Title page                   –                                   –                                   –                       i

Certification              –                                   –                                   –                       ii

Approval page          –                                   –                                   –                       iii

Dedication                 –                                   –                                   –                       iv

Acknowledgements –                                   –                                   –                       v

Table of contents     –                                   –                                   –                       vii

List of tables                         –                                   –                                   –                       x

List of appendices    –                                   –                                   –                       xi

Abstract                     –                                   –                                   –                       xii


Background of the study                             –                                   –                       1

Statement of problem                                  –                                   –                       11

Purpose of the study                                    –                                   –                       13

Significance of the study                            –                                   –                       13

Research questions                                      –                                   –                       14

Hypotheses                                                   –                                   –                       15

Scope of the study                                       –                                   –                       15


Conceptual Framework                            –                                   –                       16

Performance Status of Students in Mathematics and Geometry-                     17

Philosophical foundation of the Pre-NCE programme               –                       19

Models of teaching and learning               –                                   –                       21

The advance organizer model                    –                                   –                       24

The concept attainment model                   –                                   –                       27

Retention of knowledge                              –                                   –                       31

Schematic diagram showing the relationship between key variables of

the study                    –                                   –                                   –                       32

Theoretical Framework

Bruner’s learning theory                             –                                   –                       32

Ausubel’s learning theory                          –                                   –                       33

Constructivism         –                                   –                                   –                       36

Review of Related Empirical Studies

Studies on models of teaching                   –                                   –                       39

Studies on AOM and CAM                         –                                   –                       39

Studies on performance of students in mathematics and geometry                43

Studies on retention                                                 –                                   –                       44

Summary of Literature Review              –                                   –                       47


Research design                                           –                                   –                       51

Area of the study                                          –                                   –                       52

Population of the study                               –                                   –                       52

Sample and sampling techniques             –                                   –                       53

Instrument for data collection                    –                                   –                       53

Validation of the instrument                      –                                   –                       53

Reliability of the instrument                      –                                   –                       55

Experimental procedure                             –                                   –                       55

Method of data analysis                              –                                   –                       58

CHAPTER FOUR: RESULTS                                                                              59

Summary of findings                                   –                                   –                       72




Discussion of results                       –                                               –                       74

Conclusion                                        –                                               –                       78

Implications                                      –                                               –                       79

Recommendations                           –                                               –                       80

Limitations of the study                  –                                               –                       81

Suggestions for further studies      –                                               –                       82

References                                        –                                               –                       83

Appendixes                                       –                                               –                       91


Table 1:    Mean achievement scores of students taught with CAM, AOM

and Conventional method                    –                                   –           59


Table 2:    Mean achievement scores of male and female students taught

with CAM and AOM                               –                                   –           60

Table 3:    Mean retention scores of students taught with CAM,

AOM and Conventional method.         –                                   –           61


Table 4:    Mean retention scores of male and female students taught with

CAM and AOM                                      –                                   –           62


Table 5:    Analysis of covariance (ANCOVA) for achievement difference

between the groups                                –                                   –           63


Table 6:    Scheffe Post Hoc analysis for the groups                               –           64


Table 7:    Analysis of covariance (ANCOVA) for achievement difference

between male and female in their groups                               –           65


Table 8:    Scheffe Post Hoc analysis of mean difference between male

and female in the groups                                                           –           66


Table 9:    Analysis of covariance (ANCOVA) for the interaction effect

between gender and instructional models                              –           67


Table 10:       Analysis of covariance (ANCOVA) for the difference in the

retention test means scores of the groups                              –           68


Table 11:       Scheffe Post Hoc analysis of difference in the mean retention

scores for the groups                 –                                               –           69


Table 12:       Analysis of covariance (ANCOVA) for the difference in the

mean retention scores for male and female students in the

groups                                          –                                               –           70


Table 13:       Scheffe Post Hoc analysis of difference in the mean retention

scores between male and female in  the groups.                   –           71


Table 14: Analysis of covariance for the interaction effect between

gender and instructional models in the retention of students         72


Appendix A: AOM Lesson plan                –                       –                       –           91

Appendix B: CAM Lesson plan                 –                       –                       –           121

Appendix C: Pre-PNGAT                            –                       –                       –           156

Appendix D: Post-PNGAT              –                       –                       –           162

Appendix E: Table of specification for the instrument             –                       –           168

Appendix F: Calculation of reliability of the instrument –                    –           169

Appendix G: Calculation of the test re-test stability measure

of the instrument                  –                       –                       –           171

Appendix H: Public Colleges of Education in Benue

and Kogi States                                             –                       –           173

Appendix I: Recent performance statistics of students

in SSCE                                                          –                       –           174

Appendix J: Performance profile of the Pre-NCE students

in geometry in Kogi State College of Education,

(KSCOE), Ankpa between 2005 and 2010                       –           175

Appendix K: Calculation of item analysis indices of the instrument  –           176

Appendix L: Training guide on the advance organizer and

concept attainment models of instruction                                    –           178

appendix M: Evidence of validation of instrument                                –           185


This study investigated the effectiveness of two instructional models – the Concept Attainment Model (CAM) and Advance Organiser Model (AOM) on the achievement and retention of Pre-NCE students in geometry. Four research questions and six hypotheses guided the study. The design of the study was pre-test pos-test equivalent control group design or quasi experimental design. The study was carried out in Kogi and Benue States in the present North Central Zone of Nigeria. The population of the study was 1100 Pre-NCE students in both the State and Federal-owned colleges of education in the two states. Three out of the four public colleges of education in the two states were randomly selected for the study. The total number of students in their intact classes who offered Pre-NCE geometry in these colleges was 830. This formed the sample for the study. 402 (48.4%) of the students were male and 428 (51.6%) were female. The instrument used for data collection was Pre-NCE Geometry Achievement Test (PNGAT). PNGAT had two versions Pre-PNGAT and Post- PNGAT which were the same except for the swapping of some of the questions. PNGAT was subjected to both face and content validation and item analysis. Using Kuder Richardson (K-R) 20, the internal consistency was found to be 0.74. Using Pearson r, the test retest stability measure was found to be 0.96. Pre- PNGAT was administered on the groups before treatment started while Post- PNGAT was administered at the end of the 5 week treatment period. After 2 weeks of administration of Post-PNGAT, it was again administered on the groups as a retention test. Scores from Pre-PNGAT, Post- PNGAT and the retention test were analysed using means and analysis of covariance (ANCOVA). Some of the major findings from the analysis were (i) AOM and CAM were more effective than the conventional method for achievement (ii) CAM was more effective than AOM for achievement; (iii) CAM and AOM were more effective than conventional method for retention (iv) CAM was more effective than AOM for retention. Based on the findings, the implications were highlighted and recommendations were made towards better achievement and retention of Pre-NCE students in geometry.



Background to the Study

Mathematics is often defined or described from the point of view of its utility, especially by those who only make use of the subject. However, a simple definition which seems to capture the overall essence of the subject of mathematics is that it is the study of quantity, structure, space and change (Agwagah, 2008). Mathematics is one of the core subjects in primary and secondary school levels of education in Nigeria. Performance in mathematics at the Senior Secondary School Certificate Examination (SSCE) is used to determine those who are qualified to enter the tertiary levels of education especially those taking courses in the sciences and science related disciplines like engineering, survey, medicine and so on.

The Pre-NCE programme is a remedial outfit mounted by National Commission for Colleges of Education, (NCCE) and run by some Colleges of Education. It is designed to redress the deficiencies of candidates who either cannot make the required number of credit passes (including Mathematics and English) at SSCE for direct entry into the NCE programme or for candidates who have the required number of passes at SSCE but cannot pass the screening exercise for entry into is aimed at addressing the challenges of weak students in colleges of education (CE programme is widely spread across colleges of education in the country. During the one year programme, students are exposed to prescribed number of courses that can remedy their deficiencies for entry into the NCE programme. Furthermore, following the recently introduced policy by JAMB that all Pre- NCE students must write the Unified Entrance Examination, the Pre- NCE programme is now saddled with additional responsibility of preparing the students in the various subject areas.Many institutions of higher learning have introduced post-Joint Admission and Matriculation Board (Post-JAMB) screening examination into their admission policy. In many of such screening exercises, mathematics features among the subject areas where candidates are tested. In some Colleges of Education running Preliminary Nigerian Certificate in Education (Pre- NCE) programme, admission into the programme is through screening examination in which mathematics forms part of the examination. The NCE certificate is awarded by Colleges of Education on successful completion of a 3-year programme. It is the minimum teaching qualification in Nigeria for primary and junior secondary school levels of education (Federal Republic of Nigeria, 2004).

It is therefore clear that mathematics is given huge consideration and plays prominent role at all levels of education system. One may ask: why are we so concerned about mathematics? Of all the disciplines in school curricula, why are we so concerned about the failure and/or success of our children in mathematics? The answer is premised on the fact that it is one of the subjects that pervades all endeavours of humanity – sciences, arts, engineering, medicine, astronomy, etc. It is in consideration of the versatility of mathematics that James (2005) asserted that it is not only an academic, a scientist, an engineer that needs mathematics but that even a shop keeper, a housewife, a sportsman, etc. needs it. Thomaskutty and George (2007) agreed with James when the authors asserted that mathematics should not be seen as a classroom discipline only. From the point of view of science and technology, mathematics takes a unique position. In fact, the tremendous achievement of science and technology towards industrialized economy and human survival seems to be buoyed up by many far reaching mathematical contributions.


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