University of Plymouth PEARL https://pearl.plymouth.ac.uk 04 University of Plymouth Research Theses 01 Research Theses Main Collection 1997 The Use of Concept Questions to Improve Student Understanding of Mechanics, and the Formulation of a Hierarchical Model of Student Understanding of Moments of Forces ROWLANDS, STUART KENNETH http://hdl.handle.net/10026.1/2161 University of Plymouth All content in PEARL is protected by copyright law. Author manuscripts are made available in accordance with publisher policies. Please cite only the published version using the details provided on the item record or document. In the absence of an open licence (e.g. Creative Commons), permissions for further reuse of content should be sought from the publisher or author. The Use of Concept Questions to Improve Student Understanding of Mechanics, and the Formulation of a Hierarchical Model of Student Understanding of Moments of Forces STUART KENNETH ROWLANDS A thesis submitted to the University of Plymouth for the degree of doctor of philosophy Centre for Teaching Mathematics School of Mathematics and Statistics May 1997 LIBRARY STORE REFERENCE ONLY ,?,9. .93593200 .'/flilOUTH Item No. 9GO : Date 1 2 MAY 1S98 Class No. Con'il. No. iX 7o3bg7iS'7 ABSTRACT The use of Concept Questions to Improve Student Understanding of Mechanics and the Formulation of Hierarchical Models of Student Understanding of Moments of Forces by Stuart Kenneth Rowlands The aims and objectives of the first part of the thesis are to create and evaluate a teaching package that would enable the teacher to facihtate student conceptual understanding of mechanics. The second part is to create a hierarchical model of student conceptual understanding of moments of forces. The thesis reports on the various conflicting theories and recommended teaching strategies from the research into student misconceptions, and examines the various underlying philosophical trends (for example, radical and social constructivism, the Vygotskian perspective and positivism) that have influenced the research into misconceptions in mechanics. As a result, the philosophical perspective of the thesis is that the analysis of the structure of Newtonian mechanics ought to be before the consideration of challenging misconceptions. The question as to how students can construct for themselves the Newtonian system ought to be prior to the consideration of designing a strategy to tackle misconceptions. With prior consideration of the structure of mechanics, the thesis examines the formation of the intuitive schema of force and motion. The thesis proposes the Socratic method of strategic questioning as the most appropriate teaching method for constructing the Newtonian system and displacing the intuitive schema of force and motion. The thesis reports on the formation, and the evaluation, of the teaching package as an aid to facilitate the construction of the Newtonian system, and concludes that teachers have to be trained in the use of the Socratic method prior to any evaluation. There has been little or no research in the area of misconceptions concerning moments. The thesis reports on the formation of a hierarchical model of understanding moments. From a sample of 417 students nation-wide, the thesis has identified 3 conceptual levels of understanding moments and discusses the teaching implications based on the responses from the sample. Ill CONTENTS Chapter 1 - Introduction 1 1.1 The Origins, Aims and Objectives of the Thesis 1 1.2 Background to the Thesis 6 1.3 On the Nature of Misconceptions 10 1.4 Remedial Approaches to Misconceptions 15 1.5 The Philosophical and Pedagogical Approach of the Thesis 18 1.6 The Formation and Evaluation of the Teaching Package 21 1.7 A Conceptual Model of Student Understanding of Moments 22 Chapter 2 - Review of Constructivism 24 2.0 Introduction to the Review 24 2.1.0 Introduction to the First Section 24 2.1.1 Interpretations of Constructivism 26 2.1.2 The Utilisation of Student Conceptions Deconstructed 29 2.1.3 Review of Medieval Women 31 2.1.4 The Pedagogical Implications of D) With respect to Energy 35 2.1.5 The Philosophical Basis of D) 37 2.2 The Radical Versus Social Constructivism Controversy Placed Within the Vygotskian Framework 42 2.2.0 Introduction 42 2.2.1 Vygotsky*s Zone of Proximal Development 49 2.2.2 The Social Verses the Radical 53 2.3.0 The Constructivism Controversy Placed Within the Context of Three Approaches in the Philosophy of Science 61 2.4.0 Summary: The Dispute Between the Constructivist/relativist Position and my own Position with Regard to Children's Learning and the Status of Knowledge 69 Chapter 3 - The Logical Structure of Newtonian Mechanics and the Pedagogical Implications 75 3.1 Introduction 75 3.2 The Logical Structure of Newtonian Mechanics 80 3.3 Modelling in Mechanics 92 Chapter 4 - A Critique of Positivism and its Pedagogical Implications 98 4.1 Introduction 98 4.2 The Influence of Positivism in the Philosophy and Teaching of Science 101 4.3 The Pedagogical Implications of Positivism in Mechanics 108 Chapter 5 - Overcoming the Intuitive Schemata of Force and Motion 119 5.1 Introduction 119 5.2 Some Preliminaries: Concepts and Schemata 125 5.3 The Psychology of Learning Mechanics 132 IV 5.4 Promoting Cognitive Conflict 141 5.5 Cognitive Conflict and Ideahsed Abstraction 14] 5.6 A Pilot-Study on the Effectiveness of Strategic Questioning 145 5.7 Further Thoughts on the Socratic Dialogue 149 5.8 The use of Computer Simulation in the Socratic Dialogue 155 5.9 Conclusion 157 5.10 Summary - How the Theoretical Position Adopted in Chapters 2 to 5 leads to the Adoption of the Socratic Method of Strategic Questioning 162 Chapter 6 - The Research Methodology that was Adopted by the Thesis 167 6.1 Introduction 167 6.2 What was Looked for in the Pilot Study 170 6.3 Review of Quantitative Methods with Respect to the Teaching Package 179 6.4 The Reason and Methodology Behind the Hierarchical Model of Student Understanding of Moments of Forces 181 Chapter 7 - The Formation of the Teaching Package: The Pilot-Study 184 7.1 Introduction 184 7.2 What is Force? The Making of Unit 1 (and 2) 188 7.3 The Force Acting on a Vertically Thrown Ball. The Making of Unit 3. 192 7.4 Uniform Motion. The making of Unit 8 200 7.5 The Force Acting on a Thrown Bail at its Maximum Height. The making of Unit 4 200 7.6 The Forces Acting on a Book That is at Rest on a Table - The Making of Unit 5 203 7.7 Broken Equilibrium - The Making of Unit 6 208 7.8 Gravitational Attraction. The Making of Unit 13 210 7.9 Newton's Second Law of Motion. The Making of Units 9, 10 and 11. 212 7.10 Force in two Dimensions. The Making of Unit 12 214 7.11 Summary - Instances When Anomalies Caused the Intuitive Schema to Become Unstable 215 Chapter 8 - The Empirical Evaluation of the Teaching Package 217 8.1 Introduction 217 8.2 Teachers Response in the Preview to the Package 199 8.3 The Response to the Questionnaire for Teachers Involved in the 9 Experimental Groups 221 8.4 The Response to the Student Questionnaire on the Introduction to Mechanics 228 8.5 Teacher comments on the Units of the Package 231 8.6 Conclusion 232 Chapter 9 - A Hierarchical Model of Student Understanding of Moments of Forces 237 9.1 Introduction 237 9.2 The Small-Scale Investigation 239 9.3 The Large-Scale Investigation 245 9.4 The Formation of the Model of Conceptual Development 246 9.5 Description of Level I 255 9.6 Description of Level 2 258 9.7 Description of Level 3 262 9.8 The Questions That lie Outside the Hierarchy 266 9.9 Implications for Teaching 267 9.10 The Socratic Dialogue in the Teaching of Moments 270 Chapter 10 - Conclusion: Implications for the Teaching of Mechanics After the Introduction of Force and Motion 273 Appendix A - The Teaching Package 281 Appendix B - Graham's Hierarchical model of the Development of Student Understanding of Force 305 Appendix C - Analysis of Covariance on the Results of the Pre- and Post-Tests Re the Pilot Study and the Quasi-Experimental Design of the Teaching Package 307 Appendix D - Introductory Letter and Response Form Re. Involvement in the Empirical Evaluation of the Teaching Package 315 Appendix E - The Pre- and Post-Test 318 Appendix F - Questionnaire on Teaching Package, Log-Sheet and Questionnaire, and Student Questionnaire on the Introduction to Mechanics 326 Appendix G - Moments Survey Questionnaire 336 Appendix H - The Product-moment Correlation Coefficient for Dichotomous Data (Phi). 345 References 348 VI LIST OF TABLES 1 The Initial Number of Schools Willing to Participate in the Experiment 217 2 Results of the Pre- and Post-Test 220 3 The Time Taken for the Experimental groups to Complete Each Unit 224 4 Responses to Question 9 of the Log-Book and Questionnaire 225 5 Teacher Responses to the Teaching Package Questionnaire (Log-Sheet and Questionnaire) 227 6 Responses to the Student Questionnaire on the Introduction to Mechanics 228 7 Some Student Responses to the Introduction to Force and Motion (Student Questionnaire on the Introduction to Mechanics) 230 8 Responses to two Questions Representing the Third Stumbling Block 244 9 Correct Response Intervals for Each Level 246 10 Phi Values for the Level 1 Questions 249 11 Phi Values for the Level 2 Questions 250 12 Phi Values for the Level 3 Questions 251 13 Phi Values and Percentage Correct for Questions That Possibly Could Have Formed Level 4 252 14 Distribution of Students to the Levels of the Hierarchy 253 15 Responses to Questions 10(a), 10(b), 10(d) and 10(e) 265 VU LIST OF FIGURES 1 Diagram Representing