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

, (Mathematics Consultant), (Mathematics Consultant, NCTM Past-President)
  • Formatas: Paperback / softback, 232 pages, aukštis x plotis: 279x215 mm, weight: 590 g
  • Serija: Corwin Mathematics Series
  • Išleidimo metai: 26-Aug-2020
  • Leidėjas: Corwin Press Inc
  • ISBN-10: 154438985X
  • ISBN-13: 9781544389851
Kitos knygos pagal šią temą:
  • Formatas: Paperback / softback, 232 pages, aukštis x plotis: 279x215 mm, weight: 590 g
  • Serija: Corwin Mathematics Series
  • Išleidimo metai: 26-Aug-2020
  • Leidėjas: Corwin Press Inc
  • ISBN-10: 154438985X
  • ISBN-13: 9781544389851
Kitos knygos pagal šią temą:
"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 Coordinator, Elementary Mathematics Howard County Public School System, Ellicott City, MD



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 K-2 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 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! 

Recenzijos

"One of the most important goals of K2 math education should be developing a robust understanding of addition and subtraction that can serve as a foundation for later learning. In Mathematize It! Morrow-Leong, Moore, and Gojak help teachers transform solving word problems from an activity focused on getting answers to an activity that supports students understanding of the mathematical principles of the operations. Teaching

suggestions are integrated throughout the book in a manner that allows teachers to make adaptations to meet the needs of their students. This book belongs on every primary grade teachers bookshelf." -- Linda Levi "Kim Morrow-Leong, Sara Delano Moore, and Linda Gojak have written an essential guide for teachers of grade K2 mathematicsboth those new to the field and those with many years of experience. Read this book and learn how to help students develop a deep understanding of the mathematical principles behind each operationin other words, effectively help students learn to mathematize problem situations." -- Beth Skipper "Help your students get into the messy fun of true problem solving, where the goal is to make sense of the worldnot just arrive at an answer! Mathematize It! will engage you in the nuance and power of teaching through context. Youll be surprised and delighted by the student examples, inspired by the teacher commentary, and ready to craft story problems that uncover the big ideas of your grade." -- Berkeley Everett "Mathematize It! is a must-have resource for teachers and teacher leaders. In this comprehensive resource the authors not only introduce a new verbmathematizeto the primary teachers vocabulary, they also provide teachers with a go-to guide for teaching problem solving. Features such as the Mathematizing Sandbox as a problem-solving model, the emphasis on the use of multiple representations, and the integration of childrens literature provide teachers with instructional tools to help students develop a strong operation sense." -- Latrenda Knighten "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 mathematizingdrawing, 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
7(7)
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(6)
Building Your Understanding of the Operations and Related Problem Situations
7(3)
Playing in the Mathematizing Sandbox: A Problem-Solving Model
10(1)
Leveraging the Power of Children's Literature
11(1)
Final Words Before You Dive In
12(2)
Chapter Two Moving From Countingrto Addition And Subtraction
14(26)
Thinking About Counting, Addition, and Subtraction
14(12)
Sandbox Notes: Explore Your Thinking
16(2)
Students and Teachers Think About the Problem
18(1)
The Development of Counting
19(2)
Counting or Add-To?
21(2)
Representing Problem Situations or Representing Answers?
23(3)
Using Children's Literature to Explore Add-To and Take-From Situations
26(1)
Transcribe the Action or Relationship
26(1)
Moving Beyond 20
27(9)
Students and Teachers Think About the Problems
29(1)
Representing Problem Situations Multiple Ways
29(3)
Translating the Five Representations: Try It Out -
32(2)
Teaching Students to Use Concrete and Pictorial Models
34(2)
Key Ideas
36(1)
Try It Out!
37(2)
Reflect
39(1)
Chapter Three Add-To Problems: Locating The Change
40(30)
Thinking About Active Addition Situations
40(15)
Sandbox Notes: Explore Your Thinking
42(2)
Students and Teachers Think About the Problems
44(4)
Finding the Unknown: Three Story Structures
48(1)
Story Structures: Implications for Teaching
49(1)
Modeling the Active Problem Situation
50(5)
Using Children's Literature to Explore Add-To Situations
55(2)
Make Predictions
55(1)
Transcribe the Action or Relationship
56(1)
Digging Deeper Into Start Unknown Situations
57(9)
Complicating Things: The Start Unknown Variation
58(2)
Strategies for Making Sense of Start Unknown Problem Situations
60(2)
Separating Computations From Operations
62(2)
Moving to Equations
64(2)
Key Ideas
66(1)
Try It Out!
67(1)
Reflect
68(2)
Chapter Four take-prom problems: locating the change
70(24)
Thinking About Active Subtraction Situations
70(11)
Sandbox Notes: Explore Your Thinking
72(2)
Students and Teachers Think About the Problems
74(1)
Finding the Unknown: Three Story Structures
75(1)
Story Structures: Implications for Teaching
75(3)
Modeling the Active Problem Situation
78(3)
Digging Deeper Into the Start and Change Unknown Situations
81(8)
Moving From Concrete to Symbolic Representations
83(6)
Using Children's Literature to Explore Take-From Situations
89(1)
Create Another Outcome
89(1)
Find the Unknown Quantity
89(1)
Key Ideas
90(1)
Try It Out!
91(1)
Reflect
92(2)
Chapter Five Tart `part' whole: Understanding The Relationship
94(26)
Thinking About Part-Part-Whole Situations
94(13)
Sandbox Notes: Explore Your Thinking
96(2)
Students and Teachers Think About the Problems
98(1)
Defining the Part-Part-Whole Situation
99(1)
Modeling Relationships Versus Action
100(1)
Moving From Counters to Bar Models
101(4)
The Special Case of Both Addends Unknown
105(1)
A Note About the Commutative Property
106(1)
Using Children's Literature to Explore Part-Part-Whole Situations
107(1)
Make Predictions
107(1)
Moving Beyond 20
108(8)
Students and Teachers Think About the Problems
109(1)
Modeling Measurement Problems
110(1)
Writing Equations: Addition or Subtraction
111(2)
Finding the Equation in the Model
113(3)
Key Ideas
116(1)
Try It Out!
117(1)
Reflect
118(2)
Chapter Six Additive comparisons: another. kind of relationship
120(26)
Thinking About Additive Comparison Situations
120(8)
Sandbox Notes: Explore Your Thinking
122(2)
Students and Teachers Think About the Problems
124(1)
Early Years Comparisons
125(1)
Additive Comparison Situations
126(2)
Building Models for Comparisons
128(4)
Students and Teachers Think About the Problems
129(1)
Making Use of Models for Thinking
130(2)
The Language of Comparison Problems
132(8)
Language Can Get Tricky
135(2)
Building Bar Models for Comparisons
137(1)
From Counters to Bar Models
138(1)
Problem Posing as an Instructional Strategy
139(1)
Using Children's Literature to Explore Additive Comparison Situations
140(1)
Create Another Outcome
140(1)
Key Ideas
141(1)
Try It Out!
142(2)
Reflect
144(2)
Chapter Seven Early twltipucation and division: patterns and predictions
146(27)
Thinking About Early Multiplicative Thinking
146(8)
Sandbox Notes: Explore Your Thinking
148(2)
Students and Teachers Think About the Problem
150(1)
Modeling Even and Odd Numbers
151(1)
Equal Groups Problem Situation
152(1)
Using Patterns to Identify Even and Odd Numbers
153(1)
Using Children's Literature to Explore Early Multiplication
154(1)
Transcribe the Action or Relationship
155(1)
Bringing in Another Dimension With Arrays
155(4)
Recognizing Area/Array as a Problem Situation
158(1)
Building an Understanding of Arrays as Structures
158(1)
Using Children's Literature to Explore Area and Array Situations
159(1)
Transcribe the Action or Relationship
160(1)
Setting the Stage for Division
160(7)
Equipartitioning
163(3)
Two Models of Division
166(1)
Using Children's Literature to Explore Early Multiplication and Division
167(1)
Transcribe the Action or Relationship
167(1)
A Final Word on Introducing Early Multiplication and Division
168(1)
Key Ideas
168(1)
Try It Out!
169(2)
Reflect
171(2)
Chapter Eight Changing How You Teach Woro Problems
173(12)
Getting Into the Mathematizing Sandbox
173(2)
Eight Shifts in Instruction for Building Students' Problem-Solving Skills
175(5)
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(3)
Finding Unexpected Mathematics in Stories
183(2)
Play With Quantities
183(2)
Appendix: Situation Tables 185(3)
References 188(3)
Index 191
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!

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.

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.