The Problem with Math Is EnglishA Language-Focused Approach to Helping All Students Develop a Deeper Understanding of Mathematics
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.
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
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.
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