Mathematizing Student Thinking: Connecting Problem Solving to Everyday Life and Building Capable and Confident Math Learners

by David Costello

Overview

How can you broaden student thinking and help them develop their independence and confidence as problem solvers? Real-life problems are a remarkable tool to stretch student thinking and help them develop a deeper understanding of mathematics and its role in everyday life. Rather than using textbook exercises, the book argues that solving real-world problems promotes flexibility and encourages students to adjust and grow their thinking. It inspires them to consider alternatives and apply math in authentic contexts. You will find practical ways to engage students in critical thinking, develop their independence, and make connections with the world.

Product Details

ISBN-13:	9781551383569
Publisher:	Pembroke Publishers Limited
Publication date:	05/02/2022
Pages:	160
Product dimensions:	8.30(w) x 10.88(h) x 0.37(d)

About the Author

Dr. David Costello is an author and professional learning facilitator who focuses on mathematics instruction and learning. He has held many roles in education, such as numeracy interventionist, numeracy coach, numeracy leader, curriculum consultant, and school administrator for Prince Edward Island, Canada. David supports educators in making impactful yet manageable changes to instruction so that students can have meaningful learning experiences.

Table of Contents

Introduction 5

Chapter 1 Redefining Problems 19

What Is a Problem? 20

Strengthening the Problem 26

Finding Problems 27

Problems Used in the Classroom 29

Defined Problems 40

Ill-Defined Problems 41

Similarities and Differences between Defined Problems and Ill-Defined Problems 42

Importance of Ill-Defined Problems 44

Summary 47

Chapter 2 Understanding the Different Ways to Problem Solve 48

Defining Problem Solving 48

The Problem Solving Stages 51

Problem Solving Stages in Action 53

Problem Solving and Classroom Connections 58

Problem Solving and Ill-Defined Problems 67

Summary 71

Chapter 3 Moving Toward Mathematical Modelling 73

Modelling in Mathematics and Mathematical Modelling 73

Defining Mathematical Modelling 75

Mathematical Modelling Process 78

The Need for Social-Emotional Learning Skills 82

Cultural Relevance 84

The Teacher's Role 85

The Student's Role 88

Summary 90

Chapter 4 Understanding Ill-Defined Problems 91

What's Involved in Understanding the Problem 92

The Teachers Role 93

The Student's Role 95

Student Work Samples 96

Anticipating Classroom Connections 99

Summary 100

Chapter 5 Analyzing the Situation 101

What's Involved in Analyzing the Situation 102

The Teacher's Role 103

The Student's Role 104

Student Work Samples 106

Anticipating Classroom Connections 109

Summary 110

Chapter 6 Creating a Mathematical Model 111

What's Involved in Creating a Mathematical Model 112

The Teacher's Role 113

The Student's Role 114

Student Work Samples 116

Anticipating Classroom Connections 118

Summary 119

Chapter 7 Analyzing and Assessing the Mathematical Model 121

What's Involved in Analyzing and Assessing the Model 122

The Teachers Role 123

The Student's Role 125

Student Work Samples 127

Anticipating Classroom Connections 130

Summary 130

Chapter 8 Assessing Mathematical Modelling 132

Types of Assessment 132

Assessment Strategies 134

Using Assessment Data 138

Summary 139

Chapter 9 Applying Mathematical Modelling Today 140

Summary 143

Glossary 144

References 148

Recommended Resources 149

Index 151