Effective teaching and assessment strategies to help students think differently about mathematics Effective mathematics instruction and numeracy development are a major focus in classrooms today. The Four Roles of the Numerate Learner introduces a framework (sense maker, skill user, thought communicator, and critical interpreter) that supports an integrated approach to effective mathematics instruction. This timely book builds on educators' understanding of how to effectively teach mathematics and borrows from successful frameworks used to teach literacy. It considers the mathematical practices that students need to learn to construct mathematical knowledge, become mathematicians, and simply do mathematics. The goal is to provide multiple entry points into a new world of mathematics instruction-a new way of thinking and learning where learners engage in critical thinking about numeracy and act on this knowledge. The framework emphasizes student voice with many opportunities for students to ask questions, pose problems, explore ideas, and change their thinking about mathematics and the way they see themselves as mathematicians. The Four Roles of the Numerate Learner shows new and experienced teachers how to foster and support daily practice that permits students to use their diverse identities to build their mathematical knowledge and incorporate their cultural experiences.
Authors
- Bibliography, etc. Note
- Includes bibliographical references (pages 89-92) and index
- Control Number Identifier
- CaOOCEL
- Description conventions
- rda
- Dewey Decimal Classification Number
- 372.7/044
- Dewey Decimal Edition Number
- 23
- Distributor
- Canadian Electronic Library (Firm),
- General Note
- Issued as part of the desLibris books collection
- ISBN
- 9781551383118 9781551389158
- LCCN
- QA135.6
- LCCN Item number
- F55 2016eb
- Modifying agency
- CaBNVSL
- Original cataloging agency
- CaBNVSL
- Physical Description | Extent
- 1 electronic text (96 pages)
- Published in
- Ottawa, Ontario
- Publisher or Distributor Number
- CaOOCEL
- Rights
- Access restricted to authorized users and institutions
- System Control Number
- (CaBNVSL)thg00970955 (OCoLC)935109068 (CaOOCEL)451212
- System Details Note
- Mode of access: World Wide Web
- Title proper/short title
- Effective teaching and assessment strategies to help students think differently about mathematics
- Transcribing agency
- CaBNVSL
Table of Contents
- Cover 1
- Title 2
- Copyright 3
- Contents 6
- Foreword 8
- Preface 10
- Chapter 1: Developing an Understanding of the Four Roles of the Numerate Learner 14
- Setting the Context 14
- Adopting an Inquiry Mindset 15
- Identifying Connections between Literacy and Numeracy 15
- Aligning Effective Literacy and Numeracy Practices 18
- Developing a New Thinking Framework in Mathematics 20
- Skill User 22
- Sense Maker 22
- Thought Communicator 23
- Critical Interpreter 23
- Why Does this Framework Matter? 23
- Using Responsive Instruction 24
- Numeracy as an Interdisciplinary Approach 24
- The Role of Thinking in the Four Roles of the Numerate Learner 25
- What is Thinking? 25
- What is Thinking in Literacy? 26
- What is Analyzing? 27
- What is Evaluating? 27
- What is Synthesizing? 28
- What is Identifying Points of View and Examining Biases? 28
- What is Mathematical Thinking? 29
- What is Reasoning and Proving? 30
- What is Connecting? 30
- What is Reflecting? 30
- Making Thinking Visible: Unpacking Justifying 31
- Attributes of Mathematical Thinking 31
- Looking Forward 32
- Chapter 2: Sense Maker 34
- What is a Sense Maker? 34
- Procedural Knowledge and Conceptual Understanding 34
- Using Rich Tasks to Develop Mathematical Thinking and Support through Sense Making 36
- Why Use Rich Tasks? 36
- What Makes a Task Rich? 37
- Using Effective Questioning 37
- Using Rich Tasks as a Bridge between Assessment and Instruction 39
- Putting it all Together 39
- Grades 1–3 40
- Grades 4–8 41
- Grades 7–10 41
- Grades 11–12 42
- Chapter 3: Skill User 44
- What is a Skill User? 44
- The Numerate Learner as a Skill User 44
- Basic Facts: The Elephant in the Room 45
- Basic Facts and Teaching and Learning in the Twenty-First Century 45
- What is Mathematics? 46
- Teaching for Conceptual Understanding 47
- Using the Big Ideas of Mathematics to Support the Numerate Learner 48
- Putting it all Together 49
- Grades 1–3 49
- Grades 4–6 50
- Grades 7–9 51
- Grades 9–10 52
- Chapter 4: Thought Communicator 54
- What is a Thought Communicator? 54
- Communicating through Meaningful Mathematical Discussions 54
- Communicating through Reading and Writing 56
- Communicating through the Use of Thinking Tools 58
- The Role of Mathematical Content Knowledge for Teaching: The Other Elephant in the Room 59
- Putting it all Together 60
- Grades 1–3 60
- Grades 6–8 61
- Grades 7–10 62
- Grades 11–12 63
- Chapter 5: Critical Interpreter 64
- What is a Critical Interpreter? 64
- Understanding Critical Literacy 66
- Connecting Critical Literacy to Critical Numeracy 68
- Using Critical Social Practice to Develop a Critical Stance 72
- Putting it all Together 75
- Grades 1–3 75
- Grades 6–8 75
- Grades 7–9 76
- Grades 9–12 77
- Chapter 6: Moving Forward 80
- Where Do We Go from Here? 80
- Appendices 84
- A: Features and Attributes of a Rich Task 84
- B: Rich Tasks – Teacher and Student Actions 86
- C: Reflecting on Assessment and Instructional Actions 87
- References 90
- Bibliography 94
- Index 96
- A 96
- B 96
- C 96
- E 96
- F 96
- G 96
- I 96
- J 96
- L 96
- M 97
- N 97
- P 97
- R 97
- S 97
- T 97
- W 97
