Mathematize It! [Grades 3-5]: Going Beyond Key Words to Make Sense of Word Problems, Grades 3-5: Corwin Mathematics Series
Autor Sara Delano Moore, Kimberly Morrow-Leong, Linda M. Gojaken Limba Engleză Paperback – 2 dec 2019
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Specificații
ISBN-10: 1506395279
Pagini: 224
Dimensiuni: 216 x 279 x 16 mm
Greutate: 0.61 kg
Ediția:First Edition
Editura: SAGE Publications
Colecția Corwin
Seria Corwin Mathematics Series
Locul publicării:Thousand Oaks, United States
Recenzii
“Mathematize It! is a must-read for anyone who has struggled to teach word problems and is ready to figure out what really works. The authors present a plethora of strategies that help students focus on the thinking part of the problem-solving process while gently helping the reader understand that so many of our ‘tried-and-true’ methods, such as key words, really don’t work. They help us realize that the real work of solving word problems is in the sense-making phase—once students have made sense of a problem, calculating the solution is the simpler part of the process.”
Mathematize It! addresses the complexity of problem solving more completely than any other individual resource. It is easy to say that we must teach students to ‘mathematize situations’ but this book helps us to actually help students learn to do it. The challenge and reflection pieces at the end of each chapter are a game changer for unveiling teaching opportunities, prompting discussion in your PLC, and moving this from a book on the professional shelf to a powerful tool to impact instruction.
“Mathematize It! is a book that should be on the shelf of every classroom teacher and division leader who supports mathematics teaching and leading. This valuable resource helps educators to think about the what, why, and the how to make sense of word problems. It gives a framework and visuals on how to support teachers’ understanding around problem types and solving problems and excels in assisting teachers in how to make a commitment to teaching for greater understanding.”
“This is a game changer… even after 20 years of supporting students and their sensemaking of word problems, I am thrilled to learn even more from this trio of authors. They offer practical suggestions, opportunities for practice, and relevant research in order to increase awareness of best practices surrounding word problems. The only key word in this case is MATHEMATIZE! To have this resource in your hands is to have an invitation to the ‘mathematizing sandbox’.”
“This dynamic author trio brings years of classroom experiences to one of the central problems of teaching and learning mathematics: making sense of word problems. Focusing on the construct of “mathematizing”—drawing, constructing, describing, representing, and making sense of situations— this clear and practical guide needs to be required reading and discussion fodder for every elementary teacher of mathematics. It’s just that clear, informative and insightful!”
“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.”
“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!”
“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.”
“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!”
“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.”
“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.”
“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.”
Cuprins
Preface
Chapter 1 Introduction: Why You Need to Teach Students to Mathematize
Problem Solving Strategies Gone Wrong
What is Mathematizing? Why Is It Important?
Teaching Students to Mathematize
Final Words Before You Dive In
Part 1 Addition and Subtraction
Chapter 2: Add-To and Take-From: Locating the Change
Thinking About Active Addition and Subtraction Situations
Moving Beyond Whole Numbers
Key Ideas
Try It Out!
Reflect
Chapter 3: Part-Part-Whole: Understanding the Relationship
Thinking About Part-Part-Whole Situations
Moving Beyond Whole Numbers
Key Ideas
Try It Out!
Reflect
Chapter 4: Additive Comparisons: Another Kind of Relationship
Thinking About Additive Comparison Situations
Moving Beyond Whole Numbers
Key Ideas
Try It Out!
Reflect
Part 2: Multiplication and Division
Chapter 5: Equal Groups Multiplication: Two Factors, Different Jobs
Thinking About Equal Groups Situations
Moving Beyond Whole Numbers
Key Ideas
Try it Out!
Reflect
Chapter 6: Equal Groups Division: When a Factor Is Missing
Thinking About Equal Groups Division
Moving Beyond Whole Numbers
Key Ideas
Try it Out!
Reflect
Chapter 7: Multiplicative Comparisons: Another Asymmetric Relationship
Thinking About Multiplicative Comparisons
Moving Beyond Whole Numbers
Key Ideas
Try It Out!
Reflect
Chapter 8: Area and Array: Two Factors, Same Job
Thinking About Area and Array Situations
Moving Beyond Whole Numbers
Key Ideas
Try It Out!
Reflect
Chapter 9: Changing How You Teach Word Problems
Getting into the Mathematizing Sandbox
8 Shifts in Instruction for Building Students’ Problem-Solving Skills
Guidance for Moving Forward: FAQ’s
Appendix A – Situation Tables
References
Index
Notă biografică
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 Mathematics Teaching in the Middle School, Teaching Children Mathematics, Science & Children, and Science Scope.
Descriere
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.
Mathematize It! 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.
This user-friendly resource for Grades 3–5
• Offers a systematic mathematizing process for solving word problems
• Provides specific examples for all four operations (addition, subtraction, multiplication, and division) with whole numbers, fractions, and decimals
• Demonstrates the use of concrete manipulatives to model problems with dozens of short videos