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

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Chinese Students' Higher Achievement in Mathematics: Comparison of Mathematics Education of Australian and Chinese Primary SchoolsSuurem pilt
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This book shares insights into the achievement gap in mathematics between East Asian and Western countries, and the ways to improve students’ mathematics achievements. Especially, it highlights the importance to integrate case studies with large-scale international comparative studies in general, and comparative studies of mathematics education in particular. This book is a must-read for mathematics teachers, mathematics educators, educational researchers, education administrators, curriculum developers, assessment designers, and student teachers who are interested in mathematics education and how to improve students’ mathematics achievements.
1 Introduction: Chinese Students Outperform in Mathematics
1(12)
1.1 Background to the Study
2(1)
1.2 Statement of the Research Problem
3(3)
1.3 The Purpose of the Study
6(1)
1.4 Definitions: Key Terms of the Study
7(1)
1.5 Research Questions and Structure of the Book
8(5)
References
9(4)
2 Review of the Literature: Factors Contributing to Achievement GAP
13(36)
2.1 A Rationale for Comparative Education
14(3)
2.1.1 The Nature of Comparative Education
14(1)
2.1.2 The Importance of Comparative Studies
14(1)
2.1.3 The Purpose of Comparative Education
15(2)
2.2 Comparative Studies on Mathematics Achievement
17(10)
2.2.1 IEA Studies on Mathematics Achievement
17(6)
2.2.2 Other Comparatives Studies on Mathematics Achievement
23(4)
2.2.3 Key Findings of Comparative Studies
27(1)
2.3 Factors Contributing to the `Achievement Gap'
27(10)
2.3.1 Cultural Context
28(2)
2.3.2 Teachers' Mathematics Knowledge
30(2)
2.3.3 Classroom Teaching
32(2)
2.3.4 Out-of-School Curricula
34(1)
2.3.5 Standards and Content of Curriculum
35(1)
2.3.6 Form and Content of Assessment
36(1)
2.4 Strengths and Limitations of Current Comparative Studies
37(3)
2.4.1 Research Frameworks
37(1)
2.4.2 Limitations in Methods
38(2)
2.5 The Relationship Between Teaching, Learning, and Assessment
40(2)
2.6 A Tentative Model for the Study
42(7)
References
44(5)
3 Research Methodology: Exploring Research Questions
49(18)
3.1 Research Approach
49(5)
3.1.1 Document Analyses
50(1)
3.1.2 Case Studies
51(1)
3.1.3 Case Selection
52(2)
3.2 Instruments for Data Collection
54(5)
3.2.1 Classroom Observation
54(2)
3.2.2 Semi-structured Interviews
56(3)
3.2.3 Analyses of Student Work Samples or Examination Papers
59(1)
3.3 The Pilot Study
59(2)
3.3.1 A Pilot Study in Sydney
60(1)
3.3.2 A Pilot Study in Guangzhou
61(1)
3.4 Data Analysis and Reporting
61(1)
3.4.1 Analysis and Reporting of Data from Documents
61(1)
3.4.2 Analysis and Reporting of Data from the Case Studies
62(1)
3.5 The Validity, Reliability, and Ethics of the Study
62(5)
3.5.1 Validity and Reliability
63(1)
3.5.2 Ethics
64(1)
References
65(2)
4 Document Analysis of Australian Mathematics Curricula and Assessment
67(30)
4.1 Documents at National Level
68(9)
4.1.1 A National Statement on Mathematics for Australian Schools
68(4)
4.1.2 Mathematics: A Curriculum Profile for Australian Schools
72(1)
4.1.3 National Numeracy Policy and Benchmarks
73(4)
4.2 NSW Mathematics Curriculum Documents
77(14)
4.2.1 Mathematics K-6
78(2)
4.2.2 The Statewide Testing Programs
80(2)
4.2.3 Mathematics K-6: Outcomes and Indicators
82(4)
4.2.4 Principles and Strategies for Assessment in NSW Primary Schools
86(2)
4.2.5 Assessment in K-6 Mathematics Support Document
88(2)
4.2.6 Documents and Programs Related to State Numeracy Policies
90(1)
4.3 Summary
91(6)
References
92(5)
5 Document Analysis of Chinese Mathematics Curricula and Assessment
97(30)
5.1 The Curriculum Scheme for Nine-Year Compulsory Education
98(5)
5.1.1 Aims of Education in China
98(1)
5.1.2 Key Learning Areas and Time Allocation
99(1)
5.1.3 Key Content Areas Within Mathematics
99(1)
5.1.4 The Principles Underpinning Chinese Mathematics Curriculum
100(1)
5.1.5 Important Factors Influencing Mathematics Curriculum
101(1)
5.1.6 Assessment and Evaluation
102(1)
5.2 National Mathematics Curriculum Standards for Compulsory Education
103(8)
5.2.1 Mathematics Curriculum Objectives
103(3)
5.2.2 The Structure and Content of Mathematical Knowledge and Skills
106(1)
5.2.3 Standards Related to Content and Stage
106(1)
5.2.4 Assessment Requirements
106(4)
5.2.5 Key Principles Underlying the Standards
110(1)
5.3 The Mathematics Syllabus for Primary Schools
111(5)
5.3.1 The Objectives of Mathematics Teaching
111(1)
5.3.2 Guidelines for Assessment
112(1)
5.3.3 The Content Scope and Sequence
112(1)
5.3.4 The Revision of the Syllabus
112(4)
5.4 Chinese Mathematics Textbooks for Primary Schools
116(9)
5.4.1 Some Features of Chinese Mathematics Textbooks
116(1)
5.4.2 The Content of Chinese Mathematics Textbooks
117(1)
5.4.3 The Structure of Textbooks
118(2)
5.4.4 The Organization of Content
120(3)
5.4.5 Teaching and Learning Units
123(2)
5.5 Summary
125(2)
References
126(1)
6 A Comparison of Australian and Chinese Mathematics Curricula and Assessment
127(20)
6.1 Common Trends in Reform in Mathematics Curricula
127(2)
6.2 A Rationale for Mathematics Curricula
129(3)
6.2.1 The Nature and Role of Mathematics
129(1)
6.2.2 Key Principles of Teaching and Learning
130(1)
6.2.3 Common Features
131(1)
6.3 Objectives of Mathematics Curricula
132(2)
6.4 Key Content of Mathematics Curricula
134(8)
6.4.1 Number
134(3)
6.4.2 Measurement
137(2)
6.4.3 Space and Geometry
139(1)
6.4.4 Other Content
139(3)
6.5 Intended Assessment
142(5)
6.5.1 Principles of Assessment
142(1)
6.5.2 The Nature and Purpose of Assessment
143(1)
6.5.3 Suggested Strategies for Assessment
143(1)
6.5.4 Other Assessment Issues
144(1)
References
145(2)
7 Case Study of Sydney Primary School A1, Australia
147(38)
7.1 Background Information on School A1
147(3)
7.1.1 Rationale: School A1
148(1)
7.1.2 Key Policies of the School
148(1)
7.1.3 The School Curriculum
149(1)
7.1.4 Outcomes-Based Approach to Teaching and Learning
149(1)
7.2 Mathematics Teaching and Assessment Practices
150(7)
7.2.1 General Description of Mathematics Teaching and Assessment
150(3)
7.2.2 An Exemplary Mathematics Lesson: Year 6
153(4)
7.3 Students' Mathematics Work Samples
157(8)
7.3.1 Work Samples Related to Number
157(3)
7.3.2 Work Samples Related to Measurement
160(2)
7.3.3 Work Samples Related to Space
162(3)
7.4 Teachers' Views of Mathematics Teaching and Assessment
165(12)
7.4.1 The Interviewees
165(2)
7.4.2 Interviewees' Beliefs About Mathematics Assessment
167(1)
7.4.3 The Content of Assessment
168(1)
7.4.4 Methods of Assessment
169(1)
7.4.5 The Frequency of Assessment
170(1)
7.4.6 Recording and Reporting of Assessment
171(2)
7.4.7 Reliability and Validity
173(1)
7.4.8 Factors Influencing Assessment Practice
174(3)
7.5 Parents' Views on Mathematics Learning and Assessment
177(5)
7.5.1 Interviewees' Backgrounds
177(1)
7.5.2 Parents' Attitudes Toward Academic Achievement
177(2)
7.5.3 Parents' Views on Students' After-School Learning
179(1)
7.5.4 Parents' Perspectives on Mathematics Teaching and Assessment
180(2)
7.6 Summary
182(3)
Reference
183(2)
8 Case Study of Sydney Primary School A2, Australia
185(28)
8.1 Background Information on School A2
185(3)
8.1.1 Rationale: School A2
186(1)
8.1.2 Key Policies of the School
186(1)
8.1.3 The School Curriculum
186(1)
8.1.4 School Policies Related to Mathematics Assessment and Reporting
187(1)
8.2 Classroom Observations
188(3)
8.2.1 General Impressions of the Mathematics Classrooms
188(1)
8.2.2 Count Me in Too Classroom Practices
189(2)
8.3 Analyses of Assessment Using the SENA
191(2)
8.4 Teachers' Views of Mathematics Teaching and Assessment
193(13)
8.4.1 The Interviewees
193(3)
8.4.2 Interviewees' Beliefs About Mathematics Assessment
196(1)
8.4.3 The Content of Teaching and Assessment
197(1)
8.4.4 Methods of Mathematics Assessment
198(2)
8.4.5 The Frequency of Assessment
200(1)
8.4.6 Recording and Reporting of Assessment
201(1)
8.4.7 Reliability and Validity
202(1)
8.4.8 Factors Influencing Assessment Practices
203(3)
8.5 Parents' Views of Mathematics Learning and Assessment
206(3)
8.5.1 Interviewees' Background
206(1)
8.5.2 Parents' Attitudes Toward Academic Achievement
207(1)
8.5.3 Parents' Views on Students' After-School Learning
207(1)
8.5.4 Parents' Perspectives on Mathematics Assessment
208(1)
8.6 Summary
209(4)
References
211(2)
9 A Case Study of a Guangzhou Primary School, China
213(36)
9.1 Background Information on School C
213(3)
9.1.1 Rationale: School C
214(1)
9.1.2 Key Policies of the School
214(1)
9.1.3 The School Curriculum
214(1)
9.1.4 Strategies for Education Reform
215(1)
9.2 Classroom Observations
216(7)
9.2.1 General Features of the Mathematics Classroom
216(4)
9.2.2 An Exemplary Mathematics Lesson: Year 5
220(3)
9.3 Analyzing Samples of Examination Papers
223(4)
9.4 Teachers' Views of Mathematics Assessment
227(12)
9.4.1 The Interviewees
227(2)
9.4.2 Interviewees' Beliefs About Assessment Practices
229(1)
9.4.3 The Content of Assessment
230(1)
9.4.4 Methods of Assessment
230(3)
9.4.5 The Frequency of Assessment
233(1)
9.4.6 Recording and Reporting Assessment
233(2)
9.4.7 Reliability and Validity of Assessment
235(1)
9.4.8 Factors Influencing Assessment Practice and Reform
235(4)
9.5 Parents' Views of Mathematics Assessment
239(8)
9.5.1 Interviewees' Backgrounds
239(1)
9.5.2 Parents' Attitudes Toward Academic Achievement
240(1)
9.5.3 Parents' Views on Students' School Lives
241(2)
9.5.4 Parents' Understanding of Students' Mathematics Learning
243(1)
9.5.5 Parents' Views on Students' After-School Learning
243(2)
9.5.6 Parents' Perspectives on Mathematics Assessment and Reporting
245(2)
9.6 Summary
247(2)
Reference
248(1)
10 Conclusions and Implications: Improve Students' Achievement in Mathematics
249(22)
10.1 Main Findings of the Study
249(7)
10.1.1 Findings from Document Analyses
249(2)
10.1.2 Findings from Case Studies
251(5)
10.2 Discussion of the Mathematics Achievement `Gap'
256(8)
10.2.1 Cultural Factors
258(3)
10.2.2 Implemented Assessment
261(1)
10.2.3 Standards and Content of Curriculum
261(1)
10.2.4 Teachers' Mathematics Knowledge
262(1)
10.2.5 Classroom Teaching
263(1)
10.2.6 Out-of-School Curricula
264(1)
10.3 Limitations of the Study
264(1)
10.4 Implications of the Study
265(2)
10.4.1 Implications for Future Research
265(1)
10.4.2 Implications for Mathematics Assessment and Teaching
266(1)
10.4.3 Implications for Professional Development of Teachers
266(1)
10.4.4 Implications for Curriculum and Assessment Policy-Makers
267(1)
10.5 Conclusions: Factors Contributing to Students' Achievement in Mathematics
267(4)
References
268(3)
Appendix A Information and Consent Letter for Principals 271(2)
Appendix B Information and Consent Letter for Teachers 273(2)
Appendix C Information and Consent Letter for Parents 275(2)
Appendix D Interview Schedule for Principals 277(2)
Appendix E Interview Schedule for Teachers 279(2)
Appendix F An Interview Schedule for Parents 281(2)
Appendix G Interview Schedule for DET Personnel 283(2)
Appendix H Classroom Observation Record 285(4)
Appendix I Mathematics K-6 Syllabus Aims 289(2)
Appendix J Content Summary of Space Strand 291(2)
Appendix K Content Summary of Measurement Strand 293(2)
Appendix L Content Summary of Number Strand 295(2)
Appendix M Content: Year 1 and Year 2 297(2)
Appendix N Content: Year 3 and Year 4 299(4)
Appendix O Content: Year 5 and Year 6 303(4)
Appendix P A Sample of Chinese End-of-Primary-School Mathematics Examination 307
Dr Dacheng Zhao is the Director of Sino-Aussie Unique Collaborative Centre for Educational Studies and Services (SUCCESS), and the Director and Editor-in-Chief of Aussie-Sino Studies. He is also a PhD supervisor at University of Western Sydney and the Principal of Hua Xia Chinese Language and Culture School (Penrith). He has published four single authored books (in Chinese) and more than one hundred research papers in the areas of mathematics education, assessment and curriculum, international and comparative education, and teacher education, etc. His work arms at building a Bridge of Understanding and Collaboration (based on sharing knowledge) between the East and the West in generally, between Australia and China in particularly.
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