University of Education, Winneba http://ir.uew.edu.gh UNIVERSITY OF EDUCATION, WINNEBA EFFECTS OF THE CONSTRUCTIVIST TEACHING APPROACH ON SENIOR HIGH SCHOOL STUDENTS’ PERFORMANCE IN ALGEBRA IN THE GOMOA EAST DISTRICT OF GHANA SAMUEL ADDO OSEI MASTER OF PHILOSOPHY 2019 University of Education, Winneba http://ir.uew.edu.gh UNIVERSITY OF EDUCATION, WINNEBA EFFECTS OF THE CONSTRUCTIVIST TEACHING APPROACH ON SENIOR HIGH SCHOOL STUDENTS’ PERFORMANCE IN ALGEBRA IN THE GOMOA EAST DISTRICT OF GHANA SAMUEL ADDO OSEI 8160110016 A thesis in the Department of Mathematics Education, Faculty of Science Education, submitted to the School of Graduate Studies, in partial fulfilment of the requirements for the award of the degree of Master of Philosophy (Mathematics Education) in the University of Education, Winneba SEPTEMBER, 2019 University of Education, Winneba http://ir.uew.edu.gh DECLARATION STUDENT’S DECLARATION I, SAMUEL ADDO OSEI, hereby declare that this thesis, with the exception of quotations and references contained in the published works which have all been identified and duly acknowledged, is entirely my own original work, and it has not been submitted, either in part or whole, for another degree elsewhere. SIGNATURE: ………………………………………… DATE: ………….…….……………………………….. SUPERVISOR’S DECLARATION I hereby declare that the preparation and presentation of this work was supervised in accordance with the guidelines for supervision of thesis as laid down by the University of Education, Winneba. NAME OF SUPERVISOR: DR. NYALA JOSEPH ISSAH SIGNATURE: …………………………………………… DATE: …………………………………………………… iii University of Education, Winneba http://ir.uew.edu.gh DEDICATION To the Almighty God for His faithfulness in fulfilling His promise to me. To my dear wife, Dorcas Osei and my children – Kennedy Asare Osei, Franklin Gyamerah Osei and Christiana Nyarko Osei – for their sacrifices in helping me come this far. I am most grateful. iv University of Education, Winneba http://ir.uew.edu.gh ACKNOWLEDGEMENT First of all, my sincere thanks go to the almighty God whose love, protection, mercies and guidance has brought me this far. May your Holy name be praised forever and ever. The immeasurable useful suggestions, corrections and excellent supervisory role played by Dr. Nyala Joseph Issah are appreciated. May God richly bless you. In the same vein, I express my appreciation and thanks to the Head of Department and lecturers of the Department of Mathematics Education, Winneba, for their tireless dedication to duty. I cannot forget to make mention of my parents, Mr. and Mrs. Osei and my siblings Mr. Richard Osei, Mrs. Kate Osei, Miss Haggah Osei, Madam Ama Serwaa and Madam Ama Konadu who in diverse ways contributed immensely to my educational pursuit. May their efforts, prayers and contributions be richly rewarded. My special thanks also go to the Management of the participating schools for granting me permission to carry out the study in their schools. My proud gratitude also goes to the mathematics instructors and the entire students in the participating schools for their support and participation during the fieldwork and for accepting to be part of the study. Finally, to my dear wife, Mrs. Dorcas Osei who has been a pillar and tower behind me throughout this thesis and my entire education. When all hope was lost, she encouraged me to carry on and never give up. Thank you dear. Once again, I say thanks to all my loved ones, God richly bless you all. v University of Education, Winneba http://ir.uew.edu.gh ,, vi University of Education, Winneba http://ir.uew.edu.gh TABLE OF CONTENTS Title Page DECLARATION iii DEDICATION iv ACKNOWLEDGEMENT v LIST OF TABLES xii LIST OF FIGURES xiii ABSTRACT xiv CHAPTER ONE: INTRODUCTION 1 1.0 Overview 1 1.1 Background of the Study 1 1.2 Statement of the Problem 5 1.3 Purpose of the Study 8 1.4 Objectives of the Study 8 1.5 Research Questions 8 1.5.1 Research Hypothesis 9 1.6 Significance of the Study 9 1.7 Limitations of the Study 10 1.8 Organization of the Study 10 1.9 Operational Definition of Terms 11 CHAPTER TWO: REVIEW OF RELATED LITERATURE 13 2.0 Overview 13 2.1 Theoretical Framework: Constructivist Theory 14 2.2 Teaching Approaches 15 vii University of Education, Winneba http://ir.uew.edu.gh 2.2.1 Traditional Teaching 16 2.2.1.1 Advantages of the Traditional Teaching 19 2.2.1.2 Disadvantages of the Traditional Teaching 21 2.2.2 Constructivist Teaching or Pedagogy 23 2.2.2.1 The Epistemological Base of Constructivist Teaching 24 2.2.2.2 Implications of Constructivism for Learning and Teaching 25 2.2.2.3 Studies on Constructivist Teaching Approach 28 2.2.3 Constructivist and Traditional Ideas about Teaching and Learning 31 2.3 Teaching Approaches used by Teachers. 33 2.4 Review of Research works on Students’ Perceptions about Constructivist Teaching 35 2.5 Conceptual Understanding of Algebra 36 2.5.1 The Concept of a Variable. 36 2.5.2 Algebraic Terms and Expressions 38 2.5.3 Solving Algebraic Expressions and Equations 40 2.5.4 The Concept of Equation / Equality 42 2.5.5 Formulating Equations from Context Problems 43 2.5.6 Modeling Equations from Verbal Representations 45 2.6 Students' Difficulties in Solving Algebraic Problems 46 2.7 Summary of the Literature Reviewed 49 CHAPTER THREE: RESEARCH METHODOLOGY 50 3.0 Overview 50 3.1 Research Design 51 3.2 Population 54 3.3 Sample and Sampling Technique 56 viii University of Education, Winneba http://ir.uew.edu.gh 3.4 Research Instruments 57 3.4.1.1 Test (Algebra Concept Achievement Test (ACAT) 57 3.4.1.2 Classroom and Lesson Observation Checklist 58 3.4.1.3 Questionnaires 59 3.4.1.4 Interview Guide 60 3.5 The Pilot Study 61 3.5.1 How the Pilot Study was conducted 61 3.6 Content Validation of Instruments 63 3.6.1 Achievement Test 63 3.6.2 Classroom and Lesson Observation Checklist 63 3.6.3 Questionnaires and Structured Interview Questions 64 3.7 Reliability of the Instrument 64 3.7.1 Achievement Test 64 3.7.2 The Lesson Observation Schedule 65 3.7.3 Questionnaire and Interview Guide 65 3.8 Treatment Procedure 65 3.8.1 Constructivist Teaching Approach as the Treatment Procedure 65 3.9 Data Analysis Procedures 69 3.9.1 Quantitative Data Analysis 69 3.9.2 Qualitative Data Analysis 70 3.9.3 Data Analysis Procedures for Research Questions 70 3.9.3.1 Research Question One 71 3.9.3.2 Research Question Two 71 3.9.3.3 Research Question Three 72 3.9.3.4 Research Question Four 72 3.10 Assumptions of the Study 73 ix University of Education, Winneba http://ir.uew.edu.gh 3.11 Logistical and Ethical Considerations 74 3.12 Chapter Summary 75 CHAPTER FOUR: DATA ANALYSIS AND DISCUSSIONS OF RESULTS 76 4.0 Overview 76 4.1 Demographic Characteristics of Participants 77 4.1.1 Background Information of Participating Teachers 77 4.1.1.1 Gender of Participating Teachers 77 4.1.1.2 Teaching Experience of Participating Teachers 78 4.1.1.3 Teaching Qualification of Participating Teachers 78 4.1.2 Background Information of Participating Students 79 4.2 Data Analysis by Research Questions 80 4.3 Summary of Statistical Findings 103 4.3.1 Participation of the Study 104 4.3.2 Descriptive Statistics 104 4.3.3 Inferential Statistics 104 4.4 Chapter Summary 105 CHAPTER FIVE: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 107 5.1 Overview 107 5.2 Revisiting the Purpose, the Objectives and Research Questions of the Study 107 5.3 Summary of Key Findings 109 5.4 Achieving the Purpose of the Study 110 5.5 Linking the Study Results to the Theoretical Framework of the Study 111 5.6 Conclusions 112 5.7 General Recommendations 114 5.8 Suggestions for Future Research 116 x University of Education, Winneba http://ir.uew.edu.gh REFERENCES 118 APPENDIX 1 Lesson Observation Schedule 133 APPENDIX 2 Teachers’ Questionnaire 134 APPENDIX 3 Interview Questions for Teachers and Students 135 APPENDIX 4 Test Instrument - Pre-test Questions 136 APPENDIX 5 Marking Scheme for Pretest Questions 138 APPENDIX 6 Test Instrument - Post-test Questions 140 APPENDIX 7 Marking Scheme for Post-test Questions 142 APPENDIX 8 Letter of Introduction from the Mathematics Department 144 APPENDIX 9 Letter of Consent to the District Director of Education 145 APPENDIX 10 Hypothesis Testing Summary by Mann-Whitney's Test 146 APPENDIX 11 Normal Q-Q Plots 147 APPENDIX 12 Students' Questionnaire 148 xi University of Education, Winneba http://ir.uew.edu.gh LIST OF TABLES 2.1: A Comparison between Traditional and Constructivist-Based Classrooms 31 3.1: Benchmarks for Teaching and Learning 53 3.2: Population for Control and Experimental Schools. 55 3.3: Summary of Sampling Technique and Sample Size 56 3.4: Reliability Statistics for the Four Conceptual Areas 65 4.1: Gender of participants 79 4.2: A summary for behaviours, skills, and approaches exhibited by the participants during lesson observations (n = 6). 82 4.3: Mean Percentage Scores for each of the Conceptual Areas in Algebra 87 4.4: Descriptive Statistics of Control and Experimental Groups 90 4.5: Independent Samples Test of Pretest and Posttest Scores 91 4.6: Test of Normality for Experimental and Control Groups 92 4.7: Results of the paired samples t-test on the pre-test and post-test achievement of students in the experimental and control groups. 94 4.8: Response of Participants on Collaborative Learning 97 xii University of Education, Winneba http://ir.uew.edu.gh LIST OF FIGURES 3.1: Basic Design of the Study 52 4.1 Gender of Participating Teachers 77 4.2 Participants’ Years of Teaching Experience 78 4.3: The Participants’ Teaching Qualification 79 4.4: Teaching Approaches Mostly Preferred by Participants 80 4.5: Agree and Disagree Responses by Categories in Percentage 100 xiii University of Education, Winneba http://ir.uew.edu.gh ABSTRACT The purpose of this study was to investigate the effects of the Constructivist Teaching Approach (CTA) on senior high school students’ performance in algebra in the Gomoa East District.