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…mehr
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
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.
Inhaltsangabe
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 JustVocabulary 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 Fire32
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 ofWhat
Ails Us? 63
The Roots of the Rules 64
The Natural Order: A Mathematical Perspective 65
Conclusion: A Conceptual Understanding of the Order ofOperations 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'' inMathematics 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 Representation161
Symbolism 161
Visual Representation 168
The Power of Interpretation: Three Perspectives of Trapezoids178
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 Recognition220
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 andChanging the System 251
