Edith Cowan University Research Online Theses: Doctorates and Masters Theses 2013 Numeracy support for year two students Gillian Dawn Hurle Edith Cowan University Follow this and additional works at: https://ro.ecu.edu.au/theses Part of the Science and Mathematics Education Commons Recommended Citation Hurle, G. D. (2013). Numeracy support for year two students. https://ro.ecu.edu.au/theses/609 This Thesis is posted at Research Online. https://ro.ecu.edu.au/theses/609 Edith Cowan University Copyright Warning You may print or download ONE copy of this document for the purpose of your own research or study. The University does not authorize you to copy, communicate or otherwise make available electronically to any other person any copyright material contained on this site. You are reminded of the following: Copyright owners are entitled to take legal action against persons who infringe their copyright. 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Gillian Hurle 10038797 Master of Education (Research) School of Education Edith Cowan University Supervisors: Dr. Fiona Budgen Dr. Deborah Callcott A thesis submitted in partial fulfilment of the requirements for the Masters in Education by coursework and research at the School of Education Edith Cowan University, Perth, Western Australia. 2012 i ii Abstract Research of teaching theories and intervention programs internationally and in Australia suggests that the implementation of numeracy support programs can improve student achievement levels (Fuchs, 2005; Ketterlin-Geller, Chard & Fien, 2008; Van Kraayenoord & Elkins, 2004). An intervention program was conducted for a small group of Year Two students with the aim of improving their numeracy skills over a 20 week period. Results of two mathematics assessments, together with information provided by teachers based on classroom observations and informal assessments were combined to select a group of twelve students who were considered to be at risk of developing mathematical difficulties. The program comprised of two 85 minute lessons and one 40 minute lesson per week in a room adjacent to the Year Two classroom. A social constructivist method of teaching was put into practice within the structure of a small group setting. A case study approach recorded the learning journey of each student with an individual profile of each participant maintained for the duration of the program. At the conclusion of the program data obtained from formative assessments, teacher observations, and feedback from the student participants were used to evaluate the program’s effectiveness. Students who were members of the intervention program improved their level of basic numeracy skills in the areas of addition, subtraction, multiplication, division, and number sequencing, and also demonstrated a positive disposition towards mathematics. iii Declaration I certify that this thesis does not to the best of my knowledge and belief: (i) incorporate without acknowledgement, any material previously submitted for a degree or diploma in any institution of higher education; (ii) contain any material previously published or written by another person except where due reference is made in the text; or (iii) contain any defamatory material. I grant permission for the Library at Edith Cowan University to make duplicate copies of my thesis as required. Signature………………………………… Date………………………………………. iv Acknowledgements My deepest thanks are extended to my ECU supervisors, Dr Jenny Jay, Dr Fiona Budgen and Dr Deborah Calcott for their amazing patience and guidance. Additional thanks and appreciation is extended to my employers and the parents of the students who permitted me to conduct the study. A special thanks to the student participants. Without them and their enthusiasm this experience would not have been possible or as fulfilling. There is no doubt their progress in the coming years will continue to be of great personal interest to me. v Table of Contents ABSTRACT iii DECLARATION iv ACKNOWLEDGEMENTS v TABLE OF CONTENTS vi LIST OF FIGURE x LIST OF TABLES xii CHAPTER ONE Context 1 Rationale 3 Purpose, Scope and Limitations of the Study 5 Research Question 7 CHAPTER TWO LITERATURE REVIEW Introduction 8 Students at Risk 8 Impact of Literacy Ability on Mathematical Ability 11 Behaviour 12 Teaching Methods 13 Numeracy Programs 17 Mathematical Assessments 21 Summary 23 CHAPTER THREE RESEARCH DESIGN Introduction 24 Research Design 26 Case Study 26 Data Collection and Participant Selection 28 Performance Indicators in Primary School 28 Diagnostic Mathematical Task Assessment 30 vi Classroom Teachers 32 Triangulation 32 Participant Selection 33 Parental/Guardian Permission 33 Schedule for Early Numbers Assessment 1 33 First Steps Diagnostic Map of Student Achievement 35 Measurement of Student Achievement 36 Journal 37 Summary 38 CHAPTER FOUR THE PROGRAM Introduction 39 Environment 39 Timetable 41 Content 42 Teaching Approach 45 Play Based Activities 49 Thinking Aloud 54 Reading and Writing Numerals and Words 54 Manipulatives 55 Visual Patterns 56 Creative Thinking 57 Books 59 Worksheets 61 Summary 63 CHAPTER FIVE RESULTS Introduction 65 Diagnostic Mathematical Tasks (DMT) 65 Schedule for Early Numbers Assessment (SENA) 67 Comparison between DMT and SENA 68 Post Program DMT 69 vii Post Program SENA 70 Student Achievement 71 Student Profiles Lowest Performing Students Pre-Assessment DMT Lance 72 Keith 75 Simon 78 Highest Performing Students Pre-Assessment DMT Kaisha 81 Rachel 83 Anne 84 Other Students Elise 86 Neil 88 Summary 89 CHAPTER SIX DISCUSSION OF RESULTS Introduction 91 Diagnostic Assessment 91 Environment 92 Lesson Content 93 Learning Difficulties 98 Literacy 100 Behaviour 100 Summary 102 CHAPTER SEVEN IMPLICATIONS Introduction 103 Early Intervention 103 Program Content 104 Creativity 105 viii Play Based Activities 106 Environment 107 Behaviour 108 Assessment 108 Reflection 109 Best Teaching Practice 111 REFERENCES 113 APPENDICES Appendix A Sample letter and parent consent forms 125 Appendix B Ethical issues 130 Appendix C Sample of DMT assessment 131 Appendix D Sample of SENA assessment 151 Appendix E Sample of PIPS assessment 156 Appendix F Journal 157 ix List of Figures Figure Page 1 Research Design 25 2 PIPS Data 2008 29 3 Example DMT answer sheet 31 4 SENA 1 Answer Sheet 34 5 Mushroom House 50 6 Mousetrap Maths 51 7 Koala Fun 52 8 Number Fun 52 9 In the Window 53 10 Toss and Add 53 11 Matching Words to Numerals 55 12 Cuisenaire Rods 55 13 Sharing Counters 56 14 Hundred Chart 57 15 Number Stories 58 16 Race – Tama 59 17 Cookie sharing – Elise 60 18 Halving – Anne 61 19 Multiplication story problems 62 20 Halving worksheet – Leanne 63 21 DMT: Year Two students - Number of errors 65 22 DMT: Participants’ average achievement 66 23 DMT: Percentage of correct answers pre and post-program 69 24 DMT: Number of errors pre and post-program 70 25 SENA: Percentage of correct answers pre and post-program 71 26 DMT: Comparison of pre and post-assessment results for individual students 71 27 Before and After worksheet - Lance 75 28 Games/Number Sentences - Keith 77 29 Measuring Activity – Simon 79 30 Car Race – Simon 81 31 Halving worksheet - Anne 85 x 32 Number Stories - Elise 87 33 DMT: Reduction in number of errors 90 34 Position Worksheet 97 xi List of Tables Table Page 1 Summary of Australian Numeracy Programs 20 2 Example Journal Entry 38 3 Support Timetable 42 4 Concepts First Steps Matching Phase 44 5 Concepts First Steps Quantifying Phase 45 6 Gardner’s Multiple Intelligences 48 7 Concepts order of Difficulty: DMT and SENA 69 xii CHAPTER ONE Introduction This chapter is divided into a number of sections beginning with the context which includes a demographic profile of the school and description of the structure within it. This provides an outline of the environment in which the study took place. Results of Performance Indicators in Primary Schools (PIPS) testing during the Early Childhood Phase and the later achievement of students during the Primary Phase present the focal point of the study. Environmental influences which have an impact on student performance conclude the first section. The second section provides the rationale for the study, highlighting the importance of early identification obtained from a formative and summative assessments followed by measurement and recording of student progress. The purpose, scope and limitations of the support program together with the creation of individual profiles direct the research question. Context The study took place in a dual campus, independent Perth school. Over 2000 students were enrolled in the school, 900 of whom were in the Primary section. The campus catered for students from Kindergarten to Year Six and had two classes