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The First Sourcebookon Asian Research in
Mathematics Education:China, Korea, Singapore, Japan,
Malaysia, and India
International Sourcebooks
in Mathematics and Science Education
Series Editor:Bharath Sriraman, The University of Montana
International Sourcebooks
in Mathematics and Science EducationBharath Sriraman, Series Editor
The First Sourcebook on Nordic Research in Mathematics Education: Norway, Sweden, Iceland, Denmark, and Contributions From Finland (2010)
edited by Bharath Sriraman, Christer Bergsten, Simon Goodchild,Gudbjorg Palsdottir, Bettina Dahl Søndergaard, and Lenni Haapasalo
The First Sourcebook on Asian Research in Mathematics Education:China, Korea, Singapore, Japan, Malaysia, and India (2014)
Edited by Bharath Sriraman, Jinfa Cai, Kyeong-Hwa Lee, Lianghuo Fan, Yoshinori Shimizu, Chap Sam Lim, and K. Subramaniam
The First Sourcebook on Mediterranean and South Central Asian Research in Mathematics and Science Education: Cyprus, Israel, Turkey, Greece, Iran,
Pakistan, and Central Asia (in development)edited by Bharath Sriraman, Constantinos Christou, Roza Leikin, Ahmet
Arikan, Constantinos Tzakanis, and Anjum Halai
The First Sourcebookon Asian Research in
Mathematics Education:China, Korea, Singapore, Japan,
Malaysia, and India
Edited by
Bharath SriramanThe University of Montana
Jinfa CaiUniversity of Delaware
Kyeong-Hwa LeeSeoul National University
Lianghuo FanUniversity of Southampton
Yoshinori ShimizuUniversity of Tsukuba
Chap Sam LimUniversiti Sains Malaysia
K. SubramaniamHomi Bhabha Centre for Science Education (TIFR), India
Information Age Publishing, Inc.
Charlotte, North Carolina • www.infoagepub.com
Copyright © 2015 IAP–Information Age Publishing, Inc.
All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted in any form or by any electronic or mechanical means, or byphotocopying, microfilming, recording or otherwise without written permission fromthe publisher.
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Advisory Board
Ahmet Arikan, Gazi University, TurkeyMarcelo Borba, São Paulo State University, Brazil
Jinfa Cai, University of DelawareLim Chapsam, Universiti Sains, Malaysia
Lyn English, Queensland University of Technology, AustraliaViktor Freiman, University of Moncton, CanadaSimon Goodchild, University of Agder, Norway
Gudbjorg Palsdottir, University of IcelandGuenter Toerner, University of Duisburg-Essen Germany
Doru Stefanescu, University of Bucharest, RomaniaK. Subramaniam, Homi Bhabha Centre for Science Education (TIFR), India
vii
CONTENTS
CHINA
1. Characterizing Mathematics Education in China:A Perspective on Improving Student LearningJinfa Cai and Stephen Hwang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
PART I. CULTURE, TRADITION, AND HISTORY
2. “Zhi Yì Xíng Nán (Knowing Is Easy and Doing Is Difficult)” or Vice Versa?—A Chinese Mathematician’s Observation on History and Pedagogy of Mathematics (HPM) ActivitiesMan-Keung Siu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
3. The Application of the History of Mathematicsin Mathematics Education in ChinaZezhong Yang and Jian Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
4. Cultural Roots, Traditions, and Characteristicsof Contemporary Mathematics Education in ChinaXuhui Li, Shiqi Li, and Dianzhou Zhang . . . . . . . . . . . . . . . . . . . . . 000
PART II. ASSESSMENT AND EVALUATION
5. Factors Affecting Mathematical Literacy Performanceof 15-Year-Old Students in Macao: The PISA PerspectiveKwok-Cheung Cheung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
6. Effect of Parental Involvement and Investmenton Mathematics Learning: What Hong KongLearned From PISAEsther Sui Chu Ho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
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7. Has Curriculum Reform Made a Difference in Classrooms? An Evaluation of the New Mathematics Curriculum in Mainland ChinaYujing Ni, Qiong Li, Jinfa Cai, Kit-Tai Hau . . . . . . . . . . . . . . . . . . . 000
PART III. CURRICULUM
8. The Evolution of Chinese Mathematics Textbooks for Primary and Secondary Schools in the 20th CenturyShi-hu Lv, Ting Chen, Aihui Peng, and Shangzhi Wang . . . . . . . . . . 000
9. Mathematics Curriculum and Teaching Materials in China from 1950–2000Jianyue Zhang, Wei Sun, and Arthur B. Powell . . . . . . . . . . . . . . . . . 000
10. Chinese Mathematics Curriculum Reformin the 21st Century: 2000-2010Jian Liu, Lidong Wang, Ye Sun, and Yiming Cao . . . . . . . . . . . . . . . 000
11. Basic Education Mathematics Curriculum Reform in the Greater Chinese Region—Trends and Lessons LearnedChi-Chung Lam, Ngai-Ying Wong, Rui Ding,Siu Pang Titus Li, Yun-Peng Ma . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
12. Early Algebra in Chinese Elementary Mathematics Textbooks: The Case of Inverse RelationsMeixia Ding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
13. Characterizing Chinese Mathematics Curriculum:A Cross-National Comparative PerspectiveLarry E. Suter and Jinfa Cai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
PART IV. MATHEMATICAL COGNITION
14. Promoting Young Children’s Mathematical Thinking: Operational Math in PreschoolZi-Juan Cheng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
15. Development of Mathematical Cognitionin Preschool ChildrenQingfen Hu and Jing Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
16. Contemporary Chinese Investigations of Cognitive Aspects of Mathematics LearningPing Yu, Wenhua Yu, and Yingfang Fu . . . . . . . . . . . . . . . . . . . . . . 000
17. Mathematical Processing and the Mathematical Brainin ChinaXinlin Zhou, Wei Wei, Chuansheng Chen, and Qi Dong . . . . . . . . . . . 000
Contents ix
18. Chinese Children’s Understandingof the Fraction ConceptZiqiang Xin and Chunhui Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
19. The Teaching and Learning of Number Sense in TaiwanDer-Ching Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
PART V. TEACHING AND TEACHER EDUCATION
20. Comparing U.S. and Chinese Teachers’Multidigit Division KnowledgeShuhua An, Zhonghe Wu, and Song A. An . . . . . . . . . . . . . . . . . . . . 000
21. Chinese Elementary Teachers' Mathematics Knowledge for Teaching: Roles of Subject Related Training, Mathematics Teaching Experience, and Current Curriculum Study in Shaping its QualityJian Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
22. Reviving Teacher Learning: Chinese Mathematics Teacher Professional Development in the Context of Educational ReformLynn W. Paine, Yanping Fang, and Heng Jiang . . . . . . . . . . . . . . . . 000
23. Problem Solving in Chinese Mathematics Education: Research and PracticeJinfa Cai, Bikai Nie, and Lijun Ye . . . . . . . . . . . . . . . . . . . . . . . . . . 000
24. Developing a Coding System for Video Analysis of Classroom InteractionYiming Cao, Chen He, and Liping Ding . . . . . . . . . . . . . . . . . . . . . . 000
25. Mathematical Discourse in Chinese Classrooms:An Insider’s PerspectiveIda Ah Chee Mok, Xinrong Yang, and Yan Zhu . . . . . . . . . . . . . . . . . 000
26. The Status Quo and Prospects for Research on Mathematics Education for Ethnic Minorities in ChinaHengjun Tang, Aihui Peng, Bifen Chen, Bo Yu,
Yanping Huang, and Naiqing Song . . . . . . . . . . . . . . . . . . . . . . . . . 000
27. Why Always Greener on the Other Side? The Complexity of Chinese and U.S. Mathematics EducationThomas E. Ricks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
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PART VI. TECHNOLOGY
28. SSP—A Chinese Software Application for the Teachingand Learning of Mathematics: Theoretical and Practical PerspectivesChunlian Jiang, Jingzhong Zhang, and Xicheng Peng . . . . . . . . . . . . 000
29. E-Learning in Mathematics EducationSiu Cheung Kong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
KOREA
30. Korean Research in Mathematics EducationKyeong-Hwa Lee, Jennifer M. Suh, Rae Young Kim,and Bharath Sriraman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
31. A Review of Philosophical Studies on Mathematics EducationJin Young Nam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
32. Mathematics CurriculumKyungmee Park . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
33. Mathematics TextbooksJeongSuk Pang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
34. Using the History of Mathematics to Teachand Learn MathematicsHyewon Chang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
35. Perspectives on Reasoning Instructionin the Mathematics EducationBo Mi Shin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
36. Mathematical ModelingYeong Ok Chong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
37. Gender and MathematicsEun Jung Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
38. Mathematics AssessmentGwi Soo Na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
39. Examining Key Issues in Research on Teacher Education Gooyeon Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
40. Trends in the Research of Teachers’ Beliefs About Mathematics EducationDong-Hwan Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
Contents xi
SINGAPORE
41. Research in Singapore Mathematics Education:An IntroductionLionel Mendoza, Swee Fong Ng, and Lianghuo Fan . . . . . . . . . . . . . 000
42. Mathematical Problem Solving Research Involving Students in Singapore Mathematics Classrooms (2001 to 2011): What’s Done and What More Can Be DoneChun Ming Eric Chan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
43. Research on Singapore Mathematics Curriculumand Textbooks: Searching for Reasons behind Students’ Outstanding PerformanceYan Zhu and Lianghuo Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
44. Teachers’ Assessment Literacy and Student Learningin Singapore Mathematics Classrooms Kim Hong Koh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
45. A Theoretical Framework for Understanding the Different Attention Resource Demands of Letter-Symbolic Versus Model MethodSwee Fong NG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
46. A Multidimensional Approach to Understandingin Mathematics among Grade 8 Students in SingaporeKok Leong Boey, Shaljan Areepattamannil,and Berinderjeet Kaur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
MALAYSIA
47. Introduction to Malaysian ChaptersLim Chap Sam, Kor Liew Kee, Chew Cheng Meng,and Bharath Sriraman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
48. Mathematics Education Research in Malaysia: An OverviewChap Sam Lim, Parmjit Singh, Liew Kee Kor,and Cheng Meng Chew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
49. Research Studies in the Learning and Understandingof Mathematics: A Malaysian ContextParmjit Singh and Teoh Sian Hoon . . . . . . . . . . . . . . . . . . . . . . . . . 000
50. Numeracy Studies in Malaysia Munirah Ghazali and Abdul Razak Othman . . . . . . . . . . . . . . . . . . . 000
xii CONTENTS
51. Malaysian Research in Geometry Cheng Meng Chew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
52. Research in Mathematical Thinking in Malaysia:Some Issues and SuggestionsShafia Abdul Rahman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
53. Studies About Values in Mathematics Teachingand Learning in MalaysiaSharifah Norul Akmar Syed Zamri and Mohd Uzi Dollah . . . . . . . . . . 000
54. Transformation of School Mathematics AssessmentTee Yong Hwa, Chap Sam Lim, and Ngee Kiong Lau . . . . . . . . . . . . 000
55. Mathematics Incorporating Graphics Calculator Technology in MalaysiaLiew Kee Kor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
56. Mathematics Teacher Professional Developmentin MalaysiaChin Mon Chiew, Chap Sam Lim, and Ui Hock Cheah . . . . . . . . . . . 000
JAPAN
57. Mathematics Education Research in Japan:An IntroductionYoshinori Shimizu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
58. A Historical Perspective on Mathematics Education Research in JapanNaomichi Makinae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
59. The Development of Mathematics Educationas a Research Field in JapanYasuhiro Sekiguchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
60. Research on Proportional Reasoning in the Japanese ContextKeiko Hino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
61. Japanese Students’ Understanding of School Algebra: Algebra, Literal Symbols, and Quasi-VariablesToshiakira Fujii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
62. Proving as an Explorative Activity in Mathematics Education: New Trends in Japanese Research Into ProofMikio Miyazaki and Taro Fujita . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
63. Developments in Research on Mathematical Problem Solving in JapanKazuhiko Nunokawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
Contents xiii
64. Teaching and Learning Mathematics With Information and Communication Technology in Japan:The Case of Geometric ConstructorYasuyuki Iijima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
65. “Inner Teacher”: The Role of Metacognitionand Its Implication to Improving Classroom PracticeKeiichi Shigematsu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
66. Cross-Cultural Studies of Mathematics Classroom PracticesYoshinori Shimizu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
67. Systematic Support of Life-Long Professional Development for Teachers through Lesson StudyAkihiko Takahashi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
INDIA
68. Introduction to the India SectionK. Subramaniam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
69. Evolving Concerns Around Mathematicsas a School Discipline: Curricular Vision, Educational Policy and the National Curriculum Framework (2005)Farida Abdulla Khan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
70. The School Mathematics Project: An Accountof a Mathematics Curriculum Development ProjectAmitabha Mukherjee and Vijaya S. Varma . . . . . . . . . . . . . . . . . . . . . 000
71. Intervening for Number Sense in Primary MathematicsUsha Menon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
72. Some Ethical Concerns in Designing the Upper Primary Mathematics Curriculum: A Report From the FieldJayasree Subramanian, Mohammed Umar, and Sunil Verma . . . . . . . 000
73. Students’ Understanding of Algebraand Curriculum ReformRakhi Banerjee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
74. Professional Development Workshops for In-Service Mathematics Teachers in IndiaRuchi S. Kumar, K. Subramaniam, and Shweta Naik . . . . . . . . . . . . . 000
75. Insights Into Students’ Errors Based on DataFrom Large Scale AssessmentsAaloka Kanhere, Anupriya Gupta, and Maulik Shah . . . . . . . . . . . . . 000
xiv CONTENTS
76. Assessment of Mathematical Learning—Issues and ChallengesShailesh Shirali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
77. Opportunities for Using Technology in Mathematics ClassroomsJonaki Ghosh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
78. Mathematics Education in Precolonialand Colonial South IndiaD. Senthil Babu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000
79. Representations of Numbers and the Indian Mathematical Tradition of Combinatorial ProblemsRaja Sridharan and K. Subramaniam . . . . . . . . . . . . . . . . . . . . . . . 000