Chinese Students' Higher Achievement in Mathematics: Comparison of Mathematics Education of Australian and Chinese Primary Schools

310 Pages·2016·6.67 MB·English

by  Dacheng Zhao (auth.)

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
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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