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Effective mathematics lessons through an eclectic Singapore approach

Author: Khoon Yoong Wong; Association of Mathematics Educators (Singapore)
Publisher: Singapore : World Scientific : Association of Mathematics Educators, [2015] ©2015
Series: Yearbook (Association of Mathematics Educators (Singapore)), 2015.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"With this seventh volume, as part of the series of yearbooks by the Association of Mathematics Educators in Singapore, we aim to provide a range of learning experiences and teaching strategies that mathematics teachers can judiciously select and adapt in order to deliver effective lessons to their students at the primary to secondary level. Our ultimate goal is to develop successful problem solvers who are able to  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Wong, Khoon Yoong.
Effective mathematics lessons through an eclectic Singapore approach
(OCoLC)910531206
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Khoon Yoong Wong; Association of Mathematics Educators (Singapore)
ISBN: 9789814696432 9814696439
OCLC Number: 910845466
Description: 1 online resource (xiii, 307 pages) : illustrations.
Contents: Foreword; Acknowledgements; Chapter 1 Curriculum: Map the Intended, Implemented, and Attained Landscape; 1 Nature of Mathematics; 2 Three Types of Curriculum; 3 Intended Mathematics Curriculum: Why?; 4 Intended Mathematics Curriculum: What?; 5 Intended Mathematics Curriculum: Curriculum Framework; 6 Mathematics Curriculum Development: How to?; 6.1 Strands of mathematics curriculum development; 6.2 Situated Socio-Cultural Framework; 7 Implemented Mathematics Curriculum: How?; 8 Attained Curriculum: How Well?; 8.1 Assessment goals; 8.2 Quality of assessment 8.3 Interpretations of assessment data9 Concluding Remarks; Chapter 2 Concepts: Build Meanings and Connections; 1 Hierarchies of Concepts; 2 Meanings, Examples, Non-examples; 2.1 Meanings; 2.2 Examples; 2.3 Non-examples; 2.4 Frayer Model; 3 Modes of Representation; 3.1 Functions of representations; 3.2 Concrete Pictorial Abstract (CPA); 3.3 Multi-Modal Strategy (MMS); 3.4 Modes of representation vs. modes of processing; 4 Conceptual Connections; 4.1 Carroll diagram; 4.2 Venn diagram; 4.3 Tree diagram; 4.4 Concept maps; 5 Concept Questions; 6 Concluding Remarks Chapter 3 Skills: Use Rules Efficiently1 Nature of Mathematical Skills; 1.1 Alternative procedures; 1.2 Conditions for procedures; 1.3 Hierarchies of mathematical skills; 2 Skills vs. Concepts; 2.1 An example from fraction division; 2.2 Procept; 2.3 Limit and recurring decimals; 3 Direct Instruction: An Overview; 4 Frameworks of Direct Instruction; 5 Telling and Explaining; 6 Worked Examples; 6.1 Correct mathematics and real-world information; 6.2 I do --
We do --
You do; 6.3 Cognitive Load Theory; 6.4 Problem solving set; 7 Deliberate Practice; 7.1 Check seatwork or classwork 7.2 Students work on the board7.3 Homework; 8 Address Student Mistakes; 9 Skill Questions; 10 Concluding Remarks; Chapter 4 Processes: Sharpen Mathematical Reasoning and Heuristic Use; 1 Mathematical Processes: Domain-Generic vs. Domain-Specific; 2 Mathematical Reasoning: Definition; 3 Intuitive-Experimental Justification; 3.1 Teaching inductive-experimental justification; 3.2 Examples of inductive-experimental justification; 3.3 Caveats about inductive thinking; 3.4 A brief summary about inductive thinking; 4 Deductive Proofs; 4.1 Some proof examples; 4.2 Logical forms 4.3 Converse of Pythagoras' Theorem4.4 Zero Product Rule (Zero Factor); 4.5 Axiomatic system; 5 Acceptance of Results without Justifications; 6 Heuristics; 6.1 Some local studies about teaching of heuristics; 6.2 Model drawing; 7 Question-and-Answer (Q&A); 8 Mathematics Discussions; 9 Reasoning Questions; 10 Concluding Remarks; Chapter 5 Applications: View the World Through Mathematical Lenses; 1 Query about Mathematical Applications; 2 Context Knowledge; 3 Direct Applications of Specific Skills; 4 Applications of Processes; 5 Applications across School Subjects
Series Title: Yearbook (Association of Mathematics Educators (Singapore)), 2015.
Responsibility: Wong Khoon Yoong.

Abstract:

"With this seventh volume, as part of the series of yearbooks by the Association of Mathematics Educators in Singapore, we aim to provide a range of learning experiences and teaching strategies that mathematics teachers can judiciously select and adapt in order to deliver effective lessons to their students at the primary to secondary level. Our ultimate goal is to develop successful problem solvers who are able to understand concepts, master fundamental skills, reason logically, apply mathematics, enjoy learning, and strategies their thinking. These qualities will prepare students for life-long learning and careers in the 21st century. The materials covered are derived from psychological theories, education praxis, research findings, and mathematics discourse, mediated by the author's professional experiences in mathematics education in four countries over the past four decades. They are organised into ten chapters aligned with the Singapore mathematics curriculum framework to help teachers and educators from Singapore and other countries deepen their understanding about the so-called "Singapore Maths". The book strikes a balance between mathematical rigor and pedagogical diversity, without rigid adherence to either. This is relevant to the current discussion about the relative roles of mathematics content knowledge and pedagogical content knowledge in effective teaching. It also encourages teachers to develop their own philosophy and teaching styles so that their lessons are effective, efficient, and enjoyable to teach."--

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