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Mathematize It! [ Grades 3-5]: Going Beyond Key Words to Make Sense of Word Problems, Grades 3-5 [Mīkstie vāki]

4.50/5 (41 ratings by Goodreads)
  • Formāts: Paperback / softback, 224 pages, height x width: 279x215 mm, weight: 580 g
  • Sērija : Corwin Mathematics Series
  • Izdošanas datums: 03-Dec-2019
  • Izdevniecība: Corwin Press Inc
  • ISBN-10: 1506395279
  • ISBN-13: 9781506395272
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  • Mīkstie vāki
  • Cena: 39,10 €
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  • Formāts: Paperback / softback, 224 pages, height x width: 279x215 mm, weight: 580 g
  • Sērija : Corwin Mathematics Series
  • Izdošanas datums: 03-Dec-2019
  • Izdevniecība: Corwin Press Inc
  • ISBN-10: 1506395279
  • ISBN-13: 9781506395272
Citas grāmatas par šo tēmu:
"The list of math books to truly synthesize what we know so far and what we need to know is a very short and exclusive list. Well, you can confidently add Mathematize It to this collection. Written by three of the most respected math educators today, the book zeros in on that often poorly traveled journey between the question and answer in problem solving. Mathematize It will be your go-to resource to install the mathematical play revolution in elementary classes everywhere!"

Suni Singh  Author of Pi of Life: the Hidden Happiness of Mathematics and Math Recess: Playful Learning in an Age of Disruption



Help students reveal the math behind the words

"I dont get what Im 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 3-5 shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problems context, and employ strong operation sense to solve it. Through the process of mathematizing, the authors provide an explanation of a consistent methodand specific instructional strategiesto 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 35

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 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 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! 

Recenzijas

"The list of generational math books to come along and truly synthesize what we know so far and what we need to know is a very short and exclusive list. Well, you can confidently add Mathematize It! to this collection. Written by three of the most respected math educators today, the book zeros in on that often poorly traveled journey between the question and answer in problem solving. Mathematize It! will be your go-to resource to install the mathematical play revolution in elementary classes everywhere!" -- Sunil Singh "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 dont work. They help us realize that the real work of solving word problems is in the sense-making phaseonce students have made sense of a problem, calculating the solution is the simpler part of the process." -- Kimberly Rimbey 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. -- Gina Kilday "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." -- Spencer Jamieson "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." -- Beth Terry "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. Its just that clear, informative and insightful!" -- Steve Leinwand "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 "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 taskone that is akin to something weve 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. Its time for you to play in the sandbox and more importantly, Mathematize It!" -- Hilary Kreisberg "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 "I cant 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 "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 teachers collection of instructional resources." -- John Sangiovanni "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 "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

List of Videos
xix
Preface xxi
Acknowledgments xxiv
About The Authors xxvii
Chapter One Introduction: Why You Need To Teach Students To Mathematize
1(13)
Problem-Solving Strategies Gone Wrong
2(1)
What Is Mathematizing? Why Is It Important?
3(3)
Focusing on Operation Sense
4(1)
Using Mathematical Representations
4(2)
Teaching Students to Mathematize
6(5)
Building Your Understanding of the Operations and Related Problem Situations
7(3)
Playing in the Mathematizing Sandbox: A Problem-Solving Model
10(1)
Final Words Before You Dive In
11(3)
PART I ADDITIONA AND SUBTRACTION
Chapter Two Add-To And Take-From: Locating The Change
14(24)
Thinking About Active Addition and Subtraction Situations
14(12)
Students and Teachers Think About the Problems
18(1)
Finding the Unknown, Three Story Structures
18(2)
Story Structures: Implications for Teaching
20(2)
Focus on Take-From Situations
22(2)
Modeling the Active Problem Situation
24(2)
Teaching Students to Use Concrete and Pictorial Models
26(1)
Moving Beyond Whole Numbers
27(6)
Students and Teachers Think About the Problems
29(1)
Teaching Opportunities in the Student Work Samples
30(1)
Complicating Things: The Start Unknown Variation
30(3)
The Power of Writing Stories
33(1)
Key Ideas
34(1)
Try It Out!
35(1)
Reflect
36(2)
Chapter Three Part-Part-Whole: Understanding The Relationship
38(20)
Thinking About Part-Part-Whole Situations
38(7)
Students and Teachers Think About the Problems
42(1)
Defining the Part-Part-Whole Situation
43(1)
Modeling Relationships Versus Action
44(1)
Improving the Accuracy of Student Models
45(1)
Writing Equations: Addition or Subtraction?
45(2)
Moving Beyond Whole Numbers
47(8)
Students and Teachers Think About the Problems
48(2)
Finding the Equation in the Model
50(1)
Modeling Measurement Problems
51(3)
The Special Case of Both Parts Unknown
54(1)
Key Ideas
55(1)
Try It Out!
56(1)
Reflect
57(1)
Chapter Four Additive Comparisons: Another Kino Op Relationship
58(22)
Thinking About Additive Comparison Situations
58(11)
Students and Teachers Think About the Problems
62(2)
Language Can Get Tricky
64(2)
Building Models for Comparisons
66(2)
Knowing When to Add and When to Subtract
68(1)
A Note About Equations
69(1)
Moving Beyond Whole Numbers
70(4)
Students and Teachers Think About the Problems
71(1)
The Anchor-Jump Strategy and Bar Models
71(1)
Modeling the Difference in Comparison Situations
72(2)
Problem Posing as an Instructional Strategy
74(1)
Key Ideas
75(1)
Try It Out!
75(2)
Reflect
77(3)
PART II Multiplication And Division
Chapter Five Equal Groups Multiplication: Two Factors, Different Joes
80(22)
Thinking About Equal Groups Situations
80(11)
Students and Teachers Think About the Problems
84(1)
Multiplier and Measure Factors
85(2)
Equal Groups and the Commutative Property
87(2)
Representing Larger Quantities
89(2)
Moving Beyond Whole Numbers
91(8)
Students and Teachers Think About the Problems
92(1)
Equal Groups and Repeated Addition
92(1)
Understanding a Portion of a Group
93(1)
Starting With an Expression to Build Multiplicative Reasoning
94(2)
Moving the Missing Term
96(3)
Key Ideas
99(1)
Try It Out!
100(1)
Reflect
101(1)
Chapter Six Equal Groups Division: When A Factor Is Missing
102(26)
Thinking About Equal Groups Division
104(9)
Students and Teachers Think About the Problems
106(1)
Partitive Division
106(2)
Measurement (Quotitive) Division
108(1)
The Unknowns in Partitive and Measurement Division
109(1)
Remainders
110(1)
Matching Models to Contexts
111(2)
Moving Beyond Whole Numbers
113(9)
Students and Teachers Think About the Problems
114(1)
Entering Challenging Division Problems
115(1)
Translating the Five Representations: Try It Out
116(2)
Tracking the Unit Whole and the Referent Whole
118(4)
Notes on Working With Manipulatives
122(1)
Key Ideas
123(1)
Try it Out!
124(2)
Reflect
126(2)
Chapter Seven Multiplicative Comparisons: Another Asymmetric Relationship
128(22)
Thinking About Multiplicative Comparisons
128(13)
Students and Teachers Think About the Problems
132(1)
Additive Versus Multiplicative Comparison
133(1)
Growing Faster
134(2)
Reasoning Around 10
136(2)
Multiplicative Comparison, Measurement, and Conversion
138(3)
Moving Beyond Whole Numbers
141(4)
Students and Teachers Think About the Problems
142(1)
Absolute and Relative Change
142(1)
Helping Students Transition to Multiplicative Thinking
143(2)
Can Multiplication Make a Quantity Smaller?
145(2)
Key Ideas
147(1)
Try It Out!
147(2)
Reflect
149(1)
Chapter Eight Area And Array: Two Factors, Same Job
150(623)
Thinking About Area and Array Situations
150(8)
Students and Teachers Think About the Problems
154(1)
Symmetric Versus Asymmetric Multiplication
154(3)
Another Symmetric Problem Situation: The Fundamental Counting Principle
157(1)
Modeling Arrays: Situations or Computation?
158(3)
Arrays as a Mathematical Structure
160(1)
Models of and Models for Thinking
161(2)
Moving Beyond Whole Numbers
163(6)
Students and Teachers Think About the Problems
164(2)
When Models Match and When They Don't
166(1)
Representing Fraction and Decimal Division
166(3)
Key Ideas
169(1)
Try It Out!
169(2)
Reflect
171(2)
Chapter Nine Changing How You Teach Word Problems
173(1)
Getting Into the Mathematizing Sandbox
173(2)
Eight Shifts in Instruction for Building Students' Problem-Solving Skills
175(1)
Do Word Problems for Sense-Making
175(1)
Treat Context and Computation Separately
176(1)
Create More and Varied Representations
176(1)
Explore All the Work Operations Can Do
177(1)
Add Operation Sense Routines to the School Day
178(1)
Offer Students Experiences With a Variety of Problem Situations
178(1)
Listen to Students and Be Curious
179(1)
Make Time for Mathematizing in the Sandbox
179(1)
Guidance for Moving Forward: FAQs
180(4)
Appendix: Situation Tables 184(3)
References 187(3)
Index 190
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.

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 59 classroom teacher, K8 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 George Mason University. Kim is the 2009 recipient of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) from Virginia. She is happiest when working with teachers and students, putting pencils down and getting messy with manipulatives!

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.