Abstracts of The First Sourcebook on Asian Research

in Mathematics Education: China, Korea, Singapore, Japan,

Malaysia, and India

Special Supplement to the

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 (2012)

Edited by Bharath Sriraman, Jinfa Cai, Kyeong-Hwa Lee, Fan Lianghuo, Yoshinori Shimuzu, Lim Chap Sam, 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 2012)edited by Bharath Sriraman, Constantinos Christou, Roza Leikin, Ahmet

Arikan, Constantinos Tzakanis, and Anjum Halai

Abstracts of The First Sourcebook on 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

Fan LianghuoUniversity of Southampton

Yoshinori ShimuzuUniversity of Tsukuba

Lim Chap SamUniversiti Sains Malaysia

K. SubramaniamTata Institute of Fundamental Research, India

Information Age Publishing, Inc.

Charlotte, North Carolina • www.infoagepub.com

Copyright © 2012 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.

Printed in the United States of America

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, Tata Institute of Fundamental Research, Mumbai, India

vii

CONTENTS

CHINA

PART I:

CULTURE, TRADITION, AND HISTORY

1. “Zhi Yì Xíng Nán (Knowing Is Easy and Doing Is Difficult)” or Vice Versa? A Chinese Mathematician’s Observationon History and Pedagogy of Mathematics ActivitiesMan-Keung Siu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

2. The Study on Application of Mathematics Historyin Mathematics Education in China 7Zezhong Yang and Jian Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

3. Cultural Roots, Traditions, and Characteristics of Contemporary Mathematics Education in ChinaDianzhou Zhang, Shiqi Li, and Xuhui Li . . . . . . . . . . . . . . . . . . . . . 000

PART II:

ASSESSMENT AND EVALUATION

4. Factors Affecting Mathematical Literacy Performance of 15-Year-Old Students in Macao: The PISA PerspectiveKwok-Cheung Cheung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

5. Has Curriculum Reform Made A Difference in the Classroom? An Evaluation of the New MathematicsCurriculum in Mainland ChinaYujing Ni, Qiong Li, Jinfa Cai, and Kit-Tai Hau . . . . . . . . . . . . . . . . 000

viii CONTENTS

PART III: CURRICULUM

6. Early Algebra in Chinese Elementary Mathematics Textbooks: The Case of Inverse OperationsMeixia Ding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

7. The Development of Chinese Mathematics Textbooksfor Primary and Secondary Schools Since the Twentieth CenturyShi-hu Lv, Ting Chen, Aihui Peng, and Shangzhi Wang . . . . . . . . . . 000

8. Mathematics Curriculum and Teaching Materials in China from 1950–2000Jianyue Zhang, Wei Sun, and Arthur B. Powell . . . . . . . . . . . . . . . . . 000

9. Chinese Mathematics Curriculum Reform in the Twenty-First Century: 2000-2010Jian Liu, Lidong Wang, Ye Sun, and Yiming Cao

10. 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, and Yun-Peng Ma . . . . . . . . . . . . . . . . . . . . . . . . 000

PART IV:

MATHEMATICAL COGNITION 29

11. Promoting Young Children’s Development of Logico-Math Thinking Through Addition, Subtraction, Multiplication and Division in Operational MathZi-Juan Cheng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

12. Developmentof Mathematical Cognition in PreSchool Children 33Qingfen Hu and Jing Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

13. Chinese Children’s Understanding of Fraction ConceptZiqiang Xin and Chunhui Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

14. Teaching and Learning of Number Sense in TaiwanDer-Ching Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

15. Chinese Contemporary Investigations of Mathematical Cognitive LearningPing Yu, Wenhua Yu, and Yingfang Fu . . . . . . . . . . . . . . . . . . . . . . 000

16. Chinese Mathematical Processing and Mathematical BrainXinlin Zhou, Wei Wei, Chuansheng Chen, and Qi Dong . . . . . . . . . . . 000

Contents ix

PART V:

TEACHING AND TEACHER EDUCATION

17. Comparing Teachers’ Knowledge on Multidigit Division Between the United States and ChinaShuhua An and Song A. An . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

18. Problem Solving in Chinese Mathematics Education: Research and PracticeJinfa Cai and Bikai Nie and Lijun Ye . . . . . . . . . . . . . . . . . . . . . . . . 000

19. Developing a Coding System for Video Analysis of Classroom InteractionYiming Cao, Chen He, and Liping Ding . . . . . . . . . . . . . . . . . . . . . . 000

20. Teaching Mathematics Through Problem Solving in Alternative Solution Methods: An Exploratory StudyShin-Yi Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

21. Mathematical Problem-Posing Instruction: From Research-Based Tasks, Teachers’ Professional Growth to Students’ LearningShuk-kwan S. Leung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

22. Mathematical Discourse in Chinese Classrooms:An Insider’s PerspectiveIda Ah Chee Mok, Xinrong Yang, and Yan Zhu . . . . . . . . . . . . . . . . . 000

23. Reviving Teacher Learning: Chinese Mathematics Teacher Professional Development in the Context of Educational Reform 57Lynn W. Paine, Yanping Fang, and Heng Jiang . . . . . . . . . . . . . . . . 000

24. The Status Quo and Prospect of Research on Mathematics Education for Ethnic Minorities in ChinaTang Hengjun, Peng Aihui, Chen Bifen, Yu Bo,

Huang Yanping, and Song Naiqing . . . . . . . . . . . . . . . . . . . . . . . . . 000

25. Achieving Instructional Coherence in Classroom Instruction: A Discourse PerspectiveTao Wang and Jinfa Cai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

26. Chinese Elementary Teachers’ Mathematics Knowledge for Teaching: Role of Subject Related Training, Mathematic Teaching Experience, and Current Curriculum Study in Shaping Its QualityJian Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

x CONTENTS

27. Why Always Greener on the Other Side?: The Complexity of Chinese and U.S. Mathematics EducationThomas E. Ricks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

PART VI:

TECHNOLOGY

28. A Chinese Software SSP for the Teaching and 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 TextbooksJeong Suk Pang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

34. Using the History of Mathematics to Teach and Learn MathematicsHye Won Chang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

35. Perspectives on Reasoning Instruction in the Mathematics EducationBo Mi Shin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

36. Mathematical Modeling Yeong Ok Chong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

37. Gender and MathematicsEun Jung Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

38. Mathematics AssessmentGwi Soo Na . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

39. Examining Key Issues in Research on Teacher EducationGoo Yeon Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

Contents xi

40. Trends in the Research of Teachers’ Beliefs About Mathematics EducationDong-Hwan Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

SINGAPORE

41. Mathematical Problem Solving Research Involving Students in Singapore Mathematics Classrooms (2001 to 2011): What Is Done and What More Can Be DoneChan Chun Ming Eric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

42. Research on Singapore Mathematics Curriculum and Textbooks: Searching for Reasons BehindStudents’ Outstanding PerformanceYan Zhu and Lianghuo Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

43. Teachers’ Assessment Literacy and Student Learningin Singapore Mathematics ClassroomsKim Hong Koh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

44. A Theoretical Framework for Understanding the Different Attention Resource Demands of Letter-Symbolic Versus Model MethodSwee Fong Ng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

45. A Multidimensional Approach to Understanding in Mathematics Among Grade 8 Students in SingaporeBoey Kok Leong, Shaljan Areepattamannil, and Berinderjeet Kaur . . . 000

MALAYASIA

46. Mathematics Education Research in Malaysia: An OverviewChap Sam Lim, Parmjit Singh, Liew Kee Kor,and Cheng Meng Chew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

47. Research Studies in the Learning and Understandingof Mathematics: A Malaysian ContextParmjit Singh and Teoh Sian Hoon . . . . . . . . . . . . . . . . . . . . . . . . . 000

48. Numeracy Studies in MalaysiaMunirah Ghazali and Abdul Razak Othman . . . . . . . . . . . . . . . . . . . 000

49. Malaysian Research in GeometryCheng Meng Chew . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

xii CONTENTS

50. Research in Mathematical Thinking in Malaysia: Some Issues and SuggestionsShafia Abdul Rahman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

51. Studies About Values in Mathematics Teaching and Learning in MalaysiaSharifah Norul Akmar Syed Zamri and Mohd Uzi Dollah . . . . . . . . . . 000

52. Transformation of School Mathematics AssessmentTee Yong Hwa, Chap Sam Lim, and Ngee Kiong Lau . . . . . . . . . . . . 000

53. Mathematics Incorporating Graphics Calculator Technology in MalaysiaLiew Kee Kor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

54. Mathematics Teacher Professional Development in MalaysiaChin Mon Chiew, Chap Sam Lim, and Ui Hock Cheah . . . . . . . . . . . . 000

JAPAN

55. Mathematics Education Research in Japan:An IntroductionYoshinori Shimizu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

56. A Historical Perspective on Mathematics Education Research in Japan 137Naomichi Makinae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

57. The Development of Mathematics Education as a Research Field in JapanYasuhiro Sekiguchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

58. Research on Proportional Reasoning in Japanese ContextKeiko Hino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

59. Learning Algebra and Use of Literal SymbolsToshiakira Fujii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

60. Proving as an Explorative Activity in Mathematics Education 151Mikio Miyazaki and Taro Fujita . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

61. Developments in Research on Mathematical Problem Solving in Japan 155Kazuhiko Nunokawa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

62. Research on Teaching and Learning Mathematics With Information and Communication TechnologyYasuyuki Iijima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

Contents xiii

63. “Inner Teacher”: The Role of Metacognition in Learning Mathematics and Its Implication to Improving Classroom PracticeKeiichi Shigematsu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

64. Cross-cultural Studies on Mathematics Classroom Practices Yoshinori Shimizu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

65. Systematic Support of Life-Long Professional Development for Teachers Through Lesson Study 169Akihiko Takahashi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

INDIA

66. Evolving Concerns Around Mathematics as a School Discipline: Curricular Vision, Classroom Practice and the National Curriculum Framework (2005)Farida Abdulla Khan and Jamia Millia Islamia . . . . . . . . . . . . . . . . . 000

67. Curriculum Development in Primary Mathematics: The School Mathematics ProjectAmitabha Mukherjee and Vijaya S. Varma . . . . . . . . . . . . . . . . . . . . . 000

68. Intervening for Number Sense in Primary MathematicsUsha Menon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

69. Some Ethical Concerns in Designing Upper Primary Mathematics curriculum: A report From the Field 193Jayasree Subramanian, Sunil Verma, and Mohd.Umar . . . . . . . . . . . . 000

70. Students’ Understanding of Algebra and Curriculum ReformRakhi Banerjee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

71. Professional Development of In-Service Mathematics Teachers in IndiaRuchi S. Kumar, K. Subramaniam, and Shweta Naik . . . . . . . . . . . . . 000

72. Insights Into Students’ Errors Based on DataFrom Large-Scale Assessments Aaloka Kanhere, Anupriya Gupta, and Maulik Shah . . . . . . . . . . . . . 000

73. Assessment of Mathematical Learning: Issues and ChallengesShailesh Shirali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

74. Technology and Mathematics Education: Issues and ChallengesJonaki B. Ghosh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

xiv CONTENTS

75. Mathematics Education in Precolonialand Colonial South IndiaSenthil Babu. D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 000

76. Representations of Numbers in the Indian Mathematical Tradition of Combinatorial ProblemsRaja Sridharan and K. Subramaniam . . . . . . . . . . . . . . . . . . . . . . . . 000