Mathematics Education – An Asian Perspective Dacheng Zhao Chinese Students’ Higher Achievement in Mathematics Comparison of Mathematics Education of Australian and Chinese Primary Schools – Mathematics Education An Asian Perspective Series editors Berinderjeet Kaur, National Institute of Education, Singapore, Singapore Catherine Vistro-Yu, Ateneo de Manila University, Manila, Philippines Aims and Scope MathematicsEducation–AnAsianPerspectivefacilitateshighqualitypublications on rigorous aspects of mathematics education in Asia. This will be achieved by producing thematic books that capture knowledge and practices on mathematics educationinAsia fromboth theinsider and outsider perspectives.The series helps toestablishamuchneededAsianperspectivetomathematicseducationresearchin the international landscape. Over the last decade or so, several international comparative studies have shed light on systems of schooling that were otherwise not very much sought after. Several educational systems in Asia, in particular East Asia have consistently produced stellar outcomes for mathematics in both TIMSS and PISA despite the factthatbothstudiesmeasureachievementinmathematicsindistinctwaysthatare verymuchorthogonaltoeachother,whileotherAsiansystemshavenotbeenable toreplicatethesamelevelofsuccess.Thoughonemayoccasionallychanceupona publicationonsomeaspectofmathematicseducationinAsia,thereappearstobein general a dearth ofpublications on mathematics educationinAsian countries from theperspectivesofscholarsfromAsia.Henceitisapparentthatthereisagapinthe availability of knowledge on mathematics education from the region in the international space. This series has a wide scope with emphasis on relevancy and timeliness. It encompassesthegeneraltrendsineducationalresearchsuchastheory,practiceand policy.Booksintheseriesarethematicandfocusbothonmacroandmicrotopics. An example of a themed book on a macro topic could be one on “School mathematic curricula – An Asian perspective” while a themed book on a micro topic could be one on “The pedagogy of ‘simultaneous equations’ in Asian classrooms”. More information about this series at http://www.springer.com/series/11679 Dacheng Zhao ’ Chinese Students Higher Achievement in Mathematics Comparison of Mathematics Education of Australian and Chinese Primary Schools 123 DachengZhao Aussie-Sino Studies Kingswood, NSW Australia ISSN 2366-0155 ISSN 2366-0163 (electronic) Mathematics Education– An AsianPerspective ISBN978-981-10-0283-0 ISBN978-981-10-0285-4 (eBook) DOI 10.1007/978-981-10-0285-4 LibraryofCongressControlNumber:2015958538 ©SpringerScience+BusinessMediaSingapore2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerScience+BusinessMediaSingaporePteLtd. Preface Why do Chinese students outperform their Western peers in mathematics? This book explores this challenging question and is based on the international comparativestudiesrelatingtostudents’achievementsinmathematics,whichhave found that students from Mainland China, Hong Kong, and Taiwan consistently outperform their Western counterparts. A most recent example is provided by Program for International Student Assessment (PISA) 2012. Results of this study, which includes about 510,000 students aged 15 from 65 countries and economies, who took part in mathematics literacy assessments, showed that students from China’s Shanghai achieved the highest score, followed by students of Singapore, HongKong,andTaipeiscoringhigherthaneveryothercountryincludingstudents fromAustralia.Overtheyears,therehasbeenconsiderableinterestwithinthefield of mathematics education in identifying the underlying factors that might account for this mathematics achievement gap between the Chinese students and their Western counterparts. This book reports a study, which compares mathematics education in primary schools in Australia and in China investigating factors that accounting for Chinese students’ high achievement in mathematics. This manuscript is composed of ten chapters. Chapter 1 gives the reader a background to the study, a description of the achievement gap, the purpose of the research, key terms used, and other interrelated research questions. Chapter 2 provides an extensive review of literature on the topic of comparative studies of mathematicsachievementandoffersarobustresearchframeworkforthestudy.The expose of research design as well as methodology is presented in Chap. 3. Chapters4and5presentanoverviewoftheeachcountry’seducationalpoliciesof mathematics education through an analysis of major mathematics curricula and assessment documents of both countries. Similarities and differences of policies of mathematics curriculum and assessment between China and Australia are painstakingly described in Chap. 6. Three case studies on how these policies of mathematics curriculum and assessment have been implemented in Australian and ChineseprimaryschoolsarereportedinChaps.7–9.Mathematicseducationoftwo primary schools in Australia is compared in Chap. 8, and a comprehensive v vi Preface comparison of mathematics education among three cases is summarized in the last chapter.Chapter10discussesthemainfindingsofthestudy,providingatheoretical account to explain the findings and how they are related to the mathematics achievement gap. Also discussed are implications of these findings to curriculum and assessment reform both in Australia and in China. This book is a very useful reference book to researchers and to higher-degree research students who enrolled in international comparative studies and mathe- maticseducation.Itcanbequiteaninstructivebookforschoolteachers,university lecturers, and instructors in mathematics, especially to teach students whose first language may not be English or with different cultural backgrounds. Evenparents, showing aninterest inreadingthis book, canimprovetheirunderstanding ofthose factors impinging on their children’s learning in general and on their children’s achievement in mathematics in particular. Contents 1 Introduction: Chinese Students Outperform in Mathematics . . . . . 1 1.1 Background to the Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Statement of the Research Problem. . . . . . . . . . . . . . . . . . . . . 3 1.3 The Purpose of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Definitions: Key Terms of the Study. . . . . . . . . . . . . . . . . . . . 7 1.5 Research Questions and Structure of the Book. . . . . . . . . . . . . 8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Review of the Literature: Factors Contributing to Achievement GAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1 A Rationale for Comparative Education . . . . . . . . . . . . . . . . . 14 2.1.1 The Nature of Comparative Education. . . . . . . . . . . . 14 2.1.2 The Importance of Comparative Studies . . . . . . . . . . 14 2.1.3 The Purpose of Comparative Education. . . . . . . . . . . 15 2.2 Comparative Studies on Mathematics Achievement . . . . . . . . . 17 2.2.1 IEA Studies on Mathematics Achievement. . . . . . . . . 17 2.2.2 Other Comparatives Studies on Mathematics Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2.3 Key Findings of Comparative Studies. . . . . . . . . . . . 27 2.3 Factors Contributing to the ‘Achievement Gap’ . . . . . . . . . . . . 27 2.3.1 Cultural Context. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Teachers’ Mathematics Knowledge. . . . . . . . . . . . . . 30 2.3.3 Classroom Teaching . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.4 Out-of-School Curricula . . . . . . . . . . . . . . . . . . . . . 34 2.3.5 Standards and Content of Curriculum . . . . . . . . . . . . 35 2.3.6 Form and Content of Assessment. . . . . . . . . . . . . . . 36 2.4 Strengths and Limitations of Current Comparative Studies. . . . . 37 2.4.1 Research Frameworks. . . . . . . . . . . . . . . . . . . . . . . 37 2.4.2 Limitations in Methods. . . . . . . . . . . . . . . . . . . . . . 38 vii viii Contents 2.5 The Relationship Between Teaching, Learning, and Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6 A Tentative Model for the Study . . . . . . . . . . . . . . . . . . . . . . 42 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3 Research Methodology: Exploring Research Questions. . . . . . . . . . 49 3.1 Research Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.1 Document Analyses . . . . . . . . . . . . . . . . . . . . . . . . 50 3.1.2 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1.3 Case Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 Instruments for Data Collection . . . . . . . . . . . . . . . . . . . . . . . 54 3.2.1 Classroom Observation . . . . . . . . . . . . . . . . . . . . . . 54 3.2.2 Semi-structured Interviews. . . . . . . . . . . . . . . . . . . . 56 3.2.3 Analyses of Student Work Samples or Examination Papers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 The Pilot Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3.1 A Pilot Study in Sydney . . . . . . . . . . . . . . . . . . . . . 60 3.3.2 A Pilot Study in Guangzhou . . . . . . . . . . . . . . . . . . 61 3.4 Data Analysis and Reporting. . . . . . . . . . . . . . . . . . . . . . . . . 61 3.4.1 Analysis and Reporting of Data from Documents. . . . 61 3.4.2 Analysis and Reporting of Data from the Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.5 The Validity, Reliability, and Ethics of the Study. . . . . . . . . . . 62 3.5.1 Validity and Reliability. . . . . . . . . . . . . . . . . . . . . . 63 3.5.2 Ethics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4 Document Analysis of Australian Mathematics Curricula and Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1 Documents at National Level. . . . . . . . . . . . . . . . . . . . . . . . . 68 4.1.1 ANationalStatementonMathematicsforAustralian Schools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.1.2 Mathematics: A Curriculum Profile for Australian Schools. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.1.3 National Numeracy Policy and Benchmarks. . . . . . . . 73 4.2 NSW Mathematics Curriculum Documents . . . . . . . . . . . . . . . 77 4.2.1 Mathematics K-6 . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.2 The Statewide Testing Programs. . . . . . . . . . . . . . . . 80 4.2.3 Mathematics K-6: Outcomes and Indicators. . . . . . . . 82 4.2.4 Principles and Strategies for Assessment in NSW Primary Schools. . . . . . . . . . . . . . . . . . . . . 86 4.2.5 Assessment in K-6 Mathematics Support Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.2.6 Documents and Programs Related to State Numeracy Policies . . . . . . . . . . . . . . . . . . . . . . . . . 90 Contents ix 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5 Document Analysis of Chinese Mathematics Curricula and Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.1 The Curriculum Scheme for Nine-Year Compulsory Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.1.1 Aims of Education in China. . . . . . . . . . . . . . . . . . . 98 5.1.2 Key Learning Areas and Time Allocation . . . . . . . . . 99 5.1.3 Key Content Areas Within Mathematics . . . . . . . . . . 99 5.1.4 The Principles Underpinning Chinese Mathematics Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.1.5 Important Factors Influencing Mathematics Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.1.6 Assessment and Evaluation . . . . . . . . . . . . . . . . . . . 102 5.2 National Mathematics Curriculum Standards for Compulsory Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2.1 Mathematics Curriculum Objectives . . . . . . . . . . . . . 103 5.2.2 The Structure and Content of Mathematical Knowledge and Skills. . . . . . . . . . . . . . . . . . . . . . . 106 5.2.3 Standards Related to Content and Stage. . . . . . . . . . . 106 5.2.4 Assessment Requirements . . . . . . . . . . . . . . . . . . . . 106 5.2.5 Key Principles Underlying the Standards. . . . . . . . . . 110 5.3 The Mathematics Syllabus for Primary Schools . . . . . . . . . . . . 111 5.3.1 The Objectives of Mathematics Teaching. . . . . . . . . . 111 5.3.2 Guidelines for Assessment. . . . . . . . . . . . . . . . . . . . 112 5.3.3 The Content Scope and Sequence. . . . . . . . . . . . . . . 112 5.3.4 The Revision of the Syllabus. . . . . . . . . . . . . . . . . . 112 5.4 Chinese Mathematics Textbooks for Primary Schools. . . . . . . . 116 5.4.1 Some Features of Chinese Mathematics Textbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.4.2 The Content of Chinese Mathematics Textbooks . . . . 117 5.4.3 The Structure of Textbooks . . . . . . . . . . . . . . . . . . . 118 5.4.4 The Organization of Content . . . . . . . . . . . . . . . . . . 120 5.4.5 Teaching and Learning Units. . . . . . . . . . . . . . . . . . 123 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 6 A Comparison of Australian and Chinese Mathematics Curricula and Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 6.1 Common Trends in Reform in Mathematics Curricula. . . . . . . . 127 6.2 A Rationale for Mathematics Curricula. . . . . . . . . . . . . . . . . . 129 6.2.1 The Nature and Role of Mathematics . . . . . . . . . . . . 129 6.2.2 Key Principles of Teaching and Learning . . . . . . . . . 130 6.2.3 Common Features. . . . . . . . . . . . . . . . . . . . . . . . . . 131