The Problem with Math Is English: A Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics

ISBN-13: 9781118095706 / Angielski / Miękka / 2012 / 304 str.

Concepcion Molina

Opis

Teaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts


Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property.

• Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math
  
• Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation

This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism.

Spis treści

The Author xiii

About SEDL xv

About This Book xvii

Introduction xix

Julian s Story xix

Rationale and Purpose xx

Who Benefits from This Book? xxii

ONE The Problem with Math Is English (and a Few Other Things) 1

Why Language and Symbolism? 1

What We Are Teaching 4

Turning the tide: A Sampling of Approaches 6

Mathematics Is About Relationships 8

Connecting the Pieces and Looking Ahead 9

TWO Why a Language Focus in Mathematics? 11

The Convergence of Mathematics and English: More Than Just Vocabulary 11

Problems Based on the English Language 13

A Number of Problems with Number 16

THREE Language and Symbolism in Traditional Instruction 21

Shortcomings of Traditional Instruction 22

More Language and Symbolism Issues: Adding Fuel to the Fire 32

Tell Me Again Why the Language Focus in Math? 38

FOUR So What Does Conceptual Understanding Look Like? 41

It Starts with Definitions 42

Making Connections in Math: Beyond Connecting Dots 51

The Interpretation and Translation Of Math 55

Conclusion 61

F I V E The Order of Operations: A Convention or a Symptom of What

Ails Us? 63

The Roots of the Rules 64

The Natural Order: A Mathematical Perspective 65

Conclusion: A Conceptual Understanding of the Order of Operations 78

S I X Using Multiplication as a Critical Knowledge Base 81

Understanding Key Definitions and Connections 81

Interpreting Multiplication 86

Using The Power of the Distributive Property 88

Feeling Neglected: The Units in Multiplication 100

Conclusion: Small Details, Huge Impact 103

SEVEN Fractions: The F Word in Mathematics 105

Defining Fractions: Like Herding Cats 105

The Fraction Kingdom 107

Interpreting Fractions 116

Conclusion 124

E I G H T Operations with Fractions 127

Adding and Subtracting Fractions 127

Multiplying Fractions 131

Dividing Fractions 150

Conclusion 160

NINE Unlocking the Power of Symbolism and Visual Representation 161

Symbolism 161

Visual Representation 168

The Power of Interpretation: Three Perspectives of Trapezoids 178

Conclusion 187

TEN Language–Focused Conceptual Instruction 189

Language Focus: Beyond the Definitions 190

The Secrets to Solving Word Problems 192

Suggested Instructional Strategies 197

Conclusion 216

ELEVEN Mathematics: It s All About Relationships! 219

Language and Symbolism: Vehicles for Relationship Recognition 220

Relationships and Fractions 224

Proportional Reasoning 227

Relationships: Important Considerations 230

Relationships: Making Powerful Connections 234

Conclusion 249

TWELVE The Perfect Non–Storm: Understanding the Problem and Changing the System 251

A Systemic Issue 251

Math Makeover 257

Conclusion 264

Bibliography 267

Index 269

O autorze

Concepcion Molina, Ed.D., is a program associate with SEDL, a private, nonprofit education research, development, and dissemination corporation based in Austin, Texas. Dr. Molina supports systemic reform efforts in mathematics and works to assist state and intermediate education agencies in their efforts to improve instruction and student achievement.

Blurb

Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at only a superficial level. Written to inspire "aha" moments, this important new book offers teachers the tools they need to help their students identify and comprehend the nuances and true meanings of essential math concepts such as multiplication, division, fractions, place value, and much more by exploring them through the lenses of language and symbolism.

The Problem with Math Is English explains how language–focused conceptual instruction leads students to a deeper understanding than traditional procedural–based teaching methods. By placing emphasis on truly understanding math concepts, Dr. Molina shows that teaching math becomes easier when teachers are able to communicate the language, symbolism, and representation of math to all of their students.

"Teachers of mathematics of all levels who read and spend time with this fun and challenging book will strengthen their content knowledge and find confidence in their own ability to think and reason. When teachers truly understand and embrace the mathematics/language connections so richly illustrated in the book, they will be able to pass on to all of their students a depth of mathematical insight and joy they may never have imagined before."

Cindy Chapman, Mathematics Education Consultant; past member, NCTM Board of Directors

"In this easy to read book, Como Molina with rare humor, insight and thoughtfulness shares many of the lessons he has learned while providing professional development for mathematics teachers in U.S. public schools. Como delightfully challenged my own understandings of the important relationships between mathematical ideas and the language we commonly use to teach them."

Dr. Stephen Marble, Associate Professor of Education, Southwestern University, Georgetown , TX