Addressing preservice student teachers negative beliefs and anxieties about mathematics

Addressing preservice student teachers’ negative beliefs and anxieties about mathematics Ms Sirkka-Liisa [Lisa] Marjatta Uusimaki B.A., Bed (Secondary) Centre for Mathematics, Science and Technology Queensland University of Technology April 2004 A 72 credit point thesis presented in fulfilment of the requirements of the Master of Education (Research) ED12 DECLARATION I, Sirkka-Liisa (Lisa) Marjatta Uusimaki, hereby declare that, to the best of my knowledge and belief, the work in this dissertation contain no material previously published or written by another person nor material which, to substantial extent, has been accepted for the award of any other degree or diploma at any institute of higher education, except where due reference is made Signature……………………………… Date…………………………………… i ACKNOWLEDGMENTS I wish to express my sincere gratitude to my principal supervisor Dr Rod Nason, Senior Lecturer in Mathematics Education, Queensland University of Technology for his brilliant ideas, excellent support and guidance throughout this study His assistance in the structuring and editing of this thesis has been greatly appreciated I would like to also thank my associate supervisor Dr Gillian Kidman, Lecturer in Science Education, Queensland University of Technology for her outstanding contribution to this study that included advice and support in the analysis of the quantitative and the qualitative data, and in the formatting of the thesis to meet American Psychological Association (APA) guidelines I am truly grateful to Gillian for her encouragement and time she so freely gave I would like to also thank and acknowledge Mr Andy Yeh for his assistance in the programming of the Online Anxiety Survey Special thanks also to Mr Paul Shield who helped with the quantitative analysis of the Online Anxiety Survey data Sincere thanks to the Director of the Centre of Mathematics, Science and Technology Education, Professor Campbell McRobbie for his kindness and support that he so generously offered throughout this study Finally, this thesis is dedicated to my son Marcus Uusimaki whose unconditional love and support inspired me to research issues of quality in education and to give my all in this study ii ABSTRACT More than half of Australian primary teachers have negative feelings about mathematics (Carroll, 1998) This research study investigates whether it is possible to change negative beliefs and anxieties about mathematics in preservice student teachers so that they can perceive mathematics as a subject that is creative and where discourse is possible (Ernest, 1991) In this study, sixteen maths-anxious preservice primary education student teachers were engaged in computer-mediated collaborative open-ended mathematical activities and discourse Prior to, and after their mathematical activity, the students participated in a short thirty-second Online Anxiety Survey based on ideas by Ainley and Hidi (2002) and Boekaerts (2002), to ascertain changes to their beliefs about the various mathematical activities The analysis of this data facilitated the identification of key episodes that led to the changes in beliefs The findings from this study provide teacher educators with a better understanding of what changes need to occur in pre-service mathematics education programs, so as to improve perceptions about mathematics in mathsanxious pre-service education students and subsequently primary mathematics teachers iii TABLE OF CONTENTS DECLARATION ……………………………………………………………… ACKNOWLEDGMENT ……………………………………………………… ABSTRACT …………………………………………………………………… Chapter 1.1 Introduction ……………………………………………………………… 1.2 Background of study …………………………………………………… 1.3 Overview of literature …………………………………………………… 1.3.1 Maths-anxiety …………………………………………………… 1.3.2 Teacher beliefs ………………………………………………… 1.3.3 Overcoming maths-anxiety ……………………………………… 1.3.4 Assessment of maths-anxiety …………………… 1.3.5 Pre-service mathematics education courses ……………………… 1.4 Significance of the study ………………………………………………… 1.5 Chapter overview ……………………………………………………… 1.6 Summary ………………………………………………………………… Chapter 2.1 Introduction ……………………………………………………………… 2.2 Maths-anxiety …………………………………………………………… 2.3 Consequences of maths-anxiety ………………………………………… 2.4 Teacher beliefs about mathematics ……………………………………… 2.5 Prior school experiences and the origins and the development of negative maths-beliefs …………………………………………………………… 2.6 2.7 2.8 2.9 2.10 2.11 i ii iii 1 3 4 5 6 8 12 13 15 Overcoming maths-anxiety in pre-service teachers 16 2.6.1 Beliefs …………………………………………………………… 17 2.6.2 Conceptual understanding of mathematics ……………………… 18 2.6.3 Subject matter knowledge and pedagogical knowledge ………… 19 Assessment of maths-anxiety …………………………………………… 21 Pre-service mathematics education courses …………………………… 23 2.8.1 Constructivist and social constructivist theories ………………… 24 2.8.2 Collaboration …………………………………………………… 25 Communities of learning and computer supported collaborative learning 27 Summary ……………………………………………… 29 Theoretical framework for the study …………………………………… 30 iv Chapter 3.1 Introduction ……………………………………………………………… 3.2 Research methodology ………………………………………………… 3.3 Participants ……………………………………………………………… 3.4 Collection of data ……………………………………………………… 3.4.1 Semi-structured pre-enactment and post-enactment interviews … 3.4.2 Online Anxiety Survey …………………………………………… 3.4.3 Knowledge Forum notes …………… 3.4.4 Written reflections ………………………………………………… 3.5 Procedure ………………………………………………………………… 3.5.1 Phase 1: Identification of origins of maths-anxiety ……………… 3.5.2 Phase 2: Enactment of intervention program …………………… 3.5.3 Phase 3: Summative evaluation ………………………………… 3.6 Data analysis …………………………………………………………… 3.6.1 Analysis of qualitative data ……………………………………… 3.6.2 Analysis of Online Anxiety Survey quantitative data …………… 3.7 Summary ………………………………………………………………… 32 32 33 34 34 34 35 35 35 35 36 43 43 43 44 45 Chapter 4.1 Introduction ……………………………………………………………… 4.2 Results from interview data …………………………………………… 4.2.1 Pre-interview results …………………………………………… 4.2.2 Comparison of pre- and post-interview results ………………… 4.3 Results from reflection documents ……………………………………… 4.4 Online Anxiety Survey results …………………………………………… 4.4.1 Introduction ……………………………………………………… 4.4.2 Overall analysis of the Online Anxiety Survey results ………… 4.4.3 Session 1: Number sense activity ………………………………… 4.4.4 Session 2: Space and measurement activity ……………………… 4.4.5 Session 3: Number and shape activity …………………………… 4.4.6 Session 4: Division operation activity …………………………… 4.5 Computer-mediated support tools ……………………………………… 4.6 Summary ………………………………………………………………… 46 46 46 57 63 65 65 66 68 70 73 75 77 80 Chapter 5.1 Introduction ……………………………………………………………… 5.2 Overview of study ……………………………………………………… 5.3 Overview of results ……………………………………………………… 5.4 Limitations ……………………………………………………………… 82 82 83 87 v 5.5 Implications ……………………………………………………………… 88 5.6 Summary and recommendations ………………………………………… 89 References ……………………………………………………………………… Appendix 1: Phone interview questions ………………………………………… Appendix 2: Pre-enactment Interview ………………………………………… Appendix 3:Post-enactment interview …… ………………………………… Appendix 4: Online Anxiety Survey …………………………………………… 91 103 104 105 106 vi LIST OF TABLES Chapter Table 3.1 The four mathematical activities ………………………………… 37 Chapter Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 4.6 Table 4.7 Table 4.8 Table 4.9 Table 4.10 Table 4.11 Table 4.12 Table 4.13 Table 4.14 Table 4.15 Table 4.16 Table 4.17 Table 4.18 Table 4.19 The nature of mathematics ……………………………………… Reasons for teaching mathematics ……………………………… Teacher knowledge and qualities ……………………………… Maths-confidence ……………………………………………… The origins of maths-anxiety …………………………………… Situations causing maths-anxiety ……………………………… Types of mathematics causing maths-anxiety ………………… Perceptions of how to overcome maths-anxiety ………………… Perceptions on how to reduce maths-anxiety in future students … The nature of mathematics ……………………………………… The relevance of mathematics ………………………………… Teacher knowledge …………………………………………… Maths-confidence ………………………………………………… Pairwise comparison: Overall results …………………………… Pairwise comparison: Session one results ……………………… Pairwise comparison: Session two results ……………………… Pairwise comparison: Session three results ……………………… Pairwise comparison: Session four results ……………………… Perceptions of computer-mediated software …………………… 48 48 49 51 52 54 55 55 56 59 59 60 61 66 68 70 73 76 78 vii LIST OF FIGURES Chapter Figure 2.1 Figure 2.2 The process of solving maths problems ……………… The theoretical framework ……………………………………… 11 30 Chapter Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Intervention Program …………………………………………… Online Anxiety Survey ………………………… MipPad model and tabular representation ……………………… MipPad model, language and symbol representation …………… Shape and measurement activity ………………………………… Number and shape activity ……………………………………… Division operation activity ……………………………………… 33 38 39 40 41 42 43 Chapter Figure 4.1 Figure 4.2 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Box plots overall positive feelings………………………………… Box plots overall negative feelings…….………………………… Number sense activity (positive feelings responses)……………… Number sense activity (negative feeling responses)……………… Space and measurement activity (positive feeling responses)…… Space and measurement activity (negative feeling responses)…… Number and shape activity (positive feelings responses)………… Number and shape activity (negative feelings responses)………… Division operation activity (positive feelings responses)………… Division operation activity (negative feelings responses)………… 67 68 69 69 71 72 74 75 76 77 viii CHAPTER INTRODUCTION 1.1 Introduction The purpose for this research study was to investigate whether supporting sixteen self-identified maths-anxious preservice student teachers within a supportive environment provided by a Computer-Supported Collaborative Learning (CSCL) community would reduce their negative beliefs and high levels of anxiety about mathematics 1.2 Background of study A considerable proportion of students entering primary teacher education programs have been found to have negative feelings towards mathematics (Cohen & Green, 2002; Levine, 1996) These negative feelings about mathematics often manifest in a phenomenon known as maths-anxiety (Ingleton & O’Regan, 1998; Martinez & Martinez, 1996; Tobias, 1993) Maths-anxiety can be described as a learned emotional response to, for example, participating in a mathematics class, listening to a lecture, working through problems, and /or discussing mathematics (Le Moyne College, 1999) People who experience maths-anxiety can suffer from, all or a combination of the following: feelings of panic, tension, helplessness, fear, shame, nervousness and loss of ability to concentrate (Trujillo, & Hadfield, 1999) Maths-anxiety 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Why are you interested in this research project? Can you avail yourself to attend workshops regularly? 103 Appendix “Mathematics is a central element in human history, society and culture” (Ernest, 2000, p.8) Pre-service student pre-enactment interview: What is mathematics? Why teach mathematics? What “knowledge” you think a teacher need to teach mathematics? What other qualities you think a teacher need to teach mathematics? How confident are you about your own math skills? How confident are you about using computers? Why you like/dislike mathematics? When/ how you think you learnt to like/dislike mathematics? When you feel most anxious about mathematics? 10 Are there particular kinds of mathematics that makes you feel anxious? 11 What you think can help you overcome your feelings of math anxiety? 12 What could a teacher to help students to overcome their negative feelings about mathematics? 13 Was there anything else you want to tell me that you think is important? 104 Appendix “Mathematics is a central element in human history, society and culture” (Ernest, 2000, p.8) Pre-service students’ post- enactment interview: What is mathematics? Why teach mathematics? What “knowledge” you think a teacher need to teach mathematics? What other qualities you think a teacher need to teach mathematics? How confident are you about your own math skills now after your participation in this research project? How did you find using MipPad? How did you find using Knowledge Forum? Was there anything else you want to tell me that you think is important? 105 Appendix Computer based anxiety scale Pre-Session Locate how you feel right now just before commencing the math activity session Uncomfortable Not nervous Not fine Not worried Not confident Not frustrated Comfortable Nervous Fine Worried Confident Frustrated Post-session Locate how you feel right now just after completing the math activity session Uncomfortable Not nervous Not fine Not worried Not confident Not frustrated Comfortable Nervous Fine Worried Confident Frustrated 106 ... is possible to change negative beliefs and anxieties about mathematics in preservice student teachers so that they can perceive mathematics as a subject that is creative and where discourse is... maths-anxious preservice students and the semi-structured interviews The interviews questions focused on issues, such as, the origins and causes of negative beliefs about mathematics, preservice student. .. & Anderson, 1996), can help the maths-anxious preservice student teacher to untangle the web of deeply held negative beliefs and anxieties about mathematics In doing so, the relearning of mathematics