The Effect of Student Attitudes and Beliefs on Mathematics Education Essay
IMPACT OF SMASSE INSET ON STUDENTS’ ATTITUDE AND PERFORMANCE IN MATHEMATICS IN SECONDARY SCHOOLS IN KOSOFE DISTRICT BY BERNARD – SAMUEL – CLEMENT MATRIC NO: PT/10/22738 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE NIGERIA CERTIFICATE OF EDUCATION (N - The Effect of Student Attitudes and Beliefs on Mathematics Education Essay introduction. C. E) DEPARTMENT OF COMPUTER/MATHEMATICS IN ADENIRAN OGUNSANYA COLLEGE OF EDUCATION IJANIKI, OGUDU CAMPUS JUNE 2013 DEDICATION To my God the beginner and the author of my life who made it possible for me to start and finished well. I say thank you for your guidance.
Also to my beloved wife, Oluwabunmi, and our great kids, Aliyat, Bernard Junior (BJ), thanks for all your support, love and encouragement ACKNOWLEGEMENT Many people have undoubtedly contributed to the success of this work. Therefore I owe them many debts of gratitude. Firstly, I would like to express my deep sense of gratitude to my supervisor. Mr. Ogundana, for his invaluable guidance and contribution towards the success of this work. His interest in my work, commitment and constant encouragement gave me the stamina and morale to work harder.
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I express my sincere gratitude to all the Principals, and Mathematics teachers of the various secondary schools I visited for their co-operation and support during the process of data collection. In the same vein, I thank the Form four students who participated in answering the questionnaires that were very useful in my study. I owe many thanks to my beloved wife whose inspiration, moral and financial support enabled me accomplish my studies, and also our children for enduring my long absence throughout the period of my study.
While it may not be possible to mention the names of all those who contributed, in one way or another, to the success of this work, I register my sincere gratitude to all of them, and may God shower them with abundant blessings. Last but not least, I thank the Almighty God for His guidance and grace that was sufficient throughout my study programme. ABSTRACT Performance in mathematics has been steadily deteriorating over the last few years. This prompted the researcher to investigate the impact of SMASSE INSET on students’ attitudes and performance in mathematics.
The objectives of the study were to investigate whether SMASSE INSET has changed the students’ attitudes, improved the performance and the teaching approaches and methodology in mathematics. This study was based on the theory of Reasoned action and the theory of Planned behaviour as proposed by Ajzen and Fishbein (1975 and 1980). This was a field study that was conducted in Kosofe district. A descriptive survey design was adopted for the study. The respondents of the study were selected from the Form four students of the year 2008.
A sample of 371 students, 20 Mathematics teachers were selected using both stratified and simple random sampling. Data was collected through the use of students’ questionnaire and Teacher’s Questionnaire. Analysis of data was done using both descriptive and inferential statistics. For descriptive statistics, frequency tables, means and standard deviations were used. Analysis of variance (ANOVA), t- test and Chi- Square (? 2) were employed for the inferential statistics. The study established that the students’ attitudes towards mathematics have greatly improved as a result of SMASSE INSET.
The study also found out that teacher’s teaching approaches and methodology have greatly improved as a result of SMASSE INSET. However the attitude and teaching approaches could not translate to good performance. In order to make SMASSE INSET more effective in schools and in the teaching of mathematics, it could be included in the programmes of Teacher Education at the level of teacher preparation. LIST OF ABBREVIATIONS / ACRONYMS ASEIActivity, Students, Experiment, Improvisation CEMASTEACentre for Mathematics, Science and Technology Education INSETIn-service Education and Training
SMASSEStrengthening of Mathematics and Science in Secondary Education WAECWest Africa Examination Council MOESTMinistry of Education Science and Technology NCTMNational Council of Teachers of Mathematics PDSIPlan, Do, See, Improve SMASSE-LAGStrengthening of Mathematics and Science in Secondary Education in Lagos State TIMSSThird International Mathematics and Science Study TPBTheory of Planned Behaviour TRATheory of Reasoned Action TABLE OF CONTENTS TITLE PAGE…………………………………………………………………………….. i DECLARATIONii DEDICATION………iii ACKNOWLEGEMENTiv ABSTRACT…….. v LIST OF ABBREVIATIONS / ACRONYMSvi
TABLE OF CONTENTSvii LIST OF TABLESx CHAPTER ONE. 1 1. 0 INTRODUCTION TO THE STUDY1 1. 1Background to the study1 1. 2Statement of the problem. 4 1. 3Purpose of the study7 1. 4Objectives of the study7 1. 5Research Questions7 1. 6 Research hypotheses8 1. 7Assumptions of the study8 1. 8Significance of the study9 1. 9Scope and Limitations of the study11 1. 10Theoretical framework11 1. 11Operational definition of terms14 1. 12Summary16 CHAPTER TWO17 2. 0LITERATURE REVIEW17 2. 1Introduction17 2. 2General Review of literature17 2. 2. 1 The learning gap and the need to improve……………………………………..
17 2. 3 Review of literature related to Attitudes…21 2. 3. 1 Mathematics Teaching in Nigeria……………………………………………. 23 2. 3. 2 Analysis of attitudes towards mathematics of standard six pupils…………… 24 2. 4The process of planned change: A theory of innovation26 2. 5Review of literature related to SMASSE INSET33 2. 5. 1 Change in attitudes towards teaching strategies in secondary school teachers in Nigeria following in-service professional Development. 33 2. 5. 2 Rationale for SMASSE In-service Education and Training (INSET)35 2. 5. 3 The ASEI Movement and the PDSI Approach38 2. 5.
4 Study on Mathematical Achievement Using the Climbing Learning Methods in Nigeria Secondary Schools40 2. 5. 5 SMASSE Project Impact Assessment Survey Results………………………. 44 2. 6 Critical review of literature….. 46 2. 7Summary48 CHAPTER THREE49 3. 0RESEARCH DESIGN AND METHODOLOGY49 3. 1Introduction49 3. 2Research Design49 3. 3. The Study Area50 3. 4The Study Population50 3. 5Sample and Sampling Procedures51 3. 6Study Variables53 3. 7Research Instruments. 53 3. 7. 1 Student’s Questionnaire (SQ)………………………………………………….. 54 3. 7. 2 Teacher’s Questionnaire (TQ)………………………………………………… 54 3. 8Validity of the Research Instruments….
55 3. 9Reliability of the research instruments. 55 3. 10Piloting of the Research Instruments56 3. 11Data Collection and Analysis58 3 . 12Summary60 CHAPTER FOUR61 4. 0DATA ANALYSIS, PRESENTATION AND DISCUSSION OF RESULTS61 4. 1Introduction61 4. 2SMASSE INSET and Student’s attitude towards mathematics. 62 4. 3SMASSE INSET and Students Performance in WAEC Mathematics Examinations. 77 4. 4SMASSE INSET and teacher’s teaching Approach and Methodology92 4. 5Teachers’ Experiences on SMASSE INSET107 4. 6Summary111 CHAPTER FIVE113 5. 0SUMMARY OF FINDINGS, CONCLUSIONS AND RECOMMENDATIONS……………
113 5. 1Introduction113 5. 2SMASSE INSET and Students’ attitude113 5. 3SMASSE INSET and Performance In Mathematics115 5. 4SMASSE INSET and Teacher’s Teaching Approach and methodology115 5. 5Conclusion116 5. 6Recommendations117 5. 7Summary123 5. 8Suggestions for Further Research124 BIBLIOGRAPHY125 APPENDIX I: STUDENT’S QUESTIONNAIRE (SQ)131 APPENDIX II: SECONDARY SCHOOL TEACHER’S QUESTIONNAIRE (SSTQ)135 LIST OF TABLES Table 1. 1 WAEC Mathematics results Analysis……………………………………………. 6 Table 4. 1: Students’ overall analysis on attitudes towards mathematics………………..
63 Table 4. 2: Analysis of students’ attitudes towards mathematics by gender…………….. 66 Table 4. 3: Further analysis of students’ attitudes toward mathematics by gender………… 67 Table 4. 4: Independent samples t- test for students’ attitudes towards mathematics by gender………………………………………………………………………………… 68 Table 4. 5: An analysis of students’ attitude towards mathematics by school category……………………………………………………………………………. 70 Table 4. 6: Further analysis of students’ attitudes towards mathematics by school category……………………………………………………………………………71 Table 4.
7: One way ANOVA of student’s attitude towards mathematics by school category……………………………………………………………………………. 72 Table 4. 8: Analysis of chi- square tests of relationship between gender of Students and attitudes towards mathematics…………………………………73 Table 4. 9: Analysis of Chi- square tests of relationship between school category and attitudes towards mathematics…………………………………………………… 75 TABLE 4:10: WAEC mathematics results analysis for sampled schools. 79 Table 4. 11: WAEC mathematics results analysis for sampled schools as per school category……………………………………………………………………………81 Table 4.
12: Percentage of students who scored C+ and above…………………….. 82 Table 4. 13 : 2007 overall candidates means performance by subject and gender……85 Table 4. 14: One-way ANOVA for WAEC results before SMASSE and After SMASSE………………………………………………………………………….. 86 Table 4. 15: Independent Samples t-test for WAEC Results Before SMASSE and after SMASSE…………………………………………………………………………. 87 Table 4. 16: Analysis of students’ response to the teaching in the classroom……………94 Table 4. 17: An analysis of students’ understanding about teaching in class room as per gender……………………………………………………………………….. 97 Table 4.
18: Further analysis of student understanding about teaching in classroom as per gender………………………………………………………………………………. 98 Table 4. 19: Further analysis of students’ understanding about teaching in classroom as per gender………………………………………………………………………. 99 Table 4. 20: An analysis of students’ under standing about teaching in classroom as per school category…………………………………………………………. 101 Table 4. 21: Further analysis of students’ understanding about teaching in classroom as per school category……………………………………………………………102 Table 4. 22: One way ANOVA of students’ understanding about teaching in classroom as per school category………………………………………………..
103 Table 4. 23: Analysis of Chi- square tests of relationship between gender of students and their responses on teaching in classroom…………………………………. 105 Table 4. 24: Analysis of chi- square tests of relationship between school category and students response on teaching in classroom……………………………………106 CHAPTER ONE 1. 0 INTRODUCTION TO THE STUDY 1. 1Background to the study The idea that the attitude towards mathematics is relevant in the teaching and learning process is shared in the mathematics education research community, but research on attitude is characterized by many problems, more or less investigated.
Amongst them the problem of a clear and shared terminology (Pekhonen and Furinghetti, 2002) and the problem of designing and experimenting observational tools that are consistent with theory (Di Martino and Zen, 2001: Di Martino 2004). Generating positive attitudes towards mathematics among students is an important goal of mathematics education in many jurisdictions. To gain some understanding of eighth- graders’ views about the utility and their enjoyment of it as a subject, third international mathematics and science study (TIMSS) created an index of positive attitudes towards mathematics (PATM).
Poor attitude towards mathematics has often been cited as one factor that has contributed to lower participation of girls in mathematics courses and less success in those courses ( Fullarton, 1993). The conceptions, attitudes and expectation of the students regarding mathematics and mathematics teaching have been considered to be very significant factor underlying their school experience and achievement (Borasi, 1990, Shoenfeld 1985).
There has always been an interest in the development of positive students’ attitude towards mathematics. The objective of any mathematics curriculum includes fostering favourable feelings towards mathematics as well as imparting cognitive knowledge (KIE, 2002). While Bolaji (1996) has provided an overview of many aspects of attitudes towards mathematics including a review of instrumentation, it is still unclear how the school environment affects the development of students’ attitudes towards mathematics.
A baseline survey carried out by SMASSE personnel in 1998, isolated the following problems in the teaching and learning of mathematics and science at the secondary level that contributed to poor performance: * Attitudinal factors 1. Poor teaching methodology 2. Lack of content mastery 3. Lack of a professional forum for teachers to share their experiences 4. Inadequate development of appropriate teaching/ learning materials 5. Administrative factors. 6. Gender disparity
SMASSE project was therefore formulated as an intervention measure to address the problem. The overall goal of the SMASSE project is to “upgrade the capability of young students in mathematics and science”. In order to realize this goal, the project was designed with the following project purpose, which is to “strengthen mathematics and science Education at Secondary school level through the INSET of serving teachers in Nigeria”. The INSET programme was organized into four cycles of ten days each with the following INSET objectives: 1.
Cycle one targets attitude change 2. Cycle two targets ASEI planning and hands- on activities with bridging 3. Cycle three targets actualization and practice in the classroom 4. Cycle four targets students growth and impact transfer In this study, the impact of SMASSE INSET on students’ attitude and performance in mathematics in secondary schools was chosen because before the implementation of the SMASSE project, the students used to have a negative attitude towards mathematics as revealed by poor performance in WAEC Examinations (WAEC,1998). 1.
2 Statement of the problem. The fields of technological and professional education require a strong foundation consisting of sound background knowledge of mathematics. Thus mathematics is of necessity a strategic subject and a prerequisite for studying science and technology. As technology develops and reaches more and more into all levels of industry and commerce, so more mathematics will be needed at all these levels. The government acknowledges the importance of mathematics. It is consistently emphasizing the study of mathematics at all levels. Infact
mathematics is one of the compulsory subjects in both primary and secondary school levels (UBE syllabus, 2002). Students in higher levels of education are also encouraged to study some mathematics as a necessary prerequisite for such subjects as physics, chemistry, economics, engineering and others. The Nigeria government has been working to improve the science and mathematics education in primary and secondary schools, which has been set as a major challenge from the perspective of developing human resources capable of promoting industrialization.
The overall research problem addressed in this study is that despite the launching of the SMASSE INSET to cover the whole country in the year 2003, the performance of secondary school students in mathematics at WAEC level has been very low as shown in Table 1. 1(P. 6). This prompted the researcher to investigate the impact of SMASSE INSET on students’ attitudes and performance in Mathematics Kosofe District Table 1. 1 WAEC Mathematics results Analysis Year| Candidates| Mean score %| 2004| 197,118| 19. 73| 2005| 205,232| 19. 31| 2006| 221,295| 18.
60| 2007| 259,280| 15. 96| 2008| 238,684| 19. 04| 2009| 274,120| 19. 74| Source: WAEC (2004-2009) The current study therefore endeavours to establish whether the SMASSE INSET has had any impact on attitude change and improved performance in mathematics in secondary schools in Kosofe District. 1. 3Purpose of the study The main purpose of this study was to investigate the impact of SMASSE INSET on students’ attitude change and performance in mathematics in secondary schools in Kosofe district. 1. 4Objectives of the study The objectives of this study were:
(1) To establish whether SMASSE INSET has changed the students’ attitudes towards mathematics (2) To find out whether SMASSE INSET has improved the performance in mathematics (3) To determine whether SMASSE INSET has improved the teaching approaches and methodology 1. 5Research Questions The following research questions were used to guide the study: (1) Does SMASSE INSET have any impact on students’ attitudes towards mathematics? (2) Does SMASSE INSET have any impact on performance in mathematics? (3) Does SMASSE INSET have any impact on teacher’s teaching approaches and methodology?
1. 6 Research hypotheses The following research hypotheses, as derived from the research questions and stated in their null form, were tested using the ANOVA and Chi-square (? 2) at alpha level of significance 0. 05. HO1There is no significant difference between SMASSE INSET and students’ attitudes towards mathematics. HO2 There is no significant difference between SMASSE INSET and performance in mathematics HO3 There is no significant difference between SMASSE INSET and the teacher’s teaching approaches and methodology. 1. 7Assumptions of the study
In this study, the following assumptions were made: (1) All the schools that were selected for the study had qualified teachers who had attended the SMASSE INSET (2) Teachers in all the schools selected for the study had fully implemented the new skills acquired in teaching approaches and methodology (3) The responses that the respondents gave constitute a true record of their opinion and views. (4) The respondents were able to do the written tasks that were given to them without interacting with one another. 1. 8Significance of the study
It is hoped that the findings of this study will be useful in the following ways: (1) The study will be of benefit to the district planning committee (DPC) in assessing the effectiveness of the SMASSE INSET implementation at the district level. (2) The findings of the study will assist the Quality Assurance and Standard officers (QASOS) both at the district and the national levels in doing the follow up of SMASSE INSET so as to give more advices and guidance to mathematics teachers on how to improve on their teaching approaches and methodology.
(3) The findings of this study will contribute new knowledge which will provide the ministry of education officials with better ways of carrying out the INSET activities in future. (4) The findings of this study will hopefully be used to improve the performance of mathematics in secondary schools in Kosofe district. According to the West Africa Examinations council report (1998), students’ overall performance in mathematics and science subjects has been declining over the years.
It has been argued that one way of addressing the difficulties students experience in Nigeria mathematics and science classrooms is through appropriate teaching interventions that can be realized through professional development of science teachers (SMASSE project, 1998). It is hoped that professional development programs for mathematics and science teachers will equip teachers with appropriate teaching skills and instruction strategies that are necessary to effectively implement mathematics and science curricula in schools. 1. 9Scope and Limitations of the study
This study was conducted in Kosofe District. This area was selected because over the last few years, the performance in mathematics has been on a downward trend (Education Insight, May-June 2007, Issue 12). This study encountered the following challenges: (1) Financial limitations. This study required a lot of money required for stationery, piloting and travel plus accommodation expenses. (2) Time- the study required enough time so as to collect comprehensive data required for the study (3) Attitude of the respondents-Some of the respondents were not willing to give the correct required information.
Some wanted to give their responses just to please the researcher. 1. 10Theoretical framework This study was based on the Theory of Reasoned Action (TRA) and the Theory of Planned Behaviour (TPB). Derived from the social psychology setting, the theory of reasoned action (TRA) was first proposed by Ajzen and Fishbein (1975 and 1980). The components of TRA are three general constructs: (1) behavioural intention (2) Attitude and (3) Subjective norm TRA suggest that a person’s behavioural intention depend on a person’s attitude about the behaviour and subjective norms. BI = A + SN
If a person intends to do behaviour then it is likely that the person will do it. Furthermore, a person’s intentions are themselves guided by two things: the person’s attitude towards the behaviour and the subjective norms. Behavioural intention measures a person’s relative strength of intention to perform behaviour. Attitude is comprised of beliefs about the consequences of performing the behaviour multiplied by his or her valuation of these consequences. Subjective norm is seen as a combination of perceived expectations from relevant individual or groups along with intentions to comply with these expectations.
In other words, “the person’s perception that most people who are important to him or her think he should or should not perform the behaviour in question” (Ajzen and Fishbein, 1980). To predict someone’s intentions, knowing their beliefs can be as important as knowing the person’s attitudes. Perceived behavioural control influences intentions. Perceived behavioural control refers to people’s perceptions of their ability to perform a given behaviour. These predictors lead to intention. A general rule, the more favourable the perceived control, the stronger should be the person’s intention to perform the behaviour in question.
The theory of planned behaviour is a theory which predicts deliberate behaviour, because behaviour can be deliberative and planned. The theory of planned behaviour holds that only specific attitudes toward the behaviour in question can be expected to predict that behaviour (Ajzen, 1991). In psychology, the Theory of Planned Behaviour (TPB) is a theory about the link between attitudes and behaviour. It was proposed by Icek Ajzen as an extension of the theory of reasoned action (TRA). It is one of the most predictive persuation theories.
It has been applied to studies of the relations among beliefs, attitudes, behavioural intentions and behaviours in various fields such as advertising, public relations, campaigns health care etc. TPB can cover people’s voluntary behaviour which cannot be explained by TRA. An individual’s behavioural intention cannot be exclusive determinant of behaviour where an individual’s control over the behaviour is incomplete. By adding perceived behavioural control, theory of planned behaviour can explain relationship between behavioural intention and the actual behaviour.
All the above views concerning the theory of reasoned action and the theory of planned behaviour helped the researcher in establishing the impact of SMASSE INSET on the student’s attitude and performance in mathematics in secondary schools. 1. 11Operational definition of terms There are few terms used in this study which merit some definition: Attitude toward behaviour:An individual positive or negative evaluation of Self- Performance of the particular behaviour. The concept is the degree to which performance of the behaviour is positively or negatively valued.
It is determined by the total set of accessible behavioural beliefs linking the behaviour to various outcomes and other attributes Attitude:This is taken to mean the student’s acquired internal state or feeling influencing their choice towards learning. Behavioural belief: An individual’s belief about consequences of particular behaviour. The concept is based on the subjective probability that the behaviour will produce a given outcome Behaviour:An individual’s observable response in a given situation with
respect to a given target Behavioural intention:An indication of an individual’s readiness to perform a given behaviour Control beliefs:An individual’s beliefs about the presence of factor that may facilitate or impede performance of the behaviour District INSET centre:An institution which has been chosen as a centre for in servicing of mathematics and science teachers at the district level Impact :Any effect, whether anticipated or unanticipated, positive or negative, brought about by an intervention . National INSET Centre: This is the headquarters of the SMASSE project in Kenya.
It is normally referred to as CEMASTEA (centre for mathematics, science and technology Education in Africa). Normative belief: An individual’s perception about particular behaviour, which is influenced by the judgment of significant others (e. g. parents, spouse, friends, teachers). Perceived behavioural control:An individual’s perceived ease or difficulty of performing the particular behaviour. It is assumed that perceived behavioural control is determined by the total set of accessible control beliefs.
Performance:This refers to the status of students with respect to acquired skills and knowledge as compared with other students or other schools, adopted standards or national educational standards. Secondary school:An institution of learning that offers four years of formal schooling preceding university education. The education offered at this level is based on the four year curriculum which is broad based and builds on concepts, principles, skills and attitudes established at the primary level.
Subjective norm:An individual’s perception of social normative pressures, or relevant others beliefs that he or she should or should not perform such behaviour. 1. 12Summary This chapter has outlined the background to the study, statement of the problem, objectives of the study, research questions, research hypotheses, theoretical framework, significance, assumptions, scope and limitations of the study. It also presented the operational definition of terms. In the next chapter, a review of related literature is presented.
CHAPTER TWO 2. 0LITERATURE REVIEW 2. 1Introduction This chapter has reviewed literature that is general in nature and some which are more specific to SMASSE INSET. Review of related literature has been done extensively, covering g both local and international research studies. Some of the literature reviewed was obtained from several websites on the internet. The study sought to investigate the impact of SMASSE INSET on students’ attitudes and performance in mathematics in secondary schools.
2. 2General Review of literature 2. 2. 1 The learning gap and the need to improve There is always room for improvement, no matter how well our students are doing now; it would be foolish not to try to improve. Interest in international studies has grown since publication of “The learning Gap”, heightened recently by release of the results of the “Third International mathematics and Science study (TIMSS)”. As the name implies, this was the third in a series of international studies.
The first was conducted in 1960s and the second in the early 1980s. In both of these studies, USA students performed quite poorly compared with their peers in most Asian and many European countries. But neither of these two earlier studies came close to matching the size and quality of the TIMSS, by far the most comprehensive and methodologically sophisticated cross- national comparison of achievement ever completed. TIMSS investigated mathematics and science achievement among fourth, eighth and twelfth grade students in 41 nations.
In the eighth grade mathematics 20 of the 41 nations scored significantly higher, on average, than the United States. The seven nations scoring lower than the United states were Luthuania , Cyprus, Portugal, Iran, Kuwait, Columbia and south Africa. Nations scoring significantly higher than the United States included Singapore, Korea, Japan, Canada, France, Australia, Hungary and Ireland (Stigler and Hiebert , 1999). American mathematics teaching is extremely limited, focused for the most part on a very narrow band of procedural skills.
Whether students are in rows working individually or sitting in groups, whether they have access to the latest technology or are working only with paper and pencil, they spend most of their time acquiring isolated skills through repeated practice. Japanese classrooms spend as much time solving challenging problems and discussing mathematical concepts as they do practicing skills (Stigler & Hiebert , 1999). Many teachers in the United States have replaced the chalkboard with the overhead projector, whereas Japanese teachers have not.
In US classrooms, Visual aids functions to guide and control students’ attention. The overhead projector is preferred because it gives teachers even more control over what students are attending to. Within the Japanese system of teaching, visual aids serve a different function. They are not used to control attention but provide a cumulative record of the lessons activities and their results. Japanese teachers do not use the overhead projector because it is not possible to fit the cumulative record on an overhead transparency.
US teachers appear to feel responsible for shaping the task into pieces that are manageable for most students, providing all the information needed to complete the task and assigning plenty of practice. Teachers act as if confusion and frustration are signs that they have not done their job. When they notice confusion, they quickly assist students by providing whatever information it takes to get students back on track. Japanese teachers apparently believe they are responsible for different aspects of classroom activity.
They often choose a challenging problem to begin the lesson, and they help students understand and present the problem so they can begin working on a solution. While students are working, the teachers monitor their solution methods so they can organize the follow-up discussion when students share solutions. They also encourage students to keep struggling in the face of difficulty, sometimes offering hints to support students’ progress. Rarely would teachers show students how to solve the problem mid-way through the lesson.
Japanese teachers lead class discussions, asking questions about the solutions methods presented, pointing out important features of student’s methods and presenting methods themselves. Because they seem to believe that learning mathematics means constructing relationships between facts, procedures and ideas, they try to create a visual record of these different methods as the lesson proceeds (Stigler and Hiebert , 1999). 2. 3 Review of literature related to Attitudes Attitudes largely determine what students learn and their willingness to learn.
Lingren (1980) supported this view by stressing the importance of students holding favourable attitudes if learning experiences are to be successful. Several definitions have been offered as to what attitudes are. Fishbein and Ajzen (1975) stated that an attitude is one’s general feeling of favour or otherwise toward some stimulus objects. A similar definition was offered by Thorndike and Hagen (1975) and Richardson (1977). They added that this judgement or feeling is towards an individual, a group ,an object, an institutions or a proposition.
However, caution must be taken as to what attitudes students have as fears passed on to students stay with them for the rest of their education (Philips, 1980). Extending this further, Tobias, (1978:54) stated that “negative attitudes can powerfully inhibit intellect and curiosity and can keep us from learning what is well within our power to understand”. In the secondary school, Fakuede (1973) found that it is common knowledge that the majority of the students in Nigerian Secondary schools dislike mathematics when comparing the two sexes.
Internationally females have been noted to have more negative attitudes (Iben, 1991; Dike, 1984; Omuoha, 1982; Oyewole, 1982; Tobias, and Weissbroad, 1980; Preece, 1979; Fennema and Sherman, 1977; Bassa, 1976). The differences between the attitudes of males and females increase as students’ progress in school (Lewy, 1982). According to Mukherjee and Umar (1989) of Kano state polytechnic, Nigeria, attitudes can be changed as theories of attitude change have shown. Research on attitudes change of individuals and their subsequent behaviour has been mainly in fields other than education.
Attitudes like values are products of the social interactions a child is likely to experience with his parents, teachers and neighbourhood community. Successful interactions depend on positive reinforcements, which in their turn lead to ego- involvement of the persons concerned. 2. 3. 1 Mathematics Teaching in Nigeria A study of factors influencing student’s attitudes towards mathematics in the Junior secondary schools There has always been an interest in the development of positive students’ attitudes towards mathematics.
The objectives of any mathematics curriculum include fostering favourable feelings toward mathematics as well as imparting cognitive knowledge. While Bolaji (1996) has provided an overview of much aspect of attitudes towards mathematics including a review of instrumentation, it is still unclear how the school environment affects the development of students’ attitudes towards mathematics. Some researches have been done on the relationship between school variables and students attitudes towards mathematics.
Several investigations have found a small but positive correlation between some schools factors and attitudes (Jacobs, 1974, Fields, 1975; Evans 1978, Paul, 1986), although these studies do not examine the influence of specific variables. Gordon (1975), cooper (1988) and MC Maham (1992) provide evidence that aspects of the classroom learning environment, or climate, are positively related to mathematics attitudes. An environment lower in intellectual demands, difficulty and amount of frictions or conflicts is likely to show more students positive attitude (Armstrong, 1985).
A number of studies have indicated that the personality and behaviour of the teachers is very important in the formation of students’ attitudes, with one notable exception by Fennema (1990). Anderson (1991) found that it is important for teachers to be enthusiastic and use more indirect teaching behaviours. Ninth grade pupils interests in mathematics was found by Reed (1968) to increase with teachers who are warm and who utilized student’s intrinsic motivation. Fennema and Sherman (1995) found that students of teachers who
were well- organized, achievement-oriented and enthusiastic tended to have more positive mathematics attitudes. In support by other studies concerning the effect of the teacher, the students mentioned the teacher, in both personality and interrelationships with students as a crucial variable in attitude formation (Bolaji Caleb, 1996). The findings of the study carried out by Bolaji (1996) suggests that the assessment of mathematics attitudes needs to differentiate enjoyment from usefulness and indicates the importance of students investment through effort in developing positive attitudes towards mathematics.
Teacher personality, relations and interactions with students’ classroom activities, rewards, assignments and students work are all controlled b the teachers. The results from this study suggests the need for the teachers to develop positive relations with students, to stress classroom activities which involve active- teaching process and student participation and to engage students meaningfully in the subject, so that a fruitful and satisfying results is assured. 2. 4The process of planned change: A theory of innovation
According to Bishop (1986) any process of innovation involves the following four major factors: (1)The Change agent- the Innovator, the person or group e. g. the headmaster, or individual teachers, or local authority, or national government) that decides upon and initiates the innovation or educational change. (2)The Innovation or change itself, e. g. an integrated approach to learning -teaching; or new mathematics in place of the old, or a comprehensive system of education as against the more traditional tripartite system of grammar school/ Secondary, modern/ technical educational; programmed instruction; education by television etc.
(3)The user system- the person or group at which the innovation is directed or targeted. These three key factors answer the simple question: Who (the change agent) says What (the innovation) To whom (the user) To ignore or underestimate the importance of any one of these key factors would be courting trouble. It is important to bear in mind too, that these three factors interact with, change and are changed by each other during the process of innovation. (4)Time, innovation is essentially a social process and so takes place over a period of time. The change agent system
Any change agent or innovator will be obviously involved with: 1. The process of innovation 2. The planning of innovation 3. Strategies of innovation Considering these under the change agent system does not imply that the user system is not involved. It sometimes happens that the change agent and the user are in opposition. But for any innovation to success the two must co-operate and collaborate. So, while considering what the change agent does, one must remember that ideally, the user will also be closely involved in the change agents activities.
The process of innovation Most innovations go through something approaching these logical phases: 1) There is some problem, some dissatisfaction, some need, that requires attention 2) Some possible solutions are considered 3) A particular solution (innovation) is selected as being the most likely to meet the solution 4) This optimum solution is trialed and evaluated 5) If promising the solution is implemented on a wide scale 6) The solution is absorbed into the system, it is institutionalized (1) The problem
Before any innovation begins there must be some problem, some situation which is causing dissatisfaction and which it is hoped some innovation will solve or at least ameliorate. Otherwise why introduce any innovation? The difficulty is often to identify the real problem, which is the one that is the root cause of the dissatisfaction. (2)Possible solutions Having identified the real problem, the next phase involves considering possible solutions, bearing in mind the economic, social and cultural
limitations. An innovation is a deliberate intrusion into the fabric of a culture. Often this entails a change in the existing order of things. Any solutions and innovations preferred must not only be feasible in terms of cost but must also be compatible with existing values. Social system and innovation systems ought to exist for the people and their welfare not the other way round. And just because something is new or different it need not necessarily be better than the system it is transplanting.
Remember too that over- ambitions, cloud- cuckoo’ solutions seldom get into orbit. (3)The innovation From the possible solutions the change agent (e. g. a government planning unit, a ministry, a head teacher etc will select that solution, innovation, educational change, that it considers will best achieve the desired results with the greatest effectiveness and at a reasonable cost. (4)Piloting The next task of the change agent is to develop and introduce this innovation, this optimum solution, into the client/user system on a trial basis.
This will involve promoting awareness and interest in the innovation, adjusting internal organizational procedures and arrangements, location and arranging appropriate resources, providing training courses (and possible incentives), setting up monitoring and feedback procedures to assess the relevance and effectiveness of the inn ovation. (5)Implementation For effective planning and execution of an innovation the implementation phase should be regarded as a distinct process from the earlier trial phase.
It is not merely an extension of the earlier ‘trial or development phase, implementation entails new and distinctive issues and problems that call for new and distinctive approaches. Initial acceptance of an innovation, even enthusiasm, is not enough to ensure implementation, as Pratt points out: ‘more good curricula sink without trace on the shoals of implementation than on any other point’. Innovation is a process, a continuous and complex negotiation between people involved in establishing new ideas and practices.
Most innovations require considerable change in the usual pattern of teacher behaviour. To break away from old modes of behaviour and begin to act in an entirely different way is far from easy and takes time. 6) Institutionalization An essential ingredient for large scale adoption and institutionalization of educational innovations is a national capacity and commitment to carry out after the initial ‘trial’ and development period. Massive change can rapidly be initiated but they cannot rapidly be adopted on a stable or permanent basis.
This is due to the fact that a system, be it an individual an institution or a series of individuals or institutions is unable to assimilate rapidly a great number and variety of new elements or behaviours which are unfamiliar. The final task for the manager (change agent) of an innovation process is to take steps to stabilize or institutionalize the innovation that is get it absorbed and structurally integrated into the system. To do this he/ she must make provision for continuing maintenance of the innovation, and for ensuring that the innovation can be adapted to meeting changing needs.
The planning of innovation The problems of innovation are very complex and nowadays can no longer be solved by mere intuitive judgments or educated guesses. If innovation is not to be a hit or miss affair, it must be planned. As innovation is always a risk affair, the effective planner (change agent) minimizes the risks not only by anticipating as many future events as possible but also by providing ‘fail- safe’ mechanisms to cover unforeseen events and in this way help to nip in the bud any potential disaster. A good plan allows any imperfections that occur to be remedied easily.
For effective planning of innovation Adams and Chen enumerate eleven elements which must be considered at each of the six stages of any innovation process. These elements are: 1) The personnel to be employed (who) At all stages of an innovation process, there must be people available all along the lines that have the expertise and capacity to carry out their allotted tasks. (2)The specification of what the actual tasks is (what); That is, what has to be done, what the innovation in action will consist of, its size and its scope, the role of teachers, of researchers etc.
Whether the specifications are detailed or more open depends on the capabilities of those who carry out the tasks. The purpose of task specification is to provide a sufficient basis for getting into the action of innovation. (3)The method (strategy or procedure to undertake the task) (4)The equipment needed (with what) (5)The plant, building or environment (where). When equipment and plant are part and parcel of an innovation, then means must be found for producing and delivering them. (6)The cost entailed.
One must face up to the costs, not only of initial trials, but also the full implementation costs of any innovation. (7)Other people or rather other social contexts on which the innovation impinges. It is wise and essential to gain the co-operation of interested parties especially if they are powerful, who might otherwise regard their territory or prerogatives as being violated or threatened. Failure to involve or at least inform interest sections can prove an innovation’s undoing. (8)The time involved (when and for how long)
Innovations take time. People and social systems are generally slow to welcome changes, which they often regard with suspicion. (9)The scheduling or sequencing or co-coordinating of activities (in what manner) Time spent in planning the sequencing and co-coordinating of events is time well spent. The more precise the co-ordination, the faster the process of innovation. (10)The rationale for undertaking the innovation (why). What are the justifications for the particular approaches used in the operational phase?
(11)The evaluation of the consequence or effects resulting (with what effects) This is the moment of truth when either a ‘thumbs up’ or a ‘thumb down’ decision has to be taken on whether or not to go ahead with the innovation. Whether an innovation is implemented on a wide scale depends on at least three factors: * The political climate, in a national sense and in an institutional or local sense; * Whether there is sufficient (energy) in the form of material and human resources to sustain it (any proposal that adds to cost is generally viewed unfavorably) * Its place in the general array of priorities.
2. 5Review of literature related to SMASSE INSET 2. 5. 1 Impact of SMASSE INSET on shift in teaching strategies. Nigeria changed her education system from 9-3-4 (nine years of uninterrupted schooling, and transition from one class to another is automatic but determined through continuous assessment) to the current 6-3-3-4 education system ( 6 years of primary, 3 years of Junior secondary and 3 years of Senior secondary school, 4 years of university education depending on the course taken) (Mackay report 1981).
The changeover made mathematics and some science subject a must pass in all schools. The new education policy found many schools ill- equipped to start mathematics and science classes coupled with the extra demand for mathematics and some science teachers. The new education system’s high demand for mathematics and science facilities and teachers hardly gave room for teachers’ professional development of how to implement the new curriculum. This has remained so for sometimes now.
However, students in Nigeria sit for national examinations that are centrally set, moderated, marked and graded (WAEC, 1998). According to the WAEC (1998), student’s overall performance in mathematics and science subjects has been declining over the years. It has been argued that one way of addressing the difficulties students experience in Nigeria science and mathematics classrooms is through appropriate teaching interventions that can be realized through professional development of mathematics and science teachers (SMASSE project,).
It is hoped that professional development programs for science and mathematics teachers will equip teachers with appropriate teaching skills and instruction strategies that are necessary to effectively implement science curricula in schools. By so doing, the Nigeria authorities hope to strengthen the teaching and learning of mathematics and science education in public schools through a pilot project called “Strengthening Mathematics and Science in Secondary Education (SMASSE)”. SMASSE targeted teachers first because of the time they spend with students.
The attitude of the teacher impacts negatively on students. Negative attitude among students is manifested in untidy incomplete homework, frequent absenteeism, lack of attention in class, poor performance and low enrolment in optional science and mathematics subjects, especially physics (Wambui and Wahome , 2006). 2. 5. 2 Rationale for SMASSE In-service Education and Training (INSET) The following are some of the factors that may disturb the education system equilibrium thereby making it necessary for teachers to undergo INSET (SMASSE Project 1998):
(1) Curriculum change Curriculum requirements of any education system do not remain constant but are ever changing with time. This may for instance be as a result of changing education policy to respond to contemporary societal needs. For example in Nigeria there has been a shift of emphasis for education for “white collar job” to education for “self- reliance”. Under such circumstances, in-service training becomes necessary if the new curriculum is to be effectively and efficiently implemented.
INSET would provide the necessary forum where the policy makers and implementers would deliberate on matters pertaining to new aims and objectives, content, sequencing, modalities of implementation etc and reach a consensus. (2)Change in Teaching Approaches/ Methodologies Changes in curriculum bring about a need for re-examination of pedagogical aspects. New teaching methods/ approaches may be required to teach new curricula. Other than new curricula there is continuous research on effectiveness of teaching/ learning methods/ approaches and as such practicing teachers need to be updated on the current trends.
For example, there has been a strong recommendation by educators for a shift from a teacher- centered approach to student- centered approach of teaching. Without in-service training during which such developments are articulated, teachers may find it difficult to discard old practices for the new ones. (3)Teacher’s Professional Development A considerable amount of in- service education for teachers is conducted in the absence of particular curricula changes. Such INSET is provided due to the potential benefits to the teachers’ professional growth.
Its degree of success is judged by the competencies that the teacher acquires or by improvement in the teacher’s classroom practices but not in terms of its contribution to some overall curricula or instructional direction established for a school or program. (4)Follow-up Much of the good practices taught and learned in college are soon undone because of lack of follow-up. Newly posted teachers very soon after entering the profession resort to outdated teaching practices most likely due to discouragement by colleagues that much of what is taught in college is theoretical and don’t work in actual practice.
Another factor could be frustrations encountered in the course of duty, etc. INSET thus provides a good opportunity to make a follow-up and undo retrogressive acts, attitudes and practices. It may be true to some extent that most teacher trainers, especially in the universities are out of touch with the realities of the classroom and that some courses are generally theoretical. It is more for such reasons that INSET, during which pre-service training can be harmonized with the realities of educational practice, becomes essential. (5)Rising Cost of Education The cost of providing quality education is ever rising in terms of money and time.
As such it is important to get out of it the best value for the investment. Facilities and resources meant for education must therefore be utilized optimally. Priority must be given to academic programmes whenever there is competition for resources in educational institutions. Teachers can be best sensitized and exposed to suitable approaches/ practices to achieve this during INSET. (6)Technological Advancement Technological advancement has brought with it the information technology (IT) revolution. It is becoming evident that any society that will be left out of this revolution risks total isolation from the global family.
Technology has also found considerable use in education. However, not many teachers have the necessary IT knowledge and skills. Capacity building in this critical area can be achieved through INSET. (7)Emerging Issues The dynamism of society ensures that passage of time always brings along with it issues that need to be addressed urgently without having to wait for curriculum change. For example, the AIDS pandemic, drug abuse, deviant behaviour, unrest in schools, etc, issues that if left unattended have the high potential of disrupting the system.
As such INSET becomes necessary where teachers, especially head teachers and those in charge of guidance and counselling are equipped with skills and competencies to deal with such situations. (8)Conclusion It is becoming widely acceptable among educators that pre- service Training (PRESET) is but only an induction into the teaching profession. On starting to teach, the teachers put into practice theories, teaching methods and student management styles as learnt at pre-service training. However, these have to be continually reviewed in the light of prevailing conditions, circumstances prevailing on the ground and of new discoveries.
INSET is thus important for professional development through sharing of experiences and continuous exposure to new ideas to keep abreast with new developments in the teaching profession, pedagogical, content, and administrative and policy issues can be handled during the interactive forum that INSET provides. 2. 5. 3 The ASEI Movement and the PDSI Approach The activity, student, experiment and improvisation (ASEI) movement is a SMASSE initiative whose focus is to assist teachers to reflect on their teaching strategies and acquire skills for effective teaching and efficient learning to occur.
It also aims at encouraging teachers to focus on instructional strategies that will support meaningful learning and make lessons interesting to the learners. Through improvisation, the teacher is able to demystify conventional experiments by scaling down experiments, thereby relating mathematics and science to real life situations. The learner is the focus of attention and activities are planned for the learners through the development of ASEI lessons. In these lessons, a bridge is created to enable learners to relate and integrate practical activities with theoretical knowledge.
This movement advocates a shift in both the teacher’s thinking and practice from teachers centred approaches to student centred approaches. In this approach teaching is for the student and the emphasis is on teaching for understanding by actively engaging the learners in the construction of knowledge (SMASSE INSET Cycle I, 2004). The ASEI movement’s strength lies in the recognition that, meaningful learning only takes place in an environment in which students are actively engaged in focused and sequenced activities of acquisition of skills and knowledge.
It further recognizes the power of improvisation in which the teacher carefully identifies and selects teaching/ learning materials from the local environment. The movement considers the quality of classroom activities as critical to achieving effective teaching and learning. The activities here can be hands-on (psychomotor i. e. manipulative skills), minds-on (cognitive i. e. Intellectual thinking, reasoning), hearts- on (the affective aspects i. e. those that stir up the learner’s interest/ feelings about the subject) and mouths -on (communicative skills i.
e. discussions). These activities should be students- centred i. e. designed to increase the participation of the learner. They should be carefully selected, sequenced and directed to provide meaningful experiences to the learners. Plan, do, see and improve (PDSI)is the vehicle that carries the ASEI movement and involves: (1) Planning, where teachers are encouraged to take time when planning to reflect on the most appropriate activities that will enhance effective learning using the resources available.
(2) Doing is shared between the teacher and the learners where the teacher’s role is facilitation and not the dispenser of knowledge (3) Seeing encourages the teachers to include a feedback mechanism in their lessons and teaching functions. Lesson evaluation is seen as the key to improvement of lesson delivery. (4) Improvement should be done by incorporating information obtained from feedback during and after lessons. This is a continuous activity which ensures that the teacher’s skills improve and confidence increases as the instructional programs are enriched. 2. 5.
4 Study on Mathematical Achievement Using the Climbing Learning Methods in Nigeria Secondary Schools Many African countries envision being industrialized by the year 2030 and Nigeria is no exception. However, looking at the performance of mathematics and science subjects at secondary education level in Nigeria the vision to be industrialized is in doubt because the performance by the students in these subjects has been very poor. Improving the performance of mathematics and science education is a great societal need in Nigeria not only for industrialization of the country but also for producing scientifically empowered citizens.
Research by one of the key stakeholders in secondary education in Nigeria, the Strengthening of Mathematics and Science in Secondary Education (SMASSE) project in 1998 has shown that consistent failure and negative attitude by students, towards mathematics continues to characterize the classroom. Based on this same research, teachers have been found to present lessons that are too much teacher- centred with the teacher as the main actor and sometimes the only actor in the classroom as students remain passive recipients. Mathematics lessons have been found to be difficult, boring and lacking in effective teaching/ learning materials.
The challenge thus has been how to make mathematics more “alive”, more “real “and more “accessible”. It is, therefore strongly felt that students’ involvement during lessons must be enhanced to increase motivation, effective teaching /learning materials used and lessons should be made more interesting. Wambui (2002) realized that a student- centred lesson should be enhanced from two complimentary elements: 1) placing more responsibility in the hands of the students, and 2) Requiring the teacher to serve as a mentor and facilitator in presenting knowledge especially to students and fellow teachers in the teaching/ learning process.
Wambui has been a national INSET trainer in mathematics since 2000 and proceeded for further study in Japan in 2002. During her study in Japan, she learned” climbing learning method” which could be applicable and more effective in the Kenyan classroom. This brings about a pedagogic paradigm shift from teacher- centred teaching/ learning practice to students- centred teaching/ learning practice. The shift also aims at shifting from theoretical approach to activity focused approach.
“Climbing learning methods” is a method which places emphasis on developing abilities while regarding the mathematics learning process as an information creation and transmission process. Knowledge must be organized structurally and functionally. If on creating knowledge, knowledge is tightly organized structurally and functionally, one can then utilize and apply the stored knowledge in the brain. Climbing learning method therefore propagates the use of a functional network by means of the structurally and functionally organizing knowledge in the students’ brains.
The learning elements in the teachers’ brains are firmly tied structurally and functionally to each other. But learning elements within the student’s brain may not be firmly tied structurally and functionally to each other and may be existing as separate entities to each other. Climbing approach utilizes a learning structural chart referred to as concept map where the students are supposed to fill in the spaces provided, the explanation of the learning elements, the formula, examples and self made problems and answers.
In the process the students understand the content and meaning of each learning elements tightly thereby extending the existing knowledge and reconstructing it. The filling in, of the concept map is assigned as homework. To overcome the challenge of making mathematics more “alive” and more “real”, Wambui used activity focused teaching/ learning. Activities here refer to minds on and hands- on activities. This is with the understanding that increased use of senses enhances understanding and promotes retention by learners.
With the use of activities, mathematics is made more real, and this arouses students’ interest and curiosity as they relate mathematics to their real life experiences. The use of hands- on and minds –on activities during the teaching/ learning process as applied in the research is yet another paradigm shift from theoretical, chalk and talk, talk and talk and knowledge/ content based approach to activity focused teaching/ learning. The Nigeria traditional method of teaching mathematics implies instruction, practice and evaluation as the simple patterns of activities in the classroom.
Wambui compared the students’ mathematics cognitions and attitude before and after being exposed to the following methods of teaching and learning mathematics: 1) Traditional method of teaching and learning mathematics in Nigeria 2) The climbing learning method. Since the results of her findings showed a great improvement in students’ cognition and attitude towards mathematics with the climbing learning method, she recommends that Nigeria teachers implement these methods in the classroom as an alternative teaching method that will assist learners in: 1) Achieving higher cognition
2) Instilling the right attitudes to students thus having an increased student interest, confidence and enthusiasm towards learning mathematics. 2. 5. 5 SMASSE Project Impact Assessment Survey Results In September 2004, SMASSE project undertook a nationwide survey to assess the impact of INSET. The aim was to find out how SMASSE activities are practiced in the classroom and how they translate in achievement. It was conducted in form two classes of selected schools, teachers taking the classes in mathematics and science subjects and principals of the schools.
The students had two sets of questionnaires, one dealing with their learning of mathematics in general, their attitudes towards the subjects and their participation in class during learning (Wambui and Wahome , 2006). The following were observations on the teachers and the learners after being exposed to the INSET: Net Impact on teachers: 1. They plan better and more consistently. 2. They attend to student’s needs more regularly. 3. They are more open to team work. 4. They are more confident to carry out practical activities and experiments previously thought to be difficult or dangerous.
5. They try out new methods. 6. They can face the challenges arising from lack of resources better. 7. They can face the challenge of large classes better. Net impact on students: 1. They are actively involved in class work 2. They show great interest and responsiveness. 3. They attend lessons more punctually and regularly. 4. They do their assignment more neatly and promptly 5. They carry out discussions beyond class time 6. They ask questions in and out of class. 7. Their curiosity is aroused and sustained as they relate mathematics to their real life experiences. 8.
It encourages team work but allow individual participation for the students. 9. It provides students with opportunities to develop key competencies such as problem- solving, analysis, synthesis and application of relevant information. 10. It demystifies mathematics because of relating it to students’ real life experiences. 11. Their attitudes towards mathematics gradually become positive. Reforms expected: The kinds of reforms expected out of these practices are like some of the positive impacts already mentioned as noted in the teachers and learners. It is also expected that: 1.
Attitude will be positive for teachers and students 2. Teachers will practice more effective teaching methodologies 3. Teachers will develop effective teaching/ learning materials 4. There will be better administration and management in schools In essence the students should become active in the learning process while the teacher carefully guides the process and there will be more meaningful activities in the mathematics classrooms. 2. 6 Critical review of literature The overall literature suggests that teacher-related variables are most important to the development of students’ attitudes towards mathematics.
The present study is structured to probe the most important school related determinants of liking or not liking mathematics from the point of view of each student. According to Bishop (1986), major factors of innovation are the change agent, the innovation itself, the user system and the time. The process of innovation involves six processes. By looking at SMASSE INSET as an innovation, it is evident that the SMASSE INSET followed all the six processes as given by Bishop. However, the time factor was not given much attention by the SMASSE INSET.
According to Bishop, an innovation takes place over a period of time. The change agent and the user must co-operate and collaborate so as to avoid any opposition. The present study will address the issue of how the SMASSE INSET should be strengthened and sustained so as to withstand the test of time. The SMASSE INSET was organized into four cycles of two weeks each. Cycle one targeted attitude change, cycle two targeted ASEI/ PDSI approach to teaching, cycle three targeted actualization and practice in the classroom whereas cycle four targeted student’s growth and impact transfer.
Rather than spending large amount of time on the philosophy and theories of teaching, teachers need help in learning practical techniques of effective classroom instruction. Good mathematics teachers develop over a long time and their development must be given greater attention. Opportunities for observing and emulating the practices of outstanding models and for practicing under the supervision of skilled teachers would provide the kinds of experience that all good professionals need. SMASSE INSET gave little attention to actualization and classroom practice.
Much time should have been allocated to cycle three. In-service training is essential for a new curriculum. The aim of in-service training must be commitment by teachers to the new goals and scripts. Change to teaching may be even more difficult since it involves change in behaviour and acquisition of new skills as well as a change in beliefs. A key to change is ownership. Teachers will persevere with an innovation if they belief that it is their innovation, not one that an outsider has imposed on them. SMASSE INSET was introduced and presented to teachers as final forms to which they have had no input.
Although the curricula can cause some change in the teaching of mathematics, teachers adapting them to their existing methods reduce their effect. The teachers’ scripts do not change much at all. It has been documented in several studies that teachers asked to change features of their teaching often modify the features to fit within their pre- existing system instead of changing the system itself. The system assimilates individual changes and swallows them up. Thus although surface features appear to change, the fundamental nature of the instruction does not.
When this happens, anticipated improvements in students’ learning fail and everyone wonders why. The present study will address the issue of how mathematics teachers can be made to own the in-service training that will be organized in future. From the review of the related literature, it is therefore evident that there are research gaps which the present study will fill. 2. 7Summary This section has reviewed literature covering the general literature review, review of literature related to attitudes, literature review related to SMASSE, some researched work on the impact of SMASSE in some pilot areas and critical review of related literature.
The next chapter presents the Research Design and Methodology that was used in the study. CHAPTER THREE 3. 0RESEARCH DESIGN AND METHODOLOGY 3. 1Introduction This chapter focuses on the research design and methodology that was used in this study. It specifically focuses on the research design, study area, study population, sample and sampling procedures, study variables, research instruments, validity and reliability of the research instruments, pilot study and the summary of the chapter. 3. 2Research Design This study adopted a descriptive survey design.
According to Gay (1981) a descriptive research is a process of collecting data in order to test hypotheses or to answer questions concerning the current status of the subjects in the study. Descriptive survey designs are used in preliminary and exploratory studies to allow researchers to gather information, summarize, present and interpret for the purpose of clarification (Orodho, 2002). Borg and Gall (1989:5) note that descriptive survey research is intended to produce statistical information about aspects of education that interest policy makers and educators.
The survey research was therefore useful because of the economy of taking a sample of the population to generalize results for the whole population. Descriptive survey design was employed because it guarantees breadth of observation and also provide for the accurate descriptive analysis of characteristics of a sample which can be used to make inferences about population (Popham, 1967, Kerlinger, 1973). Descriptive survey is a method of collecting information by interviewing or administering a questionnaire to a sample of individuals (Orodho, 2003).
It can be used when collecting information about people’s attitudes, opinions, habits or any of the variety of education or social issues (Orodho and Kombo, 2002). For example, teachers in schools can carry out a survey to find out student’s attitudes towards their teaching styles or discipline. 3. 3. The Study Area This study was carried out in Kosofe district of Lagos State. The district was selected for the study due to the fact that the performance at WAEC level is still low as compared to some of the districts in the Local government. (Education Insight May-June 2007, Issue 12).
3. 4The Study Population Kosofe district has 20 secondary schools with student population of 22,556. The total number is shared between the private and public school. All distributed in the Local government. (MOEST, 2007). A sample of 30% of the schools in the district was selected for the study. The study however covered all the divisions of Kosofe District. To calculate the number of sampled schools by category, the total number of schools in each category was multiplied by the ratio of schools sampled to the total number of secondary schools in the Districts.
Therefore from 4 schools to be sampled, 2 private schools and 2 public schools were selected. This was done to ensure that there is an adequate representation of the different categories of schools. 3. 5Sample and Sampling Procedures Sampling is the procedure a researcher uses to gather people, places or things to study. It is a process of selecting a number of individual or objects from a population such that the selected group contains elements representative of the characteristics found in the entire group (Orodho and Kombo, 2002).
A sample is finite part of a statistical population where properties are studied to gain information about the whole (Webster, 1985). The subjects of this study were drawn from Form four students. The choice of form four students was based on the assumption that they had a longer experience in learning mathematics soon after the SMASSE INSET was implemented in August 2004. The current Form four students joined form I in January 2005. It was also assumed that the form four students would be more mature in their opinions and attitudes towards mathematics.
Sample of 375 students were used comprising of Girls and Boys from private and public Schools. This figure was arrived at by using a generalized scientific guideline for sample size decision by Krejcie, and Morgan (1970). The two private schools were selected using simple random sampling. The 2 public schools were distributed throughout the entire district. This was done by placing the names of schools in a container and then picking the required number of schools at random. The purpose of these strata is to ensure that each category of school is represented in the study as the selection was made from these categories.
Stratified random sampling was used in selecting the subjects for the study. In stratified random sampling, the population is divided into two or more groups using a given criterion and then a given numbers of cases are randomly selected from each population sub group (Mugenda and Mugenda , 2003). To use stratified random sampling, one must first decide on the criteria under which the population and hence the sample will be stratified. The actual method of sampling from each sub group of the population can be proportionate random sampling.
The obvious advantage in stratified random sampling is that it ensures inclusion, in the sample of sub group, which otherwise would be omitted entirely by other sampling methods because of their small numbers in the population (Mugenda & Mugenda , 2003). The researcher also gathered information from mathematics teachers of the schools that participated in the study. Their information was hoped to strengthen the validity of the results. A total of 27 mathematics teachers were selected for the interview. 3. 6Study Variables The study variables were grouped into two categories, namely independent variables and the dependent variable.
The independent variable is the SMASSE INSET. The dependent variables are the students’ attitudes toward mathematics and performance in mathematics. 3. 7Research Instruments. In the study, the following instruments and techniques will be used. (a) student’s questionnaire (SQ) (b) Teacher’s questionnaire (TQ) The two instruments were used to supplement each other and to give a deeper and wider exploration into research perspective which gave the research more quality. 3. 7. 1Student’s Questionnaire (SQ) Tuckman (1987) says that a questionnaire is a way of getting data about persons by asking them rather than watch them behave.
A questionnaire is a research tool whereby the respondent gives the responses to the questions asked through the written mode. The use of questionnaire as a tool in research is quite efficient because through them the researcher is able to obtain personal views from the respondents. In this questionnaire closed ended questions were used. Closed ended questions were used with the aim of helping the researcher to obtain the personal views of the respondents (Appendix I). For closed ended questionnaire, five-point likert scale was used to measure attitudes and experiences associated with mathematics.
The higher the score the more positive the attitude towards mathematics, with the exception of questions which are negative and should show a lower score to indicate a more positive attitude. Responses from negatively worded items were reversed before inclusion in the computation of the average value. 3. 7. 2Teacher’s Questionnaire (TQ) Teachers questionnaire in this study sought information on the following items : teaching experiences, in-services courses attended apart from the SMASSE INSET, experiences gained after undergoing the SMASSE INSET and frequency of in-service courses among others (Appendix II). 3.
8Validity of the Research Instruments Validity is the extent to which the instrument measures what it appears to measure according to the researcher’s subjective assessment (Nachmias: 158). Validity deals with the adequacy of the instruments for example, the researcher needs to have adequate questions in the written task in order to collect the required data for analysis that can be used to draw conclusion. Frenekel (1993) suggest that the individual who is supposed to render an intelligent judgment about the adequacy of the instruments should be given the instruments before the actual research is carried out.
The instruments were amended according to the expert’s comments and recommendations before being administered. In this study, the researcher sought help from the supervisors and lecturers in the school of education to judge the validity of the questionnaire and the questions in the written task. 3. 9Reliability of the research instruments. Reliability is a measure of the degree to which a research instrument yields consistent results or data after repeated trials (Mugenda and Mugenda : 95).
According to Seliger and Shohamy (1989) reliability is the extent to which data collection procedures and research tools are consistent and accurate. In a research study, a reliability coefficient can be computed to indicate how reliable data are. A coefficient of 0. 80 or more implies that there is a higher degree of reliability of the data (Mugenda and Mugenda , 2003). Reliability of the data is in fact a very important aspect of a research study and should be addressed early in the research process and also reported in the final document.
In this study, the Test-retest method was employed to assess the reliability of the research instruments. The results were used to compute the correlation coefficient. The Pearson’s product moment formula for the test- retest was employed in order to establish the extent to which the contents of the questionnaire elicit the same responses every time the instruments are used. 3. 10Piloting of the Research Instruments Piloting is trying out of research instruments on the respondents who will not be used in the main study.
Groll (1986:50) notes that a pilot study is necessary because” a researcher embarking on classroom research for the first time will find it valuable to spend some time in the classroom using one or more established systems and looking at the kind of issues which will arise in turning his/ her own research questions into a set of criteria and definition for use in the classroom. ” It is important for a pilot study to be carried out before any research is done as stated by Peter (1994:88). He states” even the most carefully constructed instrument cannot guarantee to obtain a hundred percent reliable data”.
Therefore it was necessary to pretest the instruments of the research on a small sample of respondents in a preparatory exercise to find out if there is any weakness so that it can be corrected. Pilot study was meant to assess reliability by checking for consistency. This helped in ensuring that the data which was expected to be produced was in line with the study objectives. Research instruments may be pre-tested on a small sample of at least ten respondents (Mulusa 1990:172). In this study, two schools that did not take part in the main study were selected for piloting.
A sample of 20 students and 4 mathematics teachers were used for piloting. The test- retest method was employed within an interval of two weeks . The responses to the items in the questionnaire were assigned numerical values. The correlation coefficients between the scores of the responses from the questionnaire administered on the two different occasions were used to calculate the reliability coefficient using the Pearson product moment correlation coefficient formula. The reliability coefficient for the students’ questionnaire was 0. 73 and the teachers’ questionnaire was 0. 68.
According to Kerlinger (1973) and Koul (1984), a positive correlation coefficient, r of 0. 5 and above is a strong one and hence the research instruments were deemed reliable. 3. 11Data Collection and Analysis The data collected was analyzed using both descriptive and inferential statistical techniques. Frequencies, percentages, means and standard deviations were employed for the descriptive statistics while the one way analysis of variances (ANOVA) and Chi-square (? 2) were employed for inferential statistics. The significance was tested by computing the P- value at a significance or alpha level of 0.
05. I visit each school that was selected from the population, and then consult the principals and explained to them the purpose of the visit. The principals called their Mathematics Teacher to the office. I explained to them what the study was all about and how they were going to participate. The respondents were informed that the information gathered was to be used as project and also to improve the teaching and learning of mathematics and that whatever information they gave was to be kept confidential. I encountered some challenges in the process of data collection.
Some mathematics teachers were not willing to fill the questionnaire. On some occasions, the WAEC mathematics results for the years 2004- 2008 were not available in schools. Such challenges inconvenience me and hindered the smooth flow of the study. There was no problem with student’s questionnaire. Out of 375 questionnaires delivered for students, 371 questionnaires were returned. That represented 98. 9% response rate, which was very good. For the teacher’s questionnaires, 27 questionnaires were delivered but only 20 were returned. That represented 74.
1 % response rate, which was fairly good. 3 . 12Summary This chapter has presented the procedures that were followed in carrying out the research. It has outlined the research design, the study area, the study population, sample and sampling procedures, the study variables, research instruments, validity and reliability of the research instruments, piloting of the research instruments, data collection and analysis. The next chapter presents data analysis, presentation and discussion of results. CHAPTER FOUR 4. 0DATA ANALYSIS, PRESENTATION AND DISCUSSION OF RESULTS
4. 1Introduction Data analysis refers to examining what has been collected in a survey or experiment and making deductions and inferences. It involves uncovering underlying structures; extracting important variables, detecting any anomalies and testing any underlying assumptions. It involves scrutinizing the acquired information and making inference (Kombo and Tromp, 2006). The study investigated students’ attitudes and performance in mathematics. Data collected was analyzed to get the overall picture of students’ attitude towards mathematics.
Specifically data was analyzed to determine whether: 1) SMASSE INSET has changed the students’ attitudes towards mathematics. 2) SMASSE INSET has improved the performance in mathematics 3) SMASSE INSET has improved the teachers teaching approach and methodology. As stated in chapter three, the main research instruments were students’ questionnaire, teachers’ questionnaire. Three research hypotheses were tested. The independent variable, SMASSE INSET was considered against students’ attitudes, performance in mathematics and teacher’s teaching approaches and methodology.
Both descriptive and inferential statistics were used to analyze the data. For descriptive statistics, frequencies, means, standard deviation and percentages were used while for the inferential statistics, the analysis for variance (ANOVA) and chi- square (? 2 )were used to test the hypotheses at alpha, ? = 0. 05 level of significance and appropriate degrees of freedom. 4. 2SMASSE INSET and Student’s attitude towards mathematics. The data collected in students attitude was analyzed so as to give a general picture about the students’ attitude towards mathematics after the implementation of SMASSE INSET.
Before the implementation of SMASSE INSET, students used to have negative attitude towards mathematics (Baseline findings, 1998). There were 15 items that were testing students’ attitudes towards mathematics. The summary of the results are as shown in table 4. 1 (p. 63). The grand mean of all the items is 4. 1003. This is a high positive value on the Likert scale. The grand mean therefore shows that the students’ attitude towards mathematics has greatly improved with the introduction of SMASSE INSET. This can be attributed to the practical teaching of mathematics as opposed to the traditional methods of lecture.
Students now enjoy the learning of mathematics because of its practical activities which are involved. As much as the student’s attitude has greatly improved with the introduction of SMASSE INSET there are some items which students still have some negative attitude. Such items are to do with problem- solving skills and confidence in mathematics. Quite a number of the students expressed lack of good background in mathematics when dealing with new mathematical situations. Table 4. 1: Students’ overall analysis on attitudes towards mathematics | Statement | N| SUM| MEAN|
1| Mathematics is very interesting to me and I enjoy my mathematics course| 371| 1630. 00| 4. 3935| 2| My mind goes blank and I am unable to think clearly when doing mathematics| 371| 1577. 00| 4. 2507| 3| If I am confronted with a new mathematics situation, I can cope with it because I have a good background in mathematics| 371| 1418. 00| 3. 8221| 4| I can draw upon a wide variety of mathematical techniques to solve a particular problem,| 371| 1489. 00| 4. 0135| 5| I do not feel that is have a good working knowledge of the mathematics course I have taken so far| 371| 1493.
00| 4. 0243| 6| I learn mathematics by understanding the underlying logical principles, not by memorizing the rules| 371| 1473. 00| 3. 9704| 7| If I cannot solve a mathematics problem, at least I know a general method of attacking it| 371| 1290. 00| 3. 4771| 8| Mathematics problems are a challenge, solving problems provides satisfactions similar to those of winning a battle| 371| 1558. 00| 4. 1995| 9| I have more confidence in my ability to deal with mathematics than in my ability to deal with other academic subjects| 371| 1228. 00| 3.
3100| 10| Mathematics classes provide the opportunity to learn values that are useful in other parts of daily living| 371| 1626. 00| 4. 3827| 11| Mathematics is a very difficult subject to study in school| 371| 1671. 00| 4. 5040| 12| People who have studied mathematics get good jobs| 371| 1612. 00| 4. 3450| 13| Mathematics require thinking, not just memorizing terminologies formulae and concepts| 371| 1657. 00| 4. 4663| 14| Mathematics is one of easiest subject| 371| 1419. 00| 3. 8248| 15| Mathematics develop critical thinking in solving problems | 371| 1677.
00| 4. 5202| | | 371| 22,818| 4. 1003| X = 4. 100NB: X= grand mean (mean of means) A number of them also expressed lack of confidence in dealing with mathematics as compared to other academic subjects. Table 4. 2 (p. 66 ) shows the comparison of students’ attitude towards mathematics by gender. The results in the table show that generally, there is a positive attitude which has been developed by students towards mathematics. However the areas of confidence and problem- solving show some negative attitudes.
In item number 3, the mean of the males is 3. 726 whereas that of females is 3. 923. This seems that the female students can cope with a new mathematical situation more than their male counterparts. In item number 7, the mean of the male students is 3. 332 whereas that of the females is 3. 630. This shows that females had a higher mean than males. This seems that females at least have an idea of attacking a mathematics problem more than boys even if they cannot solve it. Item number 9 gave the mean of males to be 3. 321 and that of females is 3. 300.
This seems that males have more confidence in their ability to deal with mathematics than in their ability to deal with other academic subjects as compared to females. Item number 14 gave the mean of males as 3. 721 and that of females as 3. 934. This shows that females had a higher mean than males. Females view mathematics more as one of the easiest subjects as compared to the males. Table 4. 3 (p. 67 ) shows the summary of the means of males and females for all the 15 items. The grand mean for the males is 4. 08 whereas that of females is 4. 119. This is higher than that of males.
This seems to suggest that the female students have developed more positive attitudes towards mathematics as compared to the male students. The results of table 4. 3 were subjected to the t- test to determine whether the differences in the means were statically significant. The results are shown in table 4. 4. (p. 68). The t- test gave a p- value of 0. 627. Since the p- value (o. 6270) > 0. 05, it shows that the differences in means of males and females are not statistically significant. This suggests that SMASSE INSET has improved the attitudes of both males and females.
The slight differences shown are not significant. Table 4. 2: Analysis of students’ attitudes towards mathematics by gender Item number| Statement | Gender| N| Meanx| 1. | Mathematics is very interesting to me and I enjoy my mathematics course| MaleFemale | 190181| 4. 3424. 448| 2. | My mind goes blank and I am unable to think clearly when doing mathematics| MaleFemale| 190181| 4. 3474. 149| 3. | If I am confronted with a new mathematics situation, I can cope with it because I have a good background in mathematics| MaleFemale| 190181| 3. 7263.
923| 4. | I can draw upon a wide variety of mathematical techniques to solve a particular problem,| MaleFemale| 190181| 4. 0114. 017| 5. | I do not feel that is have a good working knowledge of the mathematics course I have taken so far| MaleFemale| 190181| 4. 1003. 945| 6. | I learn mathematics by understanding the underlying logical principles, not by memorizing the rules| MaleFemale| 190181| 3. 8844. 061| 7. | If I cannot solve a mathematics problem, at least I know a general method of attacking it| MaleFemale| 190181| 3. 3323. 639| 8.
| Mathematics problems are a challenge, solving problems provides satisfactions similar to those of winning a battle| MaleFemale| 190181| 4. 1684. 232| 9. | I have more confidence in my ability to deal with mathematics than in my ability to deal with other academic subjects| MaleFemale| 190181| 3. 3213. 300| 10. | Mathematics classes provide the opportunity to learn values that are useful in other parts of daily living| MaleFemale| 190181| 4. 4004. 365| 11. | Mathematics is a very difficult subject to study in school| MaleFemale| 190181| 4. 4844.
492| 12. | People who have studied mathematics get good jobs| MaleFemale| 190181| 4. 2164. 481| 13. | Mathematics require thinking, not just memorizing terminologies formulae and concepts| MaleFemale| 190181| 4. 5424. 387| 14. | Mathematics is one of easiest subject| MaleFemale| 190181| 3. 7213. 934| 15. | Mathematics develop critical thinking in solving problems | MaleFemale| 190181| 4. 6054. 431| Table 4. 3: Further analysis of students’ attitudes toward mathematics by gender. | Statement | N| Mean of Males( x1)| Mean of females( x2 )| 1.
| Mathematics is very interesting to me and I enjoy my mathematics course| 371| 4. 342| 4. 448| 2. | My mind goes blank and I am unable to think clearly when doing mathematics| 371| 4. 347| 4. 149| 3. | If I am confronted with a new mathematics situation, I can cope with it because I have a good background in mathematics| 371| 3. 726| 3. 923| 4. | I can draw upon a wide variety of mathematical techniques to solve a particular problem,| 371| 4. 011| 4. 017| 5. | I do not feel that is have a good working knowledge of the mathematics course I have taken so far| 371| 4.
100| 3. 945| 6. | I learn mathematics by understanding the underlying logical principles, not by memorizing the rules| 371| 3. 884| 4. 061| 7. | If I cannot solve a mathematics problem, at least I know a general method of attacking it| 371| 3. 332| 3. 630| 8. | Mathematics problems are a challenge, solving problems provides satisfactions similar to those of winning a battle| 371| 4. 168| 4. 232| 9. | I have more confidence in my ability to deal with mathematics than in my ability to deal with other academic subjects| 371| 3. 321| 3. 300| 10.
| Mathematics classes provide the opportunity to learn values that are useful in other parts of daily living| 371| 4. 400| 4. 365| 11. | Mathematics is a very difficult subject to study in school| 371| 4. 484| 4. 492| 12. | People who have studied mathematics get good jobs| 371| 4. 216| 4. 481| 13. | Mathematics require thinking, not just memorizing terminologies formulae and concepts| 371| 4. 542| 4. 387| 14. | Mathematics is one of easiest subject| 371| 3. 721| 3. 934| 15. | Mathematics develop critical thinking in solving problems | 371| 4. 605| 4.
431| Key: X1 = grand mean of males X2 = grand mean of females | | X1= 4. 08| X2= 4. 119| Table 4. 4: Independent samples t- test for students’ attitudes towards mathematics by gender | t-test for Equality of means| | T| df| Sig. (2-tailed| Equal variancesAssumedEqual variancesNot assumed| -0. 491-0. 491| 2827. 888| 0. 6270. 627| Table 4. 5 (p. 70) shows the analysis of students’ attitude towards mathematics as per school category. Generally, the attitude towards mathematics has improved in all the school categories. In item number 3, the mean of boys’ school is 4.
073, the mean of girls’ schools in 3. 927 and that of mixed school is 3. 363. This shows that students in single sex schools rated the item higher than those in co- educational schools. It suggests that students in co-educational schools are disadvantaged when it comes to having a good background in mathematics. A good number of them seem not to cope with a new mathematical situation. Item number 7 gave the mean of boys’ schools as 3. 500, girls’ schools as 3. 700 and that of mixed schools as 3. 324. Again, the mean of the single sex schools is higher than that of co-educational schools.
Students in single sex schools are better equipped in having at least a general idea of attacking a mathematics problem than those in co-educational schools. In item number 9, the mean of boys’ schools is 3. 134, that of girls’ schools is 3. 445 and that of mixed schools is 3. 307. The means for this item is the lowest for all the 15 items. This suggests that generally, students have not developed more confidence in their ability to deal with mathematics than in their ability to deal with other academic subjects. In item number 14, the mean for boys’ schools is 3. 585, that of girls’ schools is 4.
018 and that of mixed schools is 3. 816. This shows that girls’ schools had the highest rating of mathematics as one of the easiest subjects as compared to boys’ schools or co-educational schools. Table 4. 6 (p. 71) gives a summary for the means of 15 items as per the school category. The grand means for boys’ schools is 4. 128, that of girls’ schools is 4. 190 and that of mixed schools is 4. 011. This shows that girls’ schools had the highest mean. This implies that SMASSE INSET has resulted more in an improved attitude towards mathematics in girls’ school as compared to either boys’ schools or co-educational schools.
The results of Table 4. 6 were subjected to one way ANOVA to determine whether there is any significant difference among the three groups of the school category. The results are as shown in Table 4. 7 (p. 72). One way ANOVA gave a p- value of 0. 464. Since the p- value (0. 464) > 0. 05, it shows that the differences in means in the three categories of schools are not statistically significant. This suggests that SMASSE INSET has improved the attitudes of students towards mathematics in all the three categories of schools. Table 4.
5: An analysis of students’ attitude towards mathematics by school category Item number| Statement | School category| N| Meanx| 1| Mathematics is very interesting to me and I enjoy my mathematics course| Boy’s SchoolGirls SchoolMixed school | 82110179| 4. 2054. 5004. 369| 2| My mind goes blank and I am unable to think clearly when doing mathematics| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 3544. 1644. 257| 3| If I am confronted with a new mathematics situation, I can cope with it because I have a good background in mathematics| Boy’s SchoolGirls SchoolMixed school| 82110179| 4.
0733. 9273. 363| 4| I can draw upon a wide variety of mathematical techniques to solve a particular problem,| Boy’s SchoolGirls SchoolMixed school| 82110179| 3. 9393. 9824. 067| 5| I do not feel that is have a good working knowledge of the mathematics course I have taken so far| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 1834. 0273. 950| 6| I learn mathematics by understanding the underlying logical principles, not by memorizing the rules| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 0374. 1643.
821| 7| If I cannot solve a mathematics problem, at least I know a general method of attacking it| Boy’s SchoolGirls SchoolMixed school| 82110179| 3. 5003. 7093. 324| 8| Mathematics problems are a challenge, solving problems provides satisfactions similar to those of winning a battle| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 2444. 1644. 201| 9| I have more confidence in my ability to deal with mathematics than in my ability to deal with other academic subjects| Boy’s SchoolGirls SchoolMixed school| 82110179| 3. 1343. 4453.
307| 10| Mathematics classes provide the opportunity to learn values that are useful in other parts of daily living| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 3784. 5004. 313| 11| Mathematics is a very difficult subject to study in school| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 5614. 6004. 385| 12| People who have studied mathematics get good jobs| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 3544. 5554. 212| 13| Mathematics require thinking, not just memorizing terminologies formulae and concepts| Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 6464. 5644.
324| 14| Mathematics is one of easiest subject| Boy’s SchoolGirls SchoolMixed school| 82110179| 3. 5854. 0183. 816| 15| Mathematics develop critical thinking in solving problems | Boy’s SchoolGirls SchoolMixed school| 82110179| 4. 6344. 5364. 458| Table 4. 6: Further analysis of students’ attitudes towards mathematics by school category | Statement | Mean of Boys school ( X1)| Means of girls school (X2)| Means of mixed school ( X3)| 1| Mathematics is very interesting to me and I enjoy my mathematics course| 4. 205| 4. 500| 4. 369| 2| My mind goes blank and I am unable to think clearly when doing mathematics| 4. 354| 4.
164| 4. 257| 3| If I am confronted with a new mathematics situation, I can cope with it because I have a good background in mathematics| 4. 073| 3. 927| 3. 363| 4| I can draw upon a wide variety of mathematical techniques to solve a particular problem,| 3. 939| 3. 982| 4. 067| 5| I do not feel that is have a good working knowledge of the mathematics course I have taken so far| 4. 183| 4. 027| 3. 950| 6| I learn mathematics by understanding the underlying logical principles, not by memorizing the rules| 4. 037| 4. 164| 3. 821| 7| If I cannot solve a mathematics problem, at least I know a general method of attacking it| 3.
500| 3. 709| 3. 324| 8| Mathematics problems are a challenge, solving problems provides satisfactions similar to those of winning a battle| 4. 244| 4. 164| 4. 201| 9| I have more confidence in my ability to deal with mathematics than in my ability to deal with other academic subjects| 3. 134| 3. 445| 3. 307| 10| Mathematics classes provide the opportunity to learn values that are useful in other parts of daily living| 4. 378| 4. 500| 4. 313| 11| Mathematics is a very difficult subject to study in school| 4. 561| 4. 600| 4. 385| 12| People who have studied mathematics get good jobs| 4. 354| 4. 555| 4.
212| 13| Mathematics require thinking, not just memorizing terminologies formulae and concepts| 4. 646| 4. 564| 4. 324| 14| Mathematics is one of easiest subject| 3. 585| 4. 018| 3. 816| 15| Mathematics develop critical thinking in solving problems | 4. 634| 4. 536| 4. 458| KEY:X1=Grand mean of boys schoolsX2= Grand mean of girls schoolsX3 = Grand mean of Mixed schools| X1=4. 128| X2=4. 190| X3=4. 011| Table 4. 7: One way ANOVA of student’s attitude towards mathematics by school category | Sum of squares| Df| Mean squares| F| Sig. | Between GroupsWithin GroupsTotal| . 2456. 5956. 841| 24244| . 123. 157| . 781| . 464|