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研究生: 潘亞衛
Weverton Ataide Pinheiro
論文名稱: THE ANALYSIS OF COGNITIVE DEMAND AND MATHEMATICAL COMPETENCIES: A CASE STUDY OF THE PYTHAGOREAN THEOREM
THE ANALYSIS OF COGNITIVE DEMAND AND MATHEMATICAL COMPETENCIES: A CASE STUDY OF THE PYTHAGOREAN THEOREM
指導教授: 左台益
Tso, Tai-Yih
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2017
畢業學年度: 105
語文別: 英文
論文頁數: 126
中文關鍵詞: textbook analysiscognitive demandmathematical competenciesPythagorean theoremPISA
英文關鍵詞: textbook analysis, cognitive demand, mathematical competencies, Pythagorean theorem, PISA
DOI URL: https://doi.org/10.6345/NTNU202203510
論文種類: 學術論文
相關次數: 點閱:105下載:10
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  • 無中文摘要

    The purpose of this study was to analyze and compare different perspectives of the way the Pythagorean theorem questions appeared in three mathematics textbooks. Tudo é Matemática (Brazilian textbook), Nani (Taiwanese book), and New Syllabus Mathematics (Singaporean textbook) regarding number of exercises and worked examples, cognitive demand and mathematical competencies. This research used content analysis as research methods and exams based on the PISA exam were applied to students from Brazil and Taiwan to check their difference in performance and mathematical reasoning.

    The analysis of the number of exercises and worked examples showed that both Taiwanese and Singaporean textbooks have a superior amount of exercises and worked examples compared with the Brazilian one which makes Taiwanese and Singaporean textbooks advantageous over the Brazilian book.

    From the perspectives of cognitive demand, results showed that Taiwanese and Singaporean textbooks are more different from each other because Taiwanese textbook opts to focus more on lower-level demand, while Singaporean textbook has a strong focus on higher-level demand questions.

    Regarding mathematical competencies results also showed that the Taiwanese textbook is more different than Singaporean textbook. Overall Singaporean textbook is more different from the other two textbooks because many of its questions use level 2 and 3, while the other two textbooks are more used to test students in between levels 0 and 1.

    Finally, the exam showed that students from Taiwan have higher performance in a PISA-based exam than Brazilian students. Through a qualitative research, the results also revealed that the cultural aspects of students from each country also influenced the way students answered to the questions.

    TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1 Introduction 1 Background 3 Problem 5 Purpose 7 Research Questions 9 Significance 10 Definition of key terms 10 CHAPTER 2: LITERATURE REVIEW 12 Introduction 12 The features and analysis of textbooks 12 Importance of textbooks 12 Cross-country textbook analysis 13 The coverage of Pythagorean theorem in mathematics curricula 17 The importance of the Pythagorean theorem 17 When and why the Pythagorean theorem is learned 19 Cognitive Demand of Mathematical Task 20 Mathematical Task 20 Cognitive Demand 21 Mathematical Competence 23 The Programme for International Student Assessment (PISA) 26 General Information about PISA 26 Conclusion 27 CHAPTER 3: METHODOLOGY 28 Introduction 28 Research Design 29 Procedure 29 Textbook Sampling 29 Cognitive demand 31 Mathematical Competencies 32 PISA-based Exam 35 Participants 36 Textbooks 36 Students 38 Measures 39 Framework of Textbook Analysis 39 Connection of PISA-based exam and mathematical competencies 42 PISA-based Exam 43 Data Analysis 49 Textbook Analysis 49 PISA-based Exam 50 Reliability of this study 53 Limitation 54 CHAPTER 4: RESULTS 55 Introduction 55 Exercises 55 Worked examples 57 Exercises 59 Cognitive Demand 60 Mathematical Competencies 63 Statistical Methods 66 PISA-based exam 82 Brazilian students’ responses 82 Taiwanese students’ responses 86 Chapter 5: DISCUSSION 93 Introduction 93 Discussion of the findings 94 Number of exercises and worked examples 94 Cognitive demand 98 Mathematical Competencies 99 PISA-based exams 100 Relationship between textbook analyses and PISA-based exam 102 Conclusion 103 Implications for practice 104 Implications for further research 104 Limitations 105 References 107 APPENDICES 111 APPENDIX A: Mathematical Competencies and its levels 111 APPENDIX B: PISA-based exams 115 PISA-based exam in Portuguese 115 PISA-based exam in Chinese 121

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