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• HalfTitle
• Series
• Title
• Copyright
• Contents
• Notes on Contributors
• Series Editor’s Foreword
• Preface
• Part I Issues in Mathematics Education
• 1 What Is Mathematics, and Why Learn It?
• Introduction
• What is mathematics? Answers from the philosophy of mathematics
• Views of the purposes of mathematics teaching
• The relationship between philosophies, aims and classroom practices
• Conclusion
• 2 Learning and Knowing Mathematics
• Introduction
• Overview of theories of learning and knowing
• Constructivist research on learning and knowing mathematics
• Cultural–historical research on learning and knowing mathematics
• Sociological approaches to learning and knowing mathematics
• Conclusion
• 3 Improving Assessment in School Mathematics
• Introduction
• Towards a didactical model for assessment design
• Formative assessment and classroom learning
• Interpretation in teachers’ assessments
• Quality and dependability in teachers’ summative assessments
• Conclusion
• 4 Integrating New Technologies into School Mathematics
• Introduction
• Studying integration into teaching of board technologies as a medium of classroom communication
• Studying integration into teaching of graphing technologies as a medium for heuristic mathematics
• Studying integration into teaching of a virtual learning environment as the mediator of whole-class
• Studying integration of dynamic geometry into personal and cultural frameworks for teaching
• Conclusion
• 5 Mathematics Textbooks and How They Are Used
• Introduction
• The mathematics textbook – curriculum material and artifact
• Mathematics textbooks and their use: artifacts and instruments
• Mathematics textbooks as artifacts
• Mathematics textbooks as instruments
• Students and mathematics textbooks
• Conclusion
• 6 The Affective Domain
• Foreword
• Introduction
• A first phenomenological encounter with the affective domain – an attempt at an inventory
• An attitude-related theory
• Conclusion
• 7 Mathematics and Language
• Introduction
• Linguistic perspectives
• Discursive perspectives on mathematical cognition
• Socio-political perspectives
• The discourse of mathematics education research
• Conclusion
• 8 Mathematics Teacher Knowledge
• Introduction
• Lee Shulman
• Deborah Ball
• Mathematical knowledge for teaching
• The Knowledge Quartet
• Conclusion
• Part II Aspects of Mathematics Curriculum
• 9 Proof
• Introduction
• A classroom episode as a context to introduce the focal issues
• Discussion of the core readings
• Conclusion
• 10 Mathematical Problem Solving
• Introduction
• What is a mathematical problem?
• Types of problems
• Scientific views on problem solving
• Phases and components of problem solving
• Instructional methods that promote problem solving
• Problem solving as a vehicle for learning mathematics
• Conclusion
• 11 Algebra
• Introduction
• Exploring the meaning of approach: Approaches to school algebra
• Substantive structures in mathematics and the curriculum
• Different ways of thinking about equations in two variables: The curricular challenge of multiple su
• Processes on Objects: One way to characterize choices made about substantive structures in school cu
• Operations on functions: One way to understand school algebra
• A second way to describe approaches to school algebra: Approaches and instructional situations
• Conclusion
• 12 Arithmetic
• Introduction
• The role of counting
• Using imagery
• Written methods for addition and subtraction
• Multiplicative reasoning
• Foundations of multiplicative reasoning
• Conclusion
• 13 Geometry
• Introduction
• Spatial visualization in geometry
• The learning of basic geometric concepts
• The van Hiele model of students’ geometrical reasoning
• Conclusion
• 14 Probability
• Introduction
• Why is probability hard?
• The ChanceMaker study
• Conclusion
• Part III Comparative Mathematics Education
• 15 European Mathematics Curricula and Classroom Practices
• Introduction
• A socio-historical commentary of education in England, France, Germany and Russia
• Mathematics teaching in England and Germany
• Textbooks and the teaching of angle in England, France and Germany
• Teacher–pupil interactions in the mathematics classrooms of Russia and England
• The intersection of mathematics curricula and teaching in Flanders and Hungary
• Conclusion
• 16 Teaching and Learning Mathematics in Chinese Culture
• Introduction
• ‘Chinese-ness’ – characteristics of the Chinese learner
• Effective mathematics teaching in the eyes of Chinese teachers
• The role of practice: Repetitive learning versus learning by rote
• A typical Chinese mathematics lesson
• Bridging the gap between basic skills and higher-order abilities
• The spiral bianshi mathematics curriculum
• Conclusion
• Acknowledgement
• 17 Classroom Culture and Mathematics Learning
• Introduction
• The constitutive role of classroom interaction
• Negotiation of mathematical meanings in inquiry classrooms
• Unequal negotiation of meanings?
• The problem of recontextualization
• Researching hidden dimensions
• Conclusion
• Index