal perception of their role in the environment of the classroom rather than students’ perception of the learning environment in the class as a whole. These two forms are the personal form and the class form. Later, there was the development of Classroom Climate Inventory (1986) and subsequently Learning Climate Inventory (1992) by Barry Fraser. Wong & Fraser (1996) further validated the instrument by administering the Personal Form to 1,592 grade 10 chemistry students in 56 classes in Singapore. Therefore, since the LEI was validated and proven reliable over several years of testing, the researcher used the instrument in its original form. Thus, the researcher did not alter the instrument in anyway. This guaranteed the validity and the reliability of the instrument in the conducting of the research. Description of Survey The Learning Climate Inventory survey is comprised of 49 items for the participants to answer. The survey has a range of four answers which include the following: SA = Strongly Agree, A = Agree, D = Disagree and SD = Strongly Disagree. A score sheet accompanies the survey that divides the required item into seven categories that are clearly defined. These categories include the following: 1. Personalization emphasizes opportunities for students to interact with the instructor and the instructor's concern for student' personal welfare; 42 2. Involvement  assesses extent to which students participate actively and attentively in class discussions and activities; 3. Student Cohesiveness looks at the extent to which students know, help and are friendly toward each other; 4. Satisfaction measures the degree of enjoyment of classes; 5. Task Orientation considers the extent to which class activities are clear and well organized; 6. Innovation is the extent to which the instructor plans new and unusual class activities, teaching techniques, and assignments; and 7. Individualization is the extent to which students are allowed to make decisions and are treated differently according to ability, interest and rate of working. The score sheet also had some underlined items that were calculated from the responses of the participants using a specific formula for each range. This survey was appropriate for this study since it specifically addressed the classroom climate variables that the researcher examined. Research Design and Procedure Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. 43 The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth graders who were eight graders when they sat the BPSE. The dependent variable in the study was student math achievement and the independent variable was classroom climate. Data for this study was gathered using the seven independent variables of LEI (personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation, and individualization) and the dependent variable (BPSE math score). Existing data from the 2011 BPSE sitting was used to correlate with the data gathered from the instrument. In this study, data on gender and school type was also collected due to the coding of the high schools. High Schools Selection In this study, the researcher used only 18 high schools in the Belize District. The Belize District has the largest high school population of the 49 high schools across the entire country. The sample was drawn from all of the high schools that fell within the Belize District. Managements for the high schools ranged from grant aided/ church state to government and privately owned status. Three of the proposed high schools are situated in the rural section of the Belize District, two are in the Cayes, and the other 14 are in Belize City. Participants Selection The researcher proposes to use a sample of 540 Belize District High School students from the total target population of (N= 2700) students. The sample was drawn from the total list of high schools in the Belize District. This was done so that the researcher can get a narrow, homogeneous or uniform sample that will make data collection and data analysis easy and simple. Once the sample was drawn, a random selection was done. Every participant was given a fair and equal chance to participate in the study. At the high school 30 surveys were 44 distributed to the participants through the principals at the school. A consent form was placed with each survey for each participant to take home in order for the participants to obtain permission from the parent or guardian to voluntarily participate in the study. The students were given LEI survey to answer. The surveys were collected one week after distribution. An appropriate day and date was arranged with the principals of the 18 high schools to collect the surveys from the institution in order to have started the data analysis process. The LEI has been used in this manner several times over the past two decades (Fraser, 1989; Fraser, 1987; Moos & Trickett, 1987 and Walberg, 1968). Therefore, the time frame for the data to be collected was suitable for the study. Ethical Considerations The researcher also ensured the adherence to the ethical standards and guidelines concerning the involvement of human subjects. Permission was obtained from Human Subject Research Board (HSRB) from Oklahoma State University to guarantee that the process of data collection was valid. Protecting participants’ information was also required, hence personal data was kept confidential and their identities remained anonymous. The researcher ensured that the participants knew that any information given was kept confidential and that their participation would have been voluntary. Thus, the participants could have chosen to discontinue their participation at any time during the data collection process if they so desired. The safety of the participants was of utmost importance so that any intention of harm and maliciousness against the participants was prevented. Additionally, the names of participating institutions were kept anonymous through the use of a coding system. Gay and Airsaian (2000) indicate that the use of descriptive designs in a study involving human subjects in real life situations, where events have already occurred, 45 reduce the chance of the researcher to influence the participants because the researcher will not be in direct contact with the participants of the study. Lack of the direct contact led to more credible data collection and the increased validity of the data on classroom climate and student achievement. Data Analysis The data in this study was analyzed using descriptive statistics. The Pearson product moment correlations, multiple regression analysis, and analysis of variance (ANOVA) tests were used in the data analysis. These tests were used in order to investigate the relationships between classroom climate perceptions and learning outcomes using LEI and the mathematics scores from the 2011 (PSE). Several steps were employed. First, the ANOVA test was performed to determine if there is a significant difference between levels of means of the independent variables. Next, a Pearson productmoment correlation between the classroom climate variables studied and the PSE math achievement scores was obtained. Therefore, the means of the LEI scores, which include personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation and individualization, were compared to the total means of the overall students’ BPSE math scores. Finally, a multiple regression analysis was done in order to verify whether a combination of classroom climate variables determined the predictive power of BPSE math achievement. Summary The purpose of the study was to investigate the relationships between classroom climate and students’ math achievement in 18 high schools in the Belize District. A random sample was drawn from the target population (N=2700). The total number of proposed participants was 540 students. The researcher used a tested instrument, the LEI, which aided in the collection of valid, reliable and necessary data for the analysis. The study was aimed at looking at correlation to 46 determine whether a relationship, if any, between the classroom climate variables and student math achievement existed. The data informed the development of graphs and tables to explain findings and solidify the study. The Statistical Package for the Social Sciences (SPSS) 19.0 by Nie (1968) was used to represent the statistical data in a form of graphs and tables for this proposed study. 47 CHAPTER 1V FINDINGS Chapter four discusses the results of the study on classroom climate and student math achievement. The purpose of study, sample population, design and findings are discussed. Population The population for the high schools in the Belize District consisted of various managing authorities. The selected schools fell into three main categories namely: governmentowned, grantaided and speciallyassisted schools. Government Schools are schools that are fully funded by the government; therefore, all expenditures such as teachers’ salaries, utilities and maintenance are paid for by the government. Grantaided schools are schools that were partially funded by the government. Therefore, the government paid 70% of the teachers’ salaries and gave a subsidy grant to the schools for students’ tuition. Speciallyassisted schools are schools that received a grant for the management to pay one or two teachers in the school. Schools were coded as Catholic, Government, Protestant and Private for analytical purposes. The target population comprised of 18 Belize District high schools, which represent a total population of 2700 male and female students collectively. From the 18 high schools selected for the sample, one was an all girl institution and one was an all boy institution. The remaining 14 schools were coeducational institutions. The population for this study represented only the first formers who took the Belize Primary School Examination in 2011. An average class size of 30 was used since this was an average of the number of students in Belize District classrooms. The sample for this study was purposive and random. Therefore, the sample from the population was a total of 540 students from the various high schools. A total of 30 students 48 were sampled from each high school. In order to differentiate between the various types of schools, the schools were grouped into four categories: Catholic, Government, Protestant, and Private. There were eight (8) Government Schools, seven (7) Catholic, five (5) Protestant schools, and two (2) Speciallyassisted or Private schools. In the study the researcher compared students’ classroom climate scores with those of students’ BPSE math achievement scores, who sat the BPSE in 2011 and are presently in ninth grade in Belize District High Schools. Purpose of the Study The purpose of the study was to investigate the relationships between classroom climate and math achievement in ninth grade. The dependent variable in the study was student achievement and the independent variable was classroom climate. Design of Study Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. Assumptions of Oneway ANOVA The following are the assumptions of a oneway ANOVA that was first used to analyze the data: 1) An independent variable consists of two or more categorical independent groups. In this study the independent variable was sex and this had two groups namely: male and female; 49 2) A dependent variable is either interval or ratio (continuous). The PSE math achievement was the dependent variable and is a ratio or continuous variable; and 3) a dependent variable is approximately normally distributed for each category of the independent variable. An assessment of the normality of data is a prerequisite for many statistical tests as normal data is an underlying assumption in parametric testing. There are two main methods of assessing normality  graphically and numerically. The following methods were used to determine whether the data was normal and if this assumption was met in the data for the statistical tests. The approaches were divided into two main themes: relying on statistical tests or visual inspection. Statistical tests have the advantage of making an objective judgment of normality, but are disadvantaged by not being sensitive enough at low sample sizes or overly sensitive to large sample sizes. As such, some statisticians prefer to use their experience to make a subjective judgment about the data from plots/graphs. Thus, graphical interpretation has the advantage of allowing good judgment to assess normality in situations when numerical tests might be over or under sensitive. However, graphical methods may also lack objectivity. Conversely, since the researcher did not have a great deal of experience interpreting normality through graphs, the best option was to use the numerical methods. Research Question 3 Are there differences between student math achievement and school type? Table 1 below presents the results from two wellknown tests of normality, namely the KolmogorovSmirnov Test (1967) and the ShapiroWilk Test (1965). The researcher used both the ShapiroWilk Test and the KolmogorovSmirnov Test as the numerical means of assessing normality. 50 Table1. Test of Normality Statistic df Sig. Statistic df Sig. PSE Math Score Male .100 222 .000 .954 222 .000 Female .097 255 .000 .961 255 .000 Sex KolmogorovSmirnova ShapiroWilk Tests of Normality The table above shows that the PSE math achievement scores for each male and female group were not normally distributed. If the significance value of the ShapiroWilk test (Shapiro & Wilk, 1965) or the KolmogorovSmirnov test (Chakravarti, Laha & Roy, 1967) is greater than 0.05, then the data is normal for each category. If it was below 0.05, then the data significantly would deviate from a normal distribution. Normal QQ Plot In order to determine normality graphically, the researcher used the output of a normal QQ Plot. In the Q Q Plot, if the data were normally distributed, then the data points will be close to the diagonal line. Conversely, if the data points stray from the line in an obvious nonlinear fashion, then the data are not normally distributed. In the Q Q Plot below the data is not normally distributed. This is easily seen by using the numerical methods since the normality of data based on plots is difficult to determine 51 Figure1.0. Normal QQ Plot of PSE Math Score The oneway ANOVA is considered to be a robust test against the normal assumption. This means that it tolerates violations to its normality assumption rather well. In regards to the normality of group data, the oneway ANOVA can tolerate data that is nonnormal (skewed or kurtotic distributions) with only a small affect on the Type I error rate. Equality of variances between the independent groups (homogeneity of variances). One of the assumptions of the oneway ANOVA is that the compared variances of the groups are similar. Table 2 Test of Homogeneity of Variances shows the result of Levene's test of homogeneity of variance, which tested for similar variances. It is noteworthy that if the significance value is greater than 0.05 (found in the significance column), then there is homogeneity of variances. Because Levene's F statistic had a significance value of 0.094 (which is more than 0.05), the assumption of Homogeneity of Variance was met. 52 Table 2.Test of Homogeneity of Variances Results and Analysis of Oneway ANOVA The descriptive table (see Table 3 below) provides some very useful descriptive statistics including the mean, standard deviation and 95% confidence intervals for the dependent variable (PSE math achievement scores) for each separate group (male and female) as well as, when all groups are combined (total). These figures are useful for the researcher to describe the data. Table3. Descriptive Statistics on PSE Math Scores and Sex Lower Bound Upper Bound 222 48.6 22.290 1.496 45.6 51.5 12.0 92.0 255 50.1 21.985 1.377 47.4 52.8 11.0 95.0 477 49.4 22.117 1.013 47.4 51.4 11.0 95.0 Std. Deviation Std. Error 95% Confidence Interval for Mean Minimum Maximum Descriptive Statistics on PSE Math Scores and Sex Male Female Total PSE Math Score Content Area N Mean The Descriptive Statistics table above (Table 3) and the Means Plot Graph (Figure: 1.1) below showed that female students reported higher mean in PSE math achievement scores compared to male students. Levene Statistic df1 df2 Sig. 16.878 3 473 0.094 Test of Homogeneity of Variances PSE Math Score 53 Figure1.1. Means Plot of PSE Math Scores and Sex Results of the ANOVA The oneway between subjects ANOVA tests were conducted to examine whether there were significant differences in the mean PSE math achievement scores in sex (male and female) group means. These tests proved that there was no significant difference in the PSE math achievement scores between male (M = 48.6, SD = 22.290) and female (M = 50.1, SD = 21.985) Sex group; F (1, 475) = 0.560, p = 0.455. These results suggested that male students have PSE Math Achievement Scores that were not significantly different from female students. Research Question 4 Are there differences in PSE math achievement scores between school types in schools? The assumptions of a oneway ANOVA in this question indicate that: 1) The independent variable consists of two or more categorical independent groups. Independent variable is school type and this has 4 groups namely Catholic, Government, Pentecostal and Private Schools; 54 2) The dependent variable is either interval or ratio (continuous). PSE Math Achievement Scores is the dependent variable and is a ratio or a continuous variable; and 3) Dependent variable is approximately normally distributed for each category of the independent variables. Table 4. Tests of Normality for School Type and PSE Score Statistic df Sig. Statistic df Sig. Catholic .106 86 .018 .960 86 .009 Government .162 224 .000 .904 224 .000 Pentecostal .076 136 .052 .985 136 .134 Private .120 31 .200 .952 31 .183 a. Lilliefors Significance Correction This is a lower bound of the true significance. Tests of Normality School Type KolmogorovSmirnova ShapiroWilk PSE Math Score Table 4 shows that the PSE math achievement scores for each group of school type was not normally distributed. How do we know this? If the significance of the ShapiroWilk test or the KolmogorovSmirnov test is greater the 0.05, then the data is normal for each category. If it is below 0.05 then the data significantly deviates from the normal distribution. In this case, Catholic and Government school type groups were not normally distributed; hence the assumption of normality was not met. However, the oneway ANOVA is considered a robust Test against the normality assumption. This means that it tolerates violations to its normality assumption rather well and, thus the reason why the researcher used this test. Equality of Variances between the Independent Groups (homogeneity of variances) One of the assumptions of the oneway ANOVA is that the variances of the groups that are being compared are similar. Table 5 below shows the test of homogeneity of variances 55 shows the result of Levene's test of homogeneity of variance, which tests for similar variances. If the significance value is greater than 0.05 (found in the Sig. column below), then there is homogeneity of variances. In the test, in Table 5, the Levene's F statistic had a significance value that was less than 0.001 and, therefore, the assumption of homogeneity of variance was met. Table 5. Test of Homogeneity of Variance Robust Tests of Equality of Means Table Even though there was a violation of the assumption of homogeneity of variances, the researcher used the traditional ANOVA by using the Welch test (Shapiro & Wilk, 1965). This was done in order to determine whether there were significant differences between the groups. Like the ANOVA test, if the significance value is less than 0.05, then there are statistically significant differences between groups. Hence, then there were statistically significant differences between school type groups since the p value in the Welch test was less than 0.05 (p <0.001). Levene Statistic df1 df2 Sig. 16.878 3 473 0.094 Test of Homogeneity of Variances PSE Math Score 56 Table 6. Robust Tests of Equality of Means Statistica df1 df2 Sig. Welch 125.811 3 151.155 .000 a. Asymptotically F distributed. Robust Tests of Equality of Means PSE Math Score Independence of cases – This assumption is that data from different subjects are independent, which means that the behavior of one participant does not influence the behavior of another. Results and Analysis of Oneway ANOVA Descriptive Statistics The descriptive statistics table (see Table 7 below) provided some very useful descriptive statistics including the mean, standard deviation and 95% confidence intervals for the dependent variable PSE math achievement scores for each separate group of School Type (Catholic, Government, Pentecostal and Private Schools) as well as, when all groups were combined. Table 7. Descriptive Statistics on PSE Math Scores and School Type Lower Bound Upper Bound Catholic 86 64.3 19.749 2.130 60.10 68.57 16 95 Government 224 40.6 21.136 1.412 37.79 43.36 11 87 Pentecostal 136 47.8 16.109 1.381 45.08 50.55 12 92 Private 31 78.3 8.537 1.533 75.16 81.42 60 91 Total 477 49.4 22.117 1.013 47.39 51.37 11 95 95% Confidence Interval for Mean Minimu m Maximum Descriptive Statistics on PSE Math Scores and School Type PSE Math Scores School Type N Mean Std. Deviation Std. Error The descriptive statistics table above and the means plot below showed that students from private schools reported higher mean of math achievement scores than students from Catholic, 57 Pentecostal and Government Schools. Students from Catholic Schools reported higher mean of PSE math achievement scores than students from Pentecostal and Government Schools. Students from Pentecostal Schools reported higher mean of PSE math achievement scores than students from Government Schools. Figure1.2. Graph of Mean of PSE Math Scores and School Type Table 8. PSE Math Score between Groups and Within Groups ANOVA Sum of Squares df Mean Square F Sig. Between Groups 62845.106 3 20948.369 58.288 .000 Within Groups 169992.722 473 359.393 Total 232837.828 476 ANOVA PSE Math Score 58 The ANOVA table above shows the output of the ANOVA analysis and tells if there was a statistically significant difference in the PSE achievement math scores among school type (Catholic, Government, Pentecostal and Private Schools) group means. In this table the significance level is 0.000 (i.e. p < 0.001), which is less than 0.05 and, therefore, there is a statistically significant difference in the PSE achievement scores among school type groups. Multiple/ PairWise Comparisons From the previous results there were significant differences in PSE math achievement scores from different school type groups as a whole. Table 9 below, Multiple Comparisons, shows which groups significantly differed from each other. The Games Howell test (Keppel & Wickens, 2004) is a generally preferred test for conducting posthoc tests in a oneway ANOVA when the assumption of homogeneity of variance has been violated. The table below indicates that there is a significant difference in PSE math achievement scores between Catholic and Government Schools, Catholic and Pentecostal Schools (p < 0.001), Catholic (p < 0.001) and Private Schools (p < 0.001), Government and Pentecostal Schools (p=0.002 < 0.05), Government and Private Schools (p < 0.001) and Pentecostal and Private Schools (p < 0.001). 59 Table 9. Multiple Comparisons of PSE Math Score and School Type Lower Bound Upper Bound Government 23.761* 2.555 .000 17.13 30.39 Pentecostal 16.521* 2.538 .000 9.93 23.11 Private 13.953* 2.624 .000 20.80 7.11 Catholic 23.761* 2.555 .000 30.39 17.13 Pentecostal 7.240* 1.975 .002 12.34 2.14 Private 37.714* 2.085 .000 43.17 32.26 Catholic 16.521* 2.538 .000 23.11 9.93 Government 7.240* 1.975 .002 2.14 12.34 Private 30.474* 2.064 .000 35.88 25.07 Catholic 13.953* 2.624 .000 7.11 20.80 Government 37.714* 2.085 .000 32.26 43.17 Pentecostal 30.474* 2.064 .000 25.07 35.88 *. The mean difference is significant at the 0.05 level. Std. Error Sig. 95% Confidence Interval Catholic Government Pentecostal Private Multiple Comparisons PSE Math ScorGe amesHowell (I) School Type (J) School Type Mean Difference (IJ) Results of the ANOVA The oneway ANOVA test was conducted to examine whether there were statistically significant differences among students in different school types in relation to their PSE math achievement scores. There was at least one statistically significant difference between groups as determined by oneway ANOVA (F (3, 473) = 58.288, p < 0.001). A Games Howell posthoc test (Keppel & Wickens, 2004) revealed that there were statistically significant differences between students PSE math achievement scores from Catholic (M = 64.3, SD = 19.749) (p < 0.001) and those Government Schools (M = 40.6, SD = 21.136) (p < 0.001), Catholic (M = 64.3, SD = 19.749) and Pentecostal Schools (M = 47.8, SD = 16.109) (p < 0.001), Catholic (M = 64.3, SD = 19.749) and Private Schools (M = 78.3, SD = 8.537) (p < 0.001), Government (M = 40.6, SD = 21.136) and Pentecostal Schools (M = 47.8, SD = 16.109) (p < 0.001), Government (M = 60 40.6, SD = 21.136) and Private Schools (M = 78.3, SD = 8.537) (p < 0.001) and Pentecostal (M = 8.1, SD = 2.040) and Private Schools (M = 78.3, SD = 8.537) (p < 0.001). From the results of the data the researcher concluded that the students from Private Schools reported significantly higher PSE math. Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. Students from Private schools reported significantly higher math achievement scores than students from Catholic, Pentecostal and Government, Schools. In addition students from Catholic Schools reported significantly higher math achievement scores than students from Pentecostal and Government Schools. Furthermore, students from Pentecostal Schools reported significantly higher math achievement scores than students from Government Schools. Pearson Product Moment Correlation In this section of the analysis, the bivariate analysis first looked at bivariate relationships between the dependent variable, PSE math achievement scores and each independent variables (i.e. personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation, individualization, school type and sex) using Pearson productmoment correlation, point biserial correlation and eta correlation ( Rosenthal, Rosnow & Rubin, 2000). These 61 coefficients were selected because the data were quantitative (continuous) and quantitative (categorical). The Pearson productmoment correlation coefficient measured the degree (strength of the relationship – i.e. weak, moderate, strong or independent [i.e. no relationships]) to which two continuous variables vary (direction of the relationship) together (i.e. direct or positive relationship) or oppositely (inverse or negative relationship). Pearson Research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. The research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. The productmoment correlation coefficient was chosen as a correlation coefficient because it was suitable for variables that were continuous (i.e. interval or ratio type). Additionally, pointbiserial correlation coefficient measured the degree to which two variables 62 vary together and are used when one of the two variables is truly dichotomous (Rosenthal, Rosnow, & Rubin, 2000). A truly dichotomous variable is a categorical variable with two (2) levels and there is no underlying continuum between the categories (e.g. sex). Thus, the pointbiserial correlation coefficient is related to a Pearson productmoment correlation coefficient since pointbiserial correlation coefficient is equal to the Pearson productmoment correlation coefficient when the dichotomous variable was coded with different values. Eta is a coefficient of nonlinear association correlation coefficient measures of the strength of a relationship between a continuous dependent variable and a categorical (nominal, ordinal, or grouped interval) independent variable. Like the pointbiserial correlation coefficient, the eta correlation coefficient is related to the Pearson productmoment correlation coefficient because for linear relationships, eta equals the Pearson productmoment correlation coefficient. After computing the correlation coefficients for each pair of variables, the bivariate analysis then examined the coefficient of determination, which is the square of each of the correlation coefficients used in this study (i.e. Pearson productmoment correlation, pointbiserial research design is important because it describes what actions need to be taken in research to continue, to assess, and to evaluate advancement. A clear plan of actions represents success in the study. For the purpose of this study a survey on classroom climate variables was used to gather the data. The quantitative approach is the design that was used since it is easier to collect, simplify and analyze data using this method. This data was used to determine if a correlation existed between classroom climate scores and student BPSE math achievement in Belize District high schools. This study was not used to determine cause or effect. 63 The coefficient of determination indicated how much variance PSE math achievement scores and each independent variable share (i.e. it described the proportion of variance in common between the two variables). Correlation Analysis A Pearson productmoment correlation coefficient was computed to assess the relationship between PSE math achievement scores and continuous independent variables (i.e. personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation, and individualization). The results revealed that there were weak positive correlations between the PSE math achievement scores and student cohesiveness (r = 0.219, n = 477, p < 0.001), task orientation (r = 0.149, n = 477, p = 0.001), personalization (r = 0.146, n = 477, p = 0.001), involvement (r = 0.139, n = 477, p = 0.002), and satisfaction (r = 0.016, n = 477, p = 0.720) (see Table 10 below). Also there were weak negative correlations between the PSE math achievement scores and innovation (r = 0.035, n = 477, p = 0.451), and individualization (r = 0.016, n = 477, p = 0.720). The weak correlations between PSE and aforementioned continuous independent variables, implied that increases or decreases in PSE math achievement scores did not relate (or relate weakly) to increases or decreases in each of the continuous independent variables. That is, PSE math achievement scores and each continuous independent variable vary separately or independently. Hence, when the magnitudes of PSE math Achievement Scores were high, the magnitudes of the continuous independent variables were sometimes high and sometimes low. 64 Table10. Pearson Product Moment Correlation PSE Math Score Personalizatio n Involvemen t Student Cohesiveness Satisfaction Task Orientatio Innovation Individualizatio n Pearson Correlation 1 0.146** 0.139** 0.219** .016 0.149** .035 .016 Sig. (2tailed) .001 .002 .000 .720 .001 .451 .720 N 477 477 477 477 477 477 477 477 Coefficient of Determination 100.00 2.13 1.93 4.80 0.03 2.22 0.12 0.03 *. Correlation is significant at the 0.05 level (2tailed). Pearson ProductMoment Correlations Between PSE Math Score, Personalization, Involvement, Student Cohesiveness, Satisfaction, Task Orientation, Innovation, and Individualization PSE Math Score **. Correlation is significant at the 0.01 level (2tailed). The independent variable School Type was then recoded into two (2) levels (Private and Non Private [i.e. Government and Churches]) to correct this Multicollinearity problem and hence this School Type variable with two levels was used in the regression analysis. To correct for the violations of the regression assumptions for Homoscedasticity and normality of errors, transformations of the continuous variables were computed and subsequent regression analyses were conducted using transformed and nontransformed continuous variables. In regression, transformation means that one changes the scale on which the variables are measured. The results of the regression analyses with transformed variables revealed that the transformation did not fix the Homoscedasticity and normality of errors violations of the regression assumptions problem. The violations of these assumptions invalidate statistical inferences such as those made using a hypothesis test (e.g. tests of significance on the multiple correlation coefficient, R), deriving the p value for the ratio of the sample estimate of the regression coefficient of interest to an estimate of the standard error of the estimate, or by using the estimated standard error to derive a confidence interval. 65 Thus, since the transformation technique did not allow for valid regression analyses to be conducted, HeteroscedasticityRobust Inference Method using a HeteroscedasticityConsistent Standard Error Estimator (Hinckley, 1977; Long & Ervin, 2000; MacKinnon & White, 1985; White, 1980) was employed in this study. This technique uses Ordinary Least Squares to estimate the regression model as is with the NonRobust Inference Method (i.e. the standard or usual Regression Method) aforementioned, however, the difference was that the standard errors were estimated using another method that does not require the Homoscedasticity assumption to be met. The Heteroscedasticity Robust Inference Method using a HeteroscedasticityConsistent Standard Error Estimator was selected since it reduced the effects of Heteroscedasticity on inferences and yet it did not require 1) the use of transformations of the independent, and/or dependent variable(s), and 2) rigorous computer simulation programs. Thus, the researcher had to look at the results of Regression using the HeteroscedasticityRobust Inference Method and the Non HeteroscedasticityRobust Inference Method. HeteroscedasticityRobust Inference Regression Method (Using a HeteroscedasticityConsistent Standard Error Estimator) The Simultaneous Method, where all predictor variables aforementioned are entered at once in the model, was used for selecting the model since the researcher: specified the set of predictor variables that make up the model, had no prior ideas of the order of entry of which independent variables, and which independent variables will contribute significantly to the model. Using the Simultaneous Method (with the HeteroscedasticityRobust Inference Method), a significant model emerged where p < 0.001 and F (9, 467) = 38.60, (see Table 11 below). Please note that this does not support the null hypothesis so we reject the null hypothesis that there is no relationship between PSE Math achievement scores and Personalization, Involvement, 66 Student Cohesiveness, Satisfaction, Task Orientation, Innovation, Individualization, School Type and Sex. Table11. Heteroscedasticity Consistent Model Summary HeteroscedasticityConsistent Model Summaryc Model R Square Adjusted R Square F df1 df2 p Full 0.166a 0.164 38.597 9 467 0.000 Parsimonious 0.150b 0.149 153.951 2 474 0.000 a  Predictors: (Constant), School Type, Individualization, Male, Task Orientation, Innovation, Student Cohesiveness, Involvement, Personalization, and Satisfaction c  Dependent Variable: PSE Math Score b  Predictors: (Constant), School Type and Student Cohesiveness Summary The Adjusted R Square value was 0.164 (see Table 12 below). This indicates that 16.4% of the variance in PSE Math Achievement Scores was explained by the model. This table also indicates a low or weak positive correlation between the combination of all independent variables and PSE Math Achievement Scores. Next to find out which of the independent variables have a significant linear relationship with PSE Math achievement scores the researcher looked at the p values in the Regression Coefficients Table. Results of the regression analysis (without the HeteroscedasticityRobust Inference Method) provided partial confirmation for the research hypothesis since the combination of variables that significantly predicted PSE Math Achievement Scores or had a significant relationship with PSE Math Achievement Scores were only with School Type (p < 0.001), and Student Cohesiveness (p = 0.003) in Table12 below). The Beta (B) weights (or coefficients), presented in Table 13 tells us the individual contribution of each independent 67 variable to the model as well as the relationship between PSE Math Achievement Scores and each independent variable. School Type was the independent variable that contributed most to this model (i.e. strongest predictor of PSE Math Achievement Scores) since it had the largest B value of 13.253 or the smallest p value. To determine the most parsimonious model for the HeteroscedasticityRobust Inference Method, a backward stepwise model was employed. In this method, all independent variables were initially entered into the regression model and they were deleted if they made insignificant contribution to the model. Hence, the outcome will be a regression model with only significant independent variables. In this study, all independent variables were removed from the regression model except for School Type and Student Cohesiveness. The parsimonious model with only School Type and Student Cohesiveness independent variables was significant (i.e. p < 0.001 and F(9, 467) = 38.60) and had an adjusted R2 value of 14.9% indicating that 14.9% of the variability in PSE Math achievement scores is explained by these independent variables (see Table 13 below ). Table12. Heteroscedasticity Consistent Regression Coefficients Results HeteroscedasticityConsistent Regression Coefficients Results Beta Coefficient SE(HC) t P>t Constant 13.253 10.851 1.221 0.223 Personalization 1.269 2.138 0.594 0.553 Involvement 2.872 2.208 1.301 0.194 Student Cohesiveness 5.078 1.670 3.040 0.003 Satisfaction 2.176 1.546 1.408 0.160 Task Orientation 4.288 2.253 1.903 0.058 Innovation 0.667 1.824 0.366 0.715 Individualization 1.272 1.914 0.665 0.506 Male 1.321 1.908 0.692 0.489 School Type 27.253 2.176 12.526 0.000 NonRobust Inference Method (Standard OLS Regression Method) 68 The Simultaneous Method (using the Standard NonRobust Inference Method), where all independent variables are entered at once in the model produced a significant model (F (9, 467) = 10.342, p < 0.001 (see Table13 below) like the results of the Heteroscedasticity Robust Inference Method. This does not support the null hypothesis so we reject the null hypothesis that there is no relationship between PSE Math achievement scores and Personalization, Involvement, Student Cohesiveness, Satisfaction, Task Orientation, Innovation, Individualization, School Type and Sex. Table13. Regression and Residual ANOVA b Sum of Squares df Mean Square F Sig. Regression 38694.931 9 4299.437 10.342 0.000a Residual 194142.897 467 415.724 Total 232837.828 476 b  Dependent Variable: PSE Math Score a  Predictors: (Constant), School Type, Individualization, Male, Task Orientation, Innovation, Student Cohesiveness, Involvement, Personalization, and Satisfaction ANOVAb Model 1 To find out which of the independent variables have a significant linear relationship with PSE Math achievement scores we will look at the p values in the Regression Coefficients Table. Results of the regression analysis provided partial confirmation for the research hypothesis since the variables that had a significant relationship with PSE Math Achievement Scores were only with School Type, Student Cohesiveness and Task Orientation. The Beta weights or coefficients, presented in Table13 below, suggest that Student Type contributed most to this model followed by Student Cohesiveness and Task Orientation. This is similar to the HeteroscedasticityRobust Inference Method which had only School Type and Student Cohesiveness significantly contributing to the model. 69 Table 14. Regression Coefficients Model Standardized Coefficients B Std. Error Beta Tolerance VIF (Constant) 13.253 10.598 1.251 0.212 Personalization 1.269 2.087 0.031 .608 0.543 0.703 1.422 Involvement 2.872 1.974 0.071 1.455 0.146 0.740 1.352 Student Cohesiveness 5.078 1.598 0.146 3.177 0.002 0.847 1.180 Satisfaction 2.176 1.535 0.074 1.417 0.157 0.652 1.535 Task Orientation 4.288 2.177 0.095 1.970 0.049 0.773 1.293 Innovation 0.667 1.809 0.016 .369 0.713 0.896 1.116 Individualization 1.272 1.856 0.030 .685 0.493 0.937 1.067 Male 1.321 1.902 0.030 .694 0.488 0.968 1.033 School Type 27.253 3.919 0.304 6.955 0.000 0.934 1.071 a  Dependent Variable: PSE Math Score 1 Regression Coefficientsa Model Unstandardized Coefficients t Sig. Collinearity Statistics The Adjusted R Square value for the full model was 0.150 (see Table14 below). This indicates that 15.0% of the variance in PSE Math Achievement Scores was explained by the model with all the independent variables. This table also indicates a low or weak positive correlation between the combination of all independent variables and PSE Math Achievement Scores. Table 15. Model Summary a Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.408a 0.166 0.150 20.389 a  Predictors: (Constant), School Type, Individualization, Male, Task Orientation, Innovation, Student Cohesiveness, Involvement, Personalization, and Satisfaction Model Summary 70 The coefficient of variation (Standard Error of the Estimate/Mean of PSE Math Achievement Scores) is 0.413 which is greater than 10% indicating that our prediction intervals of this model will be wide. Hence, this model would not be useful for prediction purposes. To determine the most parsimonious model a backward stepwise model was employed. All independent variables were removed from the regression model except for School Type, Student Cohesiveness and Task Orientation. The parsimonious model with only School Type, Student Cohesiveness and Task Orientation independent variables had an adjusted R2 value of 15.2% indicating that 15.2% of the variability in PSE Math achievement scores is explained by these independent variables (see Table15 below). Table 16. Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.397a 0.158 0.152 20.362 Model Summaryb a  Predictors: (Constant), School Type, Task Orientation, Student Cohesiveness b  Dependent Variable: PSE Math Score It is worthy to note that the full model with all independent variables yielded an adjusted R2 value that is less than the model with just three independent variables (School Type, Student Cohesiveness and Task Orientation). This should not be the case and is a direct consequence of the violation of the Homoscedasticity and normality assumptions in the regression. 71 CHAPTER V CONCLUSIONS, IMPLICATIONS AND REFLECTIONS The purpose of the study was to examine the relationship that exist classroom climate and student math achievement. The study also sought to determine the classroom climate variables that affect student math achievement. In this study, students’ perception of classroom climate was determined by using Learning Climate Inventory (LEI) and its seven subscales of personalization, involvement, student cohesiveness, satisfaction, task orientation, innovation and individualization. The dependent variable used was the PSE mathemat 



A 

B 

C 

D 

E 

F 

I 

J 

K 

L 

O 

P 

R 

S 

T 

U 

V 

W 


