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Open Middle Math: Problems That Unlock Student Thinking, 6-12 [Pehme köide]

  • Formaat: Paperback / softback, 192 pages, kõrgus x laius: 229x178 mm, kaal: 369 g
  • Ilmumisaeg: 30-Oct-2019
  • Kirjastus: Stenhouse Publishers
  • ISBN-10: 1625311745
  • ISBN-13: 9781625311740
Teised raamatud teemal:
  • Formaat: Paperback / softback, 192 pages, kõrgus x laius: 229x178 mm, kaal: 369 g
  • Ilmumisaeg: 30-Oct-2019
  • Kirjastus: Stenhouse Publishers
  • ISBN-10: 1625311745
  • ISBN-13: 9781625311740
Teised raamatud teemal:
Kaplinsky, who has been a classroom teacher, teacher specialist, and university instructor, shows teachers how to use open middle math problems to engage all students in grades six through 12. He describes how open middle problems will help teachers; how they differ from other problems by making learning accessible, easy to differentiate, and having many possible ways to solve the problem (an open middle); problems that help detect student misconceptions and strengthen conceptual understanding; what to do before using a problem with students, including how to help students feel comfortable with solving a new type of problem with undefined steps, how to decide which problems to use, and how to use planning to minimize anxiety and lead to powerful experiences; how to get students started on open middle problems; and how to find pre-made problems online and create one's own problems. Annotation ©2020 Ringgold, Inc., Portland, OR (protoview.com)

Imagine that you assign a math problem and your students, instead of getting discouraged after not solving it on the first attempt, start working harder&;as if on a quest to figure out the answer. They talk to each other and enthusiastically share their discoveries. What could possibly make this fantastic scenario come true? The answer is: the Open Middle math problems and strategies in this book.

Open Middle Math by Robert Kaplinsky gives middle and high school teachers the problems and planning guidance that will encourage students to see mathematics in an entirely different light. These challenging and rewarding Open Middle math problems will help you see your students build genuine conceptual understanding, perseverance, and creativity.

Inside, you&;ll learn how to:

  • Implement Open Middle math problems that are simultaneously accessible for both students who are struggling and those looking for more challenge.
  • Select and create Open Middle math problems that will help you detect students' misconceptions and strengthen their conceptual understanding.
  • Prepare for and facilitate powerful classroom conversations using Open Middle math problems.
  • Access resources that will help you continue learning beyond this book.

With these practical and intuitive strategies, extensive resources, and Robert&;s own stories about his journey learning to use Open Middle math problems successfully, you will be able to support, challenge, and motivate all your students.

Arvustused

This book is an amazing resource for teachers who are striving to help students develop both procedural fluency and conceptual understanding. Dr. Margaret Peg Smith "Open Middle Math is a quick read. A must read. A read with the potential for immediate transformation of the quality of discourse in your classroom." - Sara VanDerWerf If you are seeking to challenge your students' thinking and build their conceptual understanding, Open Middle Math: Problems That Unlock Student Thinking, Grades 6--12 is a must-have resource. Dr. Kristopher J. Childs WARNING: Your students may not leave your mathematics classroom when the bell rings if you start using Open Middle tasks. - Sara VanDerWerf "The mathematics education community will simply devour this delicious book" - Lauren Baucom "In reading and applying Open Middle Math, I feel like I have an experienced coach cheering me on! Cathy Yenca Robert Kaplinsky's Open Middle Math provides teachers with readymade resources and practical strategies so their students can enjoy learning math through challenging problems theyll look forward to solving. Andrew Stadel Robert offers teachers strategies for adding openness and richness to problems that are at first closed and meager. Dan Meyer Open Middle Math gives teachers valuable guidance on creating safe and discovery-rich conversational spaces where students find learning math can be fun. Robert Kaplinsky's Open Middle Math provides teachers with ready-made resources and practical strategies so their students can enjoy learning math through challenging problems theyll look forward to solving.

This book is an amazing resource for teachers who are striving to help students develop both procedural fluency and conceptual understanding. Open Middle problems provide students with the opportunity to move beyond traditional procedural practice problems to explore mathematical relationships more deeply. In addition, Open Middle problems provide teachers with insights into what students really understand about the procedures they learned and important formative assessment data they can use to modify instruction. This book is a very practical guide to implementing a new class of tasks that have the potential to improve student learning!

Do you ever wish you could get a glimpse into a designers mind for how they implement their innovation? Robert Kaplinskys Open Middle Math gives educators an inside look into how Open Middle problems are designed to assist students to engage in, learn from, and persevere in productive struggle. Robert has always been willing to share his learning progress, struggles, and mistakes openly. Through his humility, he encourages readers to remember the joy that comes with productively struggling with a mathematics problem, and that we often learn more from the journey of solving than arriving at a solution. The mathematics education community will simply devour this delicious book.

Robert offers teachers strategies for adding openness and richness to problems that are at first closed and meager. So take heart, teachers! The interest and learning of your students arent dictated by the problems in your textbook as you first find them, only by your imagination and design.

WARNING: Your students may not leave your mathematics classroom when the bell rings if you start using Open Middle tasks. In his book, Robert Kaplinsky gives math educators a roadmap to effectively implement Open Middle Math with tips, multiple examples at each secondary level, answers to the what ifs, resources, and structures for creating your own tasks. . . . Open Middle Math is a quick read. A must-read. A read with the potential for immediate transformation of the quality of discourse in your classroom.

Foreword viii
Nanette Johnson
Acknowledgments xi
Introduction What Does an Open Middle Classroom Look Like? 1(7)
Chapter One How Will These Problems Help Me?
8(5)
Chapter Two How Are Open Middle Problems Different?
13(42)
Problems at Each Grade Level
19(29)
Sixth-Grade Example: Dividing Fractions
21(3)
Seventh-Grade Example: Solving Two-Step Equations
24(3)
Eighth-Grade Example: Evaluating Exponents
27(3)
Algebra Example: Interpreting Key Features of Quadratics in Vertex Form
30(4)
Geometry Example: Finding the Midpoint of a Line Segment
34(4)
Algebra 2 Example: Multiplying Complex Numbers
38(3)
Trigonometry and Pre-Calculus Example: Evaluating Trigonometric Functions
41(3)
Calculus Example: Evaluating Definite Integrals
44(4)
What Are Open Middle Problems?
48(4)
Connections to Other Kinds of Problems
52(3)
Chapter Three What Do We Need to Do Before Using a Problem with Students?
55(21)
How Should We Get Started?
57(2)
When Would We Want to Use an Open Middle Problem?
59(1)
How Do We Choose a Problem?
60(3)
How Do We Prepare to Use the Problem?
63(7)
What Understandings Do We Want Students to Gain from the Problem?
70(6)
Chapter Four How Do We Use a Problem with Students?
76(54)
How Do We Get Students Started on the Problem?
77(1)
What Happens After We Explain the Directions to Students?
78(1)
What Should We Do While Students Are Working?
79(3)
What If Students Don't Use the Method We Had Hoped?
82(3)
What If Students Solve the Problem Using a Method We Don't Understand?
85(3)
What Should We Do If Students Give Up After Trying the Problem a Couple of Times?
88(10)
How Can We Tell When Productive Struggle Becomes Unproductive Struggle?
98(3)
What Should We Do If Students Are Unproductively Struggling?
101(1)
What Should We Do When Kids Get Stuck in Unexpected Ways?
102(3)
What Should We Do After Students Are Finished with the Problem?
105(9)
How Do We Facilitate the Classroom Conversation?
114(6)
What If Students Are Not Ready for a Conversation by the End of Class?
120(2)
How Do We Avoid Hurting Students' Feelings?
122(1)
What Should We Do If Students Struggle to Explain Their Thinking?
123(3)
How Much Class Time Should This All Take?
126(1)
What Should We Do with the Information We Learn About What Students Know?
127(3)
Chapter Five Where Can I Get More Open Middle Problems?
130(29)
Find Them on Open Middle
130(2)
Make Your Own Open Middle Problems
132(18)
Step 1: Start with a Level 1 Problem
136(2)
Step 2: Increase the Problem from Level 1 to Level 2
138(5)
Step 3: Increase the Problem from Level 2 to Level 3
143(7)
Make More Advanced Problems
150(8)
Share Your Open Middle Problems with Other Math Educators
158(1)
Chapter Six What Comes Next?
159(12)
Actions to Consider
163(4)
Final Thoughts
167(4)
References 171(2)
Index 173
Robert Kaplinsky has worked in education since 2003 as a classroom teacher, teacher specialist for Downey Unified School District, instructor for the University of California, Los Angeles (UCLA), and presenter at conferences around the world. He is also the co-founder of the website OpenMiddle.com, as well as the Southern California Math Teacher Specialist Network, a group that includes over 200 math teacher specialists from more than five countries. His work has been published by the American Educational Research Association (AERA), Education Week, and many others.