簡易檢索 / 詳目顯示

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:132下載:10
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 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

    References

    Alajmi, A. (2009). Addressing computational estimation in the Kuwaiti curriculum: Teachers’ views. Mathematics Teacher Education, 12(4), 263–283.

    Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Educational Studies in Mathematics, 79(2), 239-261.

    Ann Kajander & Miroslav Lovric (2009) Mathematics textbooks and their potential role in supporting misconceptions, International Journal of Mathematical Education in Science and Technology, 40(2), 173-181, DOI: 10.1080/00207390701691558

    Bronowski, J. (2011). The ascent of man. Random House.
    Cai, J., Lo, J. J., & Watanabe, T. (2002). Intended treatments of arithmetic average in US and Asian school mathematics textbooks. School Science and Mathematics, 102(8), 391-404.

    Campbell, R. J., & Kyriakides, L. (2000). The national curriculum and standards in primary schools: A comparative perspective. Comparative Education, 36(4), 383-395.

    Charalambos Y. Charalambous, Seán Delaney , Hui-Yu Hsu & Vilma Mesa (2010) A Comparative Analysis of the Addition and Subtraction of Fractions in Textbooks from Three Countries, Mathematical Thinking and Learning, 12:2, 117-151, DOI: 10.1080/10986060903460070

    Dante, L. R. (2010). Tudo é Matemática (3rd ed., Vol. 9, Tudo é Matemática). São Paulo , SP: ática . (In Portuguese).

    EDITORIAL. (1911). EDITORIAL. The Mathematics Teacher, 4(2), 45–49. Retrieved from http://www.jstor.org/stable/27949701

    Field, Andy (2009). Discovering Statistics Using SPSS. London: Sage. pp. 372–373. ISBN 978-1-84787-906-6.
    Gak, D. (2011).

    TEXTBOOK – AN IMPORTANT ELEMENT IN THE TEACHING PROCESS. Методички видици, 2(2), 78-82. Retrieved from http://epub.ff.uns.ac.rs/index.php/MV/article/view/771

    Habibi, M. (2010).Short Proofs for Pythagorean Theorem (Notes in Geometry, Part 1). In International Mathematical Forum (Vol. 5, No. 66, pp. 3273-3282).

    Haggarty, L., & Pepin, B.. (2002). An Investigation of Mathematics Textbooks and Their Use in English, French and German Classrooms: Who Gets an Opportunity to Learn What?.. British Educational Research Journal, 28(4), 567–590. Retrieved from http://www.jstor.org/stable/1501441

    Kirsch, I. S. (2001). The international adult literacy survey (IALS): Understanding what was measured. ETS Research Report Series, 2001(2), i-61.

    Kung Chan Chien Pei Chung Cheng Kuo Chung Tsui Shen Yung. (2014). Retrieved January 07, 2016, from http://www.chinatimes.com/newspapers/20140805000536-260107

    Maor, E. (2007). The Pythagorean theorem: a 4,000-year history. Princeton University Press.

    Mayer, R. E., Sims, V., & Tajika, H. (1995). Brief note: A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32(2), 443-460.

    Ministry of Education. (2005). Mathematics syllabus (Secondary Education). Taiwan: K-12 Education Administration.

    Ministry of Education. (2012). Mathematics syllabus (Lower Secondary). Singapore: Curriculum Planning Division.

    Morris, S. J. (1997). The Pythagorean Theorem. Math Essays, University of Georgia.

    Monaghan, S. R. (2013). Textbooks, teachers, and middle school mathematics student achievement. (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 3603466)

    Niss, M., & Jensen, T. H. (Eds.). (2002). Kompetencer og matematiklæring. Ideer og inspiration til udvikling af matematikundervisning i Danmark. Uddannelsesstyrelsens temahæfteserie nr. 18. Copenhagen: Ministry of Education.


    Niss, M. (2004). Mathematical competencies and the learning of mathematics: The danish KOM project. In A. Gagtsis & Papastavridis (eds): 3rd Mediterranean Conference on mathematical education, 3-5 January 2003,
    Athens, Greece. (pp. 115-124). Athens: The Hellenic mathematical society, 2003.

    Niss, M. (2015). Mathematical competencies and PISA. In Stacey, K., & Turner, R. (Eds.), Assessing mathematical literacy: the PISA experience (pg. 41). Switzerland: Springer.

    Ojose, B. (2011). Mathematics Literacy: Are We Able To Put The Mathematics We Learn Into Everyday Use?. Journal of Mathematics Education, 4(1), 89-100.

    Organisation for Economic Co-operation and Development (OECD). (2003). The PISA 2003 assessment framework—Mathematics, reading, science and problem solving knowledge and skills. Paris: OECD.

    Organisation for Economic Co-operation and Development (OECD). (2013). PISA 2012 assessment and analytical framework. Mathematics, reading, science, problem solving and financial literacy. Paris: OECD.

    OECD (2016), PISA 2015 Results (Volume II): Policies and Practices for Successful Schools, OECD Publishing, Paris. DOI: http://dx.doi.org/10.1787/9789264267510-en

    Pehkonen, L. (2004). The magic circle of the textbook–an option or an obstacle for teacher change. Paper presented at the Proceedings of the 28th Conference of the International Mathematics Education.

    Pepin, B. and Haggarty, L., (2001). Mathematics textbooks and their use in English, French and German classrooms: a way to understand teaching and learning cultures. ZDM – The International Journal on Mathematics Education, 33 (5), 158– 75.

    Po-Hung, L. (2003). Do teachers need to incorporate the history of mathematics in their teaching?. The Mathematics Teacher, 96(6), 416.

    Ray, A., & Margaret, W. (Eds.). (2003). PISA Programme for international student assessment (PISA) PISA 2000 technical report: PISA 2000 technical report. OECD Publishing.

    Remillard, J. T., (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75 (2), 211– 46.

    Rezat, S. (2006). The structures of German mathematics textbooks. Zentralblatt für Didaktik der Mathematik, 38(6), 482–487.

    Rezat, S., (2008). Learning mathematics with textbooks. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano and A. Sepúlveda, eds, Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education and PME-NA XXX, Vol. 4. Morelia, Mexico: PME, 177– 84.

    Rezat, S. (2010). The utilization of mathematics textbooks as instruments of learning. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of CERME 6, Working Group 7 (pp. 1260-1269) Lyon, France: Institut National De Recherche Pédagogique.
    Rezat, S., & Straesser, R. (2014). Mathematics Textbooks and How They Are Used. Masterclass in Mathematics Education: International Perspectives on Teaching and Learning, 75(2), 51.

    R. J. Campbell & L. Kyriakides (2000) The National Curriculum and Standards in Primary Schools: A comparative perspective, Comparative Education, 36:4, 383-395, DOI: 10.1080/713656661
    Secretaria de Educação do Distrito Federal. (2014). Currículo em Movimento da Educação Básica. Retrieved December 19, 2016, from http://www.se.df.gov.br/component/content/article/282-midias/443-curriculoemmovimento.html

    Steen, L. A. (2001). Mathematics and numeracy: Two literacies, one language. The mathematics educator, 6(1), 10-16.

    Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2, 50-80.

    Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics teaching in the middle school, 3(4), 268-275.

    Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E.
    A. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.

    Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 289-321.

    Tam, H. P., & Wang, H. H. (2012). On the arrangement of topics in plane geometry in the textbooks of Taiwan: Using Pythagoras theorem as an example. In Pre-proceedings of the 12th international congress on mathematical education (ICME-12), Topic Study Group 10 (pp. 2484-2492). Seoul. Retrieved from http://icme12.org/data/ICME12_Proceedings_20121226.zip

    Tanner, D., & Tanner, L. N. (1980). Curriculum development: Theory into practice. New York: Macmillan.

    Tso, T.-Y. (2011) (Ed.). Junior High School Mathematics (Vol. 1). Tainan, Taiwan: Nani Publishers (In Chinese).

    Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H. and Houang, R. T., (2002). According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht, Netherlands: Kluwer, 139– 52.

    Veljan, D.. (2000). The 2500-Year-Old Pythagorean Theorem. Mathematics Magazine, 73(4), 259–272. http://doi.org/10.2307/2690973

    Xenofontos, C., & Papadopoulos, C. E. (2015). Opportunities of learning through the history of mathematics: the example of national textbooks in Cyprus and Greece. International Journal for Mathematics Teaching & Learning.

    What is PISA?. (2016, 03). Retrieved from http://www.oecd.org/pisa/aboutpisa/

    Wimmer, R. D., & Dominick, J. R. (1997). Mass media research: An introduction (5th ed.). Belmont [Calif.]: Wadsworth Pub..

    Yeo, J., Dr, Seng, T. K., Yee, L. C., Chow, I., Meng, N. C., Liew, J., & Hong, O. C. (2014). New Syllabus Mathematics (7th ed., Vol. 2, New Syllabus Mathematics). Singapore: Shinglee.

    下載圖示
    QR CODE