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Mathematize It! [Grades K-2]
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Mathematize It! [Grades K-2]
Going Beyond Key Words to Make Sense of Word Problems, Grades K-2

First Edition


May 2020 | 232 pages | Corwin

“This book is a must-have for anyone who has faced the challenge of teaching problem solving. The ideas to be learned are supported with a noticeably rich collection of classroom-ready problems, examples of student thinking, and videos. Problem solving is at the center of learning and doing mathematics. And so, Mathematize It! should be at the center of every teacher’s collection of instructional resources.”

John SanGiovanni
Coordinator, Elementary Mathematics
Howard County Public School System, Ellicott City, MD


Help students reveal the math behind the words


“I don’t get what I’m supposed to do!” This is a common refrain from students when asked to solve word problems.

Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution.  Many students often pluck numbers from the problem and plug them into an equation using the first operation they can think of (or the last one they practiced). Students also tend to choose an operation by solely relying on key words that they believe will help them arrive at an answer, which without careful consideration of what the problem is actually asking of them.

Mathematize It! Going Beyond Key Words to Make Sense of Word Problems, Grades K-2 shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. Through the process of mathematizing, the authors provide an explanation of a consistent method—and specific instructional strategies—to take the initial focus off specific numbers and computations and put it on the actions and relationships expressed in the problem.
 
Sure to enhance teachers’ own operation sense, this user-friendly resource for Grades K-2

·         Offers a systematic mathematizing process for students to use when solving word problems

·         Gives practice opportunities and dozens of problems to leverage in the classroom

·         Provides specific examples of questions and explorations for addition and subtraction of whole numbers as well as early thinking for multiplication and division

·         Demonstrates the use of concrete manipulatives to model problems with dozens of short videos

·         Includes end-of-chapter activities and reflection questions

How can you help your students understand what is happening mathematically when solving word problems? Mathematize it! 


 
Publisher's Acknowledgements
 
Table of Contents
 
Video List
 
About the Authors
 
Introduction: Why You Need to Teach Students to Mathematize
 
Problem Solving Strategies Gone Wrong
 
What is Mathematizing? Why Is It Important
Focus on Operation Sense

 
Using Mathematical Representations

 
 
Teaching Students to Mathematize
Building your Understanding of Operations and Related Problem Situations

 
Playing in the Mathematizing Sandbox: A Problem-Solving Model

 
 
Final Words Before You Dive
 
Chapter 2: Moving From Counting to Addition & Subtraction
 
Thinking About Counting, Addition, and Subtraction
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problem

 
The Development of Courting

 
Counting or Add-To?

 
Representing Problem Situations or Representing Answers

 
 
Using Children's Literature to Explore add-To and Take From Situations
Transcribe the Action or Relationship

 
 
Moving beyond Twenty
Students and Teachers Think About the Problems

 
Representing Problem Situations Multiple Ways

 
Translating the Five Relationships: Try It Out

 
Teaching Students to Use Concrete and Pictorial Models

 
 
Key Ideas
 
Try It Out!
Identify the Principle

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 3: Add-To Problems: Locating the Change
 
Thinking About Active Addition Situations
 
Thinking About Active Addition Situations
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problems

 
Finding the Unknown, Three Story Structures

 
 
Story Structures: Implications for Teaching
 
Modeling the Active Problem Situation
Model Actions

 
Distinguish Pictures from Pictorial Representation

 
Identify Important Features

 
Creatively Meet Students' Needs

 
 
Using Children's Literature to Explore Add-To Problems
Make Predictions

 
Transcribe the Action or Relationship

 
 
Digging Deeper into Start Unknown Situations
Complicating Things: The Start Unknown Variation

 
Strategies for Making Sense of Start Unknown Problem Situation

 
Separating Computation from Operation

 
Moving to Equations

 
 
Key Ideas
 
Try It Out!
Identify the Problem Situation

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 4: Take-From Problems: Locating the Change
 
Thinking About Active Subtraction Situations
Sandbox Notes: Explore Your Thinkin

 
Students and Teachers Think About the Problems

 
Finding the Unknown, Three Story Structures

 
Story Structures: Implications for Teaching

 
Modeling the Active Problem Situation

 
 
Digging Deeper into the Start and Change Unknown Situations
Moving from Concrete to Symbolic Representation

 
 
Using Children's Literature to Explore Take-From Situations
Create Another Outcome

 
Finding the Unknown Quantity

 
 
Key Ideas
 
Try It Out!
Identify the Problem Situatoon

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 5: Part-Part-While: Understanding the Relationship
 
Thinking About Part-Part-Whole Situations
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problems

 
Defining the Part-Part-Whole Situation

 
Modeling Relationships vs. Action

 
Moving from Counters to Bar Models

 
The Special Case of Both Parts Unknown

 
Modeling Measurement Problems

 
A Note About the Commutative Property

 
 
Using Children's Literature to Explore part-Part-Whole Situations
Make Predictions

 
 
Moving to Larger Whole Numbers
Students and Teachers Think about the Problems

 
Modeling Measurement Problems

 
Writing Equations: Addition or Subtraction

 
Writing Equations: Addition or Subtraction

 
Finding the Equation in the Model

 
 
Key Ideas
 
Try It Out!
Identify the Problem Sitaution

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 6: Additive Comparison: Another Kind of Relationship
 
Thinking About Additive Comparison Situation
Students and Teachers Think about the Problems

 
Early Years Comparisons

 
Additive Comparison Situations

 
 
Building Models for Comparisons
Students and Teachers Think About the Problems

 
Making Use of Models For Thinking

 
 
The Language of Comparisons
Language Can Get Tricky

 
Building Bar Models for Comparisons

 
Problem Posing as an Instructional Strategy

 
 
Using Children's Literature to Explore Additive Comparison Situations
Create Another Outcome

 
 
Key Ideas
 
Try It Out
Identify the Problem Situation

 
Write a Problem

 
Change It Up

 
 
Reflect
 
Chapter 7: Early Multiplication and Division: Patterns and Predictions
 
Thinking about Early Multiplicative Thinking
Sandbox Notes: Explore Your Thinking

 
Students and Teachers Think About the Problem

 
Modeling Even and Odd Numbers

 
Equal Groups Problem Situation

 
Using Patterns to Identify Even and Odd Numbers

 
 
Using Children's Literature to Explore Early Multiplication
Transcribe the Action or Relationship

 
 
Bringing Another Dimension with Arrays
Recognizing Area/Array as a Problem Situation

 
Building an Understanding of Arrays as Structures

 
 
Using Children's Literature to Explore Arrays
Transcribe the Action or Relationship

 
 
Setting the Stage Division
Equipartitioning

 
Two Models for Division

 
 
Using Children's Literature to Explore Early Division
Transcribe the Action or Relationship

 
 
Key ideas
 
Try It Out
Identify the Problem Situation

 
Write the Problem

 
Change It Up

 
 
Reflect
 
Chapter 8: Changing How You Teach Word Problems
 
Getting into the Mathematizing Sandbox
 
8 Shifts in Instruction for Building Students' Problem-Solving Skills
Do Word Problems for Sense-Making

 
Treat Context and Computation Separately

 
Create More and Varied Representations

 
Explore All the Work Operations can Do

 
Add Operation Sense Routines with a Variety of Problem Situatons

 
Listen to Students and Be Curious

 
Make Time for Mathematizing in the Sandbox

 
 
Guidance for Moving Forward: FAQ's
Finding Unexpected Mathematics in Stories

 

“As our students begin to mathematize the world around them, it becomes extremely important that we listen to their thinking so that we can continue to move their understanding forward. What makes Mathematize It! such a useful tool for teachers is that it thoughtfully unpacks student strategies, which helps inform and guide our next move as a classroom teacher.”

Graham Fletcher
Math Specialist, Atlanta, GA

“Mathematize It! engages readers deeply in the mathematics content through an easy-to-use visual analogy: playing in a sandbox. The authors have found a way to make problem-solving seem like a fun task—one that is akin to something we’ve all been doing forever: playing. Their clever and applicable problem-solving model of thinking provides a structure teachers can use to support students in tackling word problems and actually enjoying the process. It’s time for you to play in the sandbox and more importantly, Mathematize It!”

Hilary Kreisberg
Director, Center for Mathematics Achievement Lesley University, Cambridge, MA Author of Adding Parents to the Equation

“The authors provide a detailed and practical guide on how to take a word problem, uncover the mathematics embedded in it, carefully consider representations, and use it all to solve the problem. The reader begins to realize that all models are not created equal. The authors’ careful attention to the nuances within mathematical relationships illustrates how mathematizing differs from answer getting, yet shows us that ideas like operation sense and computation are related. The authors’ plain-language explanations empower us to leverage those relationships in order to help students become better mathematicians.”

Paul Gray
Chief Curriculum Officer, Cosenza & Associates, LLC Past President, Texas Council of Teachers of Mathematics NCTM Representative for NCSM: Leadership in Mathematics Education

“I can’t wait to use Mathematize It! in my work with teachers and students! The excellent examples, including actual student work and teacher commentaries, highlight the complexity of the problem situations in a way that is clear and usable for classroom teachers and for those of us who support them. The focus on operation sense, understanding the role that each quantity plays, and connecting representations to problems makes this a must read for anyone helping students become successful problem solvers. I especially appreciate the inclusion of non-whole-number examples!”

Julie McNamara
Associate Professor, Author of Beyond Pizzas & Pies (With Meghan Shaughnessy) and Beyond Invert & Multiply, California State University, East Bay, Hayward, CA

“This book is a must-have for anyone who has faced the challenge of teaching problem solving. The ideas to be learned are supported with a noticeably rich collection of classroom-ready problems, examples of student thinking, and videos. Problem solving is at the center of learning and doing mathematics. And so, Mathematize It! should be at the center of every teacher’s collection of instructional resources.”

John SanGiovanni
Coordinator, Elementary Mathematics, Howard County Public School System, Ellicott City, MD

“Finally! An answer for equipping students in making sense of word problems. Mathematize It! clarifies the challenges in problem solving and gives concrete steps and advice on understanding problem contexts and the mathematics involved. The examples, student work, and videos throughout the book bring ideas to life, and make their implementation doable. This is a must-read for every math teacher who desires their students to truly understand the role of mathematics in the world.”

Nanci N. Smith
Associate Professor, Mathematics and Education, Arizona Christian University, Glendale, AZ, Author of Every Math Learner

“Leaving behind the procedures and the gimmicks, Mathematize It! will effectively help develop teachers’ understanding of problem types and the pedagogical techniques necessary to teach students how to solve problems through understanding. Using comprehension strategies and varied representations are key to student success with contextualized computation. The sandbox notes, structured techniques, and videos make this book very teacher friendly. The ideas are easily transferable to the mathematics classroom.”

Natalie Crist
Coordinator of Elementary Mathematics, Baltimore County Public Schools
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Sample Materials & Chapters

Preface (PDF)

Chapter 1 (PDF)

TOC + Video List (PDF)


Kimberly Morrow-Leong

Kimberly Morrow-Leong is an adjunct instructor at George Mason University in Fairfax, Virginia, a part-time researcher at American Institutes for Research, and a consultant for Math Solutions. She is a former grade 5–9 classroom teacher, K–8 mathematics coach, and coordinator of elementary professional development for the National Council of Teachers of Mathematics (NCTM). She recently completed an elected term as vice president and 2018 program chair for NCSM, Leadership in Mathematics Education. She holds a BA in French language and a masters in linguistics (TESOL). She also holds an MEd and PhD in mathematics education leadership from... More About Author

Sara Delano Moore

Sara Delano Moore is an independent mathematics education consultant at SDM Learning.  A fourth-generation educator, her work focuses on helping teachers and students understand mathematics as a coherent and connected discipline through the power of deep understanding and multiple representations for learning. Sara has worked as a classroom teacher of mathematics and science in the elementary and middle grades, a mathematics teacher educator, Director of the Center for Middle School Academic Achievement for the Commonwealth of Kentucky, and Director of Mathematics & Science at ETA hand2mind. Her journal articles appear in... More About Author

Linda M. Gojak

Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, Linda M. Gojak directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics. More About Author

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ISBN: 9781544389851
$ 32.95