![Mathematize It! [Grades 6-8] - Kimberly Morrow-Leong Corwin Mathematics Series](/cover_863768.jpg "Mathematize It! [Grades 6-8] - Kimberly Morrow-Leong")
Morrow-Leong, Kimberly, author. | Moore, Sara Delano, 1966- author. | Gojak, Linda, author.
Title: Mathematize it! : going beyond key words to make sense of word problems, grades 6-8 / Kimberly Morrow Leong, Sara Delano Moore, and Linda M. Gojak.
Description: Thousand Oaks, California : Corwin, [2021] | Includes bibliographical references and index.
Identifiers: LCCN 2020012020 | ISBN 9781506354484 (paperback) | ISBN 9781071819876 (epub) | ISBN 9781071819869 (ebook) | ISBN 9781071819852 (adobe pdf)
Subjects: LCSH: Word problems (Mathematics) | Mathematics—Study and teaching (Middle school)
Classification: LCC QA63 .M656 2021 | DDC 510.71/2—dc23 LC record available at https://lccn.loc.gov/2020012020
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Publisher, Mathematics: Erin Null
Associate Content Development Editor: Jessica Vidal
Editorial Assistant: Caroline Timmings
Production Editor: Tori Mirsadjadi
Copy Editor: Amy Marks
Typesetter: Integra
Proofreader: Susan Schon
Indexer: Integra
Cover and Interior Designer: Scott Van Atta
Marketing Manager: Margaret O’Connor
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Preface
The three of us (Kim, Sara, and Linda) spend a lot of time with teachers, talking about how students are successful and what challenges they face. Over and over, we hear that students struggle with problem solving, especially with word problems. We see challenges expressed in teacher comments on Twitter, on Facebook, on community sites like MyNCTM, in conference sessions, even in the news and on other social media. We hear this frustration from parents, from principals, and from math coaches across the country and internationally. We’ve written this book for classroom teachers and coaches who want to help their students have a more successful and meaningful approach to problem solving. If the approaches you have tried, such as using key words, or even using reading strategies to help students comprehend the problem, have yielded only spotty or unsatisfying results, this book is for you. If your students compute naked numbers efficiently, but when faced with a word problem they seem to pull numbers at random from problems and end up successfully calculating the wrong equations, this book is for you. If your students have ever looked at an equation and wondered how it fits the problem, this book is for you. We’ve written this book for all the teachers whose students look at a word problem and say, “I just don’t get what they want me to do!”
How This Book Can Help You
Would you be surprised to know that every addition word problem you can think of can be classified into one of four categories? It’s true! The same is true for every subtraction problem. Multiplication and division are a bit more complicated, but not as much as you might think. The hard part about a word problem isn’t in using the operations (+ − × ÷) to compute an answer but, rather, it’s in figuring out which operation to use in a problem and why. Once you understand the four kinds of addition problem types and can recognize them in a problem’s story, the puzzle pieces can start to come together. We don’t mean to oversimplify the learning that needs to take place, because it isn’t simple, but we want you to know that there is something you can do to help students learn to tackle word problems productively. More important, we want students to tackle real problems that interest them and learn more mathematics as they do so.
Solving problems is not only a goal of learning mathematics but also a major means of doing so. Students should have frequent opportunities to formulate, grapple with and solve complex problems that require a significant amount of effort and should then be encouraged to reflect on their thinking.
—Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000, p. 52)
There is no magic elixir to solve the problem of word problems. This book shares our approach, which focuses on helping children mine the problem to uncover the underlying mathematics. Much needs to happen between the reading comprehension and computation stages of the problem-solving process. Yes, students need support to read and comprehend the words, context, and language of the problem. Yes, they need to know how to compute the answer. But there is a whole middle ground of exploration and understanding that students often rush through, where they could instead turn what they read into a solvable mathematical story and apply their operation sense to solve the puzzle. This is where we so often see a gap. We’ve written this book to fill that gap. We want students to see their world mathematically and to know that mathematics can help them solve real problems. This is bigger (and more important) than passing a test.
To that end, this book is about problem solving. It’s about deciphering the kinds of word problems you see in normal, everyday lessons in classrooms like yours. It’s about the kinds of problems that are placed at the end of the lessons in your textbooks, the ones that your kids skip because they don’t know what to do. It’s about word problems. Story problems. Make-sense-of-the-math, practice-a-skill, not-quite-mathematical-modeling problems. Sometimes these problems can seem artificial or contrived, but their straightforward simplicity is also a strength because they target the mathematical thinking we want students to develop. Wrestling productively with word problems can lay a foundation for the more complex and open-ended problems students will also encounter. These problems also have the potential to do and be more in their own right when students can build the mathematical models that solve problems that interest them.
Solutions to these (routine word) problems, particularly the solutions of younger children, do in fact involve real problem-solving behavior… . Word problems can provide insights into the development of more complex problem-solving abilities.
(Carpenter, 1985, p. 17)
How to Use This Book
As a reader, you’ll get the most out of this book if you dig in and do the mathematics along the way. We’ve given you space to restate problems and draw pictures of your thinking with a focus on the mathematics. You’ll also find a collection of manipulatives helpful as you work through the book. Gather some counters, some base 10 blocks, and a fraction tool or two to use as aids while you solve problems. Think about how your students can use them too. Even in the middle grades, pictures, manipulatives, number lines, and bar models can hold an idea in place right in front of you so that you can think about it more deeply. With manipulatives, you can do even more. You can make a change more quickly and easily: Manipulatives allow students to act out what happens in a problem, and to use attributes like color and size to highlight features of a problem. As you’ll see, the best tool for the job depends on the problem. There will be plenty of examples for you to explore.
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