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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Hardcover:

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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

viii CONTENTS

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

x CONTENTS

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