Reciprocal Learning for Cross-Cultural Mathematics Education: A Partnership Project Between Canada and China

Series Editors’ Foreword: Intercultural Reciprocal Learning in Chinese and Western Education
Acknowledgments
Introduction
Contents
List of Contributors
List of Figures
List of Tables
Part I Contextualizing Our Reciprocal Learning Environment in Canada & China
1 General and Education Context in Ontario, Canada and Mainland China
1 Introduction
2 The Background of China’s Basic Education Reform and Development
2.1 The Main Elements of Basic Education
3 The Background of Education in Canada and Ontario
3.1 History of Mathematics Education in Ontario
4 International Large-Scale Exams in Canada and China
References
2 Mathematics Teacher Education in Ontario, Canada and Mainland China
1 Overview of Mathematics Teacher Education
2 Pre-Service Mathematics Teacher Education in China
3 Pre-Service Mathematics Teacher Education in Canada
4 Professional Development of In-Service Mathematics Teachers in Mainland China
4.1 National Training Plan in China
5 Professional Development in Ontario
6 Conclusion
References
3 Mathematics Curriculum in Ontario, Canada and Mainland China
1 Overview of Mathematics Curricula
2 Mainland China: Mathematics Curriculum for Compulsory Education
2.1 Mathematics Course Objectives
2.2 The Function of Curriculum
2.3 General Characteristics of the Mathematics Curriculum
2.4 Structure of the Mathematics Curriculum
2.5 The Goals of Mathematics Curriculum
2.6 Assessment
3 Ontario’s Elementary Grade 1–8 Mathematics Curriculum
3.1 Ontario’s Current Curriculum
3.2 Curriculum and Pedagogy
3.3 Assessment Within the Curriculum
3.4 Considerations for Planning
3.5 Curriculum Expectations
3.6 Controversy Over Ontario’s Curriculum
4 Conclusion
References
4 Mathematics Resources in Ontario, Canada and Mainland China
1 Introduction
2 Mathematics Textbooks in Mainland China
3 Use of the Textbooks in Ontario Mathematics Classrooms
4 Classroom Environment and Manipulatives Use in China
5 Classroom Environment and Manipulatives Use in Ontario
6 Technology in Chinese Elementary Schools
7 Technology Use in Ontario Schools
8 Teacher as a Resource in Ontario
9 Conclusion
References
Part II Reciprocal Learning Between Teacher Pairs
5 Mrs. Smith and Mr. Jun’s Reciprocal Learning Partnership
1 Introduction
2 Methods
3 Getting to Know Mr. Jun
4 Getting to Know Mrs. Smith
5 Learning About and from Each Other
6 Learning Over Synchronous Video Chat
7 Learning Over Asynchronous WeChat
8 Learning Through Asynchronous Lesson Study
9 Teacher Exchange and Learning Together
9.1 March 2017
9.2 May 2017
10 Discussion
11 Conclusion
References
6 Professional Development in Mathematics Education Through Reciprocal Learning: The Case of Mrs. Yang and Ms. Ko
1 Introduction
2 Methods
3 Getting to Know Ms. Ko
4 Getting to Know Mrs. Yang
5 Learning About, from, and with Each Other
5.1 Learning Through Asynchronous Lesson Study
6 Learning with and Through Their Students
7 Discussion
8 Conclusion
References
7 Mathematics Teachers’ Perspectives on Effective Learning Through Reflections on Their Experiences in a Canada–China Learning Partnership
1 Introduction
2 Conceptual Foundations
2.1 Social Theories of Learning
2.2 Teacher Learning in Collaboration
3 Research Methodology
3.1 Data Collection Methods
4 Effective Learning Experiences for Teachers
4.1 Effective Learning Achieved Through Dialogues on Teaching in Classrooms
4.2 Effective Learning Achieved Through Principal Involvement
4.3 Effective Learning Achieved Through Student Engagement
4.4 Teachers’ Opinions on Effective Learning for Teachers
4.4.1 Sabrina
4.4.2 Yang
5 Discussion
References
8 Reciprocal Learning Between Chinese and Canadian Middle School Mathematics Teachers
1 Introduction
2 Context of the Study
2.1 Co-Teaching as a Model for Teacher Learning
2.2 The Teacher Pair
2.2.1 The Chinese Teacher: Ming
2.2.2 The Canadian Teacher: Annette
3 Data Resources
3.1 Chat History on WeChat
3.2 Written and Oral Reflections from Each Teacher
4 Findings
4.1 Collaboration: Designing the Lesson
4.2 The Lesson Goals and the Task
4.2.1 The Actual Teaching Day
4.2.2 Scholars’ on-Site Commentary of the Lesson
5 Discussion
5.1 The Product or the Process of Learning
5.2 Different Considerations About Student Behaviors
5.3 National Policies of Education
6 Concluding Remarks
References
Part III Specific Content Topics in Mathematics
9 Analysis of Students’ Systematic Errors and Teaching Strategies for 3-Digit Multiplication
1 Introduction
1.1 Teaching and Learning Plays a Decisive Role in Curriculum Reform
1.2 PCK Affects Teaching Effectiveness
1.3 Student Errors Are Vital Instructional and Learning Resources
1.4 Research Questions
2 Theoretical Framework
3 Research Methodology
3.1 Research Topic: 3-Digit Multiplication in Primary Mathematics
3.2 Research Design
3.3 Participants: Teachers and Students
3.4 Methods of Collecting Data
3.5 Data Analysis
4 Results and Discussion
4.1 Students’ Error Types
4.1.1 Multiplication Misconception
4.1.2 Computational Error
4.1.3 Procedural Error
4.1.4 Summary
4.2 Teachers’ Understanding of Student’s Error and Awareness Actions
4.2.1 Teachers Presuppositions and Understanding of Students’ Errors
4.2.2 Teachers’ Inadequate Awareness of Students’ Error Patterns
4.3 Teachers’ Instructional Strategies Related to Student Errors
4.3.1 Instructional Strategies on Improving Student Errors
4.3.2 Using Appropriate Instructional Strategies
5 Conclusion
5.1 Teachers Are Able to Predict Students’ Errors and Ability of Rules Exploration and Application Should Be Further Improved
5.2 Teachers’ Understanding the Subject Matter Knowledge and Students’ Errors Have an Impact on Their Instructional Implementation
5.3 Influence of Textbook Arrangement on Teaching and Learning
6 Implications
6.1 Student’s Errors: A New Perspective to Study Teachers’ PCK
6.2 Curriculum Resources to Promote Teaching Research and Practice
6.3 A Way to Help Students’ Mathematical Communication and Thinking
Appendix 1
References
10 Utilizing Multiple Methods in Mathematics Problem Solving: Contrasts and Commonalities Between Two Canadian and Chinese Elementary Schools
1 Theoretical Background
2 Research Context
2.1 The Reciprocal Learning Between Canada and China Project
2.2 The Canadian and Chinese Elementary Schools’ Context
3 Data Collection and Data Analysis
3.1 Data Collection
3.2 Data Analysis
4 Findings
4.1 Commonalities in the Teaching of Problem Solving Between the Two Canadian and Chinese Schools
4.2 Multiple Methods of Solving a Problem
4.3 Contrasts in the Teaching of Problem Solving Between the Two Canadian and Chinese Schools
4.3.1 Teachers’ Teaching Strategies and Their Effects on Student Learning
4.3.2 Class Involvement and Interactions Emanating from Student-Posed Problems
5 Conclusion
6 Further Studies
References
11 Research on the Teaching of Understanding Mathematics Problems in Elementary Schools
1 Background
2 Literature Review
3 Method
4 Case Study of Mathematics Problem Understanding Teaching for a Primary School Teacher in Chongqing, China
5 Case Study of Mathematics Problem Understanding for Primary School Teachers in Windsor, Canada
6 Findings and Teaching Suggestions
7 Suggestions
7.1 Teaching Problem Solving Conforms to Students’ Cognitive Process
7.2 The Problem Should Be Presented in Accordance with the Internal Characteristics of Primary School Students
7.3 Activate Students’ Existing Knowledge and Experience to Stimulate Decoding
References
12 The Use of Manipulatives for Teaching Fractions in Two Canadian and Chinese Elementary Schools: A Comparative Research Analysis
1 Introduction
2 Research Context
3 Literature Review
4 Research Methodology
4.1 Data Resources
4.2 Analytical Framework
5 Findings
5.1 Manipulatives Presented to Teach Fractions in Canadian and Chinese Textbooks
5.2 Manipulatives Used to Teach Fractions in Canadian and Chinese Classrooms
6 Discussion and Conclusion
References
Part IV Special Topics in Mathematics Education
13 A Canadian Elementary Teacher’s Differentiated Instruction in Mathematics Teaching: From the Perspective of a Chinese Researcher
1 Introduction
2 Theoretical Framework
3 Methods and Data Sources
4 The Case of Kelly
4.1 Kelly’s Practices of Teaching in Catering to Students’ Diverse Learning Needs
4.1.1 The Content of Teaching
4.1.2 The Process of Teaching
4.1.3 The Product of Teaching
4.1.4 The Learning Environment
4.2 Conceptions of Teaching in Catering to Students’ Diverse Learning Needs
4.2.1 The Conceptions of the Nature of Mathematics Learning and Students’ Roles
4.2.2 The Conceptions of the Nature of Mathematics Teaching and Teachers’ Roles
4.2.3 The Conceptions of the Aims and Expected Outcomes of Teaching
4.2.4 The Conceptions of the Content of Teaching
4.2.5 The Conceptions in the Methods of Teaching
4.2.6 The Conceptions in the Assessments of Learning
5 Conclusions and Discussions
References
14 Meaningful and Sustainable Mathematics Education for Students of Indigenous and Ethnic Minority Cultural Backgrounds in Canada and China
1 Identification
2 Pre-contact Indigenous Education
3 Differences Between Indigenous and Western (Eurocentric) Educational Paradigms/Models
4 Conflicts that Arose in the Educational Realm or Arena During the Post-contact Era
5 Next Steps and Directions for the Future
5.1 The Schema Theory
6 Some Actual Examples on the Utilization of Indigenous and Ethnic Minority Learners’ Cultural Knowledge in Mathematics and Science Teaching/Learning Classrooms
6.1 The Use of the “Bow and Arrow” to Teach the “Conservation of Energy” Concept in Physics
6.2 The Use of Environmentally Sourced Materials and Illustrations in STEM Program/Classes
7 Summary, the Way Forward, and Conclusion
References
15 A Case Study of the Change of Teacher’s Teaching Belief Based on International Understanding
1 Introduction
2 Research Methods
2.1 Observation
2.2 Interview
2.3 Data Analysis
2.4 Video Analysis
3 Findings
3.1 The Lesson on “Vertical and Parallel” Lines
3.1.1 Discussion of R’s Class
3.2 The Lesson on “Calculate Simple Elapsed Time”
3.2.1 Discussion of R’s Class
3.3 The Lesson of “Using Estimation to Solve Problems”
3.3.1 Discussion of the Third Class
4 Discussion and Conclusions
4.1 The Changes and Reasons of Teacher Z’s Teaching Belief
4.2 The Paths to Enhance Teachers’ International Literacy Understandings and to Promote Their Teaching Belief Transformations
5 Limitations
References
16 Mathematics as a Cultural Role Player in School Development: Perspectives from the East and West
1 Background and Introduction
2 Mathematics in Today’s World
3 Why Do Many Students from Ethnic Minority and Indigenous Cultural Backgrounds Shy Away from and Perform Poorly in Mathematics?
4 Addressing Setbacks and Tackling Obvious Constraints and Barriers
5 What Can Be Done? How Can It Be Done?
6 Building Mathematics Education on Identified and Available Cultural Resources
7 Next Phase
8 Summary, Suggestions, and Conclusion
Appendix I
Appendix II
Appendix III
References
Index