We Reason & We Prove for ALL Mathematics: Building Students’ Critical Thinking, Grades 6-12 de Fran Arbaugh

We Reason & We Prove for ALL Mathematics: Building Students’ Critical Thinking, Grades 6-12: Corwin Mathematics Series

Autor Fran Arbaugh, Margaret (Peg) S. Smith, Justin D. Boyle, Gabriel J. Stylianides, Michael D. Steele

en Limba Engleză Paperback – 17 sep 2018

This book transcends all mathematical content areas with a variety of activities for teachers that include

Solving and discussing high-level mathematical tasks
Analyzing narrative cases that make the relationship between teaching and learning salient
Examining and interpreting student work
Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove

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Specificații

ISBN-13: 9781506378190
ISBN-10: 1506378196
Pagini: 272
Dimensiuni: 187 x 232 x 41 mm
Greutate: 0.56 kg
Ediția:1
Editura: SAGE Publications
Colecția Corwin
Seria Corwin Mathematics Series

Locul publicării:Thousand Oaks, United States

Recenzii

"Simply stated, this book is a must-have for preservice and inservice mathematics teachers and teacher leaders who are looking to enhance their understanding of how reasoning-and-proving are critical processes for increasing proficiency across all mathematics content domains. This expert author team has illustrated a clear vision and plan, supported by key strategies and exceptional tools, for guiding teacher teams as they help their students learn how to make conjectures and develop and judge the effectiveness of their arguments and proofs. This book is an exceptionally useful and timely resource for schools and districts that are looking to connect and deepen their professional focus with the Effective Mathematics Teaching Practices (NCTM, 2014) and other evidence-based practices."
"Reasoning-and-proving are central to investigating ideas, solving problems, and establishing mathematics knowledge at all levels. Built around rich classroom cases, this book provides research-supported frameworks and practical resources for teachers to deepen their understanding and develop practices to aid students in reasoning-and-proving as powerful mathematical thinkers."

"We Reason & We Prove for ALL Mathematics provides an enlightening and engaging examination of reasoning-and-proving in secondary mathematics classrooms. Filled with carefully designed tasks and task sequences, along with illustrative classroom cases, it clearly articulates the nature of reasoning-and-proving, what students need to know and understand about it, and how teachers can support this learning. The thought-provoking discussion questions and recommended classroom activities support readers’ implementation of reasoning-and-proving activities into their own classrooms. We Reason & We Prove for ALL Mathematics is an outstanding resource for practice-based learning on this essential component of mathematics learning. I recommend it most highly."
"The authors of We Reason & We Prove for ALL Mathematics have taken aim at a long-standing challenge in mathematics education: helping students become proficient with mathematical reasoning and proof. In so doing they have produced a book that will be useful to teachers and scholars alike in addressing a topic that is both difficult to teach and difficult to learn. This volume blends knowledge obtained through rigorous research with practical wisdom derived from extensive experience. Building upon a solid foundation of prior research on students’ mathematical reasoning, the authors offer a collection of narrative cases and mathematics activities designed to deepen the understanding of teachers in ways that will enhance the teaching and learning of proof and reasoning."
"Grounded in the research on effective mathematics teaching practices and connected to the mathematical content taught in middle and high school, We Reason & We Prove for ALL Mathematics offers exceptional guidance, superb exemplars, and important classroom discussion questions to support student reasoning-and-proving. The ideas in this book are what we need to move away from repeat-after-me mathematics toward a convince-me mathematics—totally transforming mathematics classrooms and increasing students’ opportunities to engage in doing authentic mathematics."

Cuprins

Preface
Acknowledgements
About the Authors
Chapter 1 Setting the Stage
Are Reasoning and Proving Really What You Think?
Supporting Background and Contents of This Book
What is Reasoning and Proving in Middle and High School Mathematics?
Realizing the Vision of Reasoning-and-Proving in Middle and High School Mathematics
Discussion Questions
Chapter 2 Convincing Students Why Proof Matters
Why Do We Need to Learn How To Prove?
The Three Task Sequence
Engaging in the Three Task Sequence, Part 1: The Squares Problem
Engaging in the Three Task Sequence, Part 2: Circle and Spots Problem
Engaging in the Three Task Sequence, Part 3: The Monstrous Counterexample
Analyzing Teaching Episodes of the Three Task Sequence: The Cases of Charlie Sanders and Gina Burrows
Connecting to Your Classroom
Discussion Questions
Chapter 3 Exploring the Nature of Reasoning-and-Proving
When is an Argument a Proof?
The Reasoning-and-Proving Analytic Framework
Developing Arguments
Developing a Proof
Reflecting on What You’ve Learned about Reasoning and Proving
Revisiting the Squares Problem from Chapter 2
Connecting to Your Classroom
Discussion Questions
Chapter 4 Helping Students Develop the Capacity to Reason-and-Prove
How Do You Help Students Reason and Prove?
A Framework for Examining Mathematics Classrooms
Determining How Student Learning is Supported: The Case of Vicky Mansfield
Determining How Student Learning is Supported: The Case of Nancy Edwards
Looking Across the Cases of Vicky Mansfield and Nancy Edwards
Connecting to Your Classroom
Discussion Questions
Chapter 5 Modifying Tasks to Increase the Reasoning-and-Proving Potential
How Do You Make Tasks Reasoning-and-Proving Worthy?
Returning to the Effective Mathematics Teaching Practices
Examining Textbooks or Curriculum Materials for Reasoning-and-Proving Opportunities
Revisiting the Case of Nancy Edwards
Continuing to Examine Tasks and Their Modifications
Re-Examining Modifications Made to Tasks Through a Different Lens
Comparing More Tasks with their Modifications
Strategies for Modifying a Task to Enhance Students’ Opportunities to Reason-and-Prove
Connecting to Your Classroom
Discussion Questions
Chapter 6 Using Context to Engage in Reasoning-and-Proving
How Does Context Affect Reasoning-and-Proving?
Considering Opportunities for Reasoning-and-Proving
Solving the Sticky Gum Problem
Analyzing Student Work from the Sticky Gum Problem
Analyzing Two Different Classroom Enactments of the Sticky Gum Problem
Connecting to Your Classroom
Discussion Questions
Chapter 7 Putting it All Together
Key Ideas at the Heart of this Book
Tools to Support the Teaching of Reasoning-and-Proving
Putting the Tools to Work
Moving Forward in Your PLC
Discussion Questions
Appendix A Developing a Need for Proof: The Case of Charlie Sanders
Appendix B Motivating the Need for Proof: The Case of Gina Burrows
Appendix C Writing and Critiquing Proofs: The Case of Vicky Mansfield
Appendix D Pressing Students to Prove It: The Case of Nancy Edwards
Appendix E Making Sure that All Students Understand: The Case of Calvin Jenson
Appendix G Helping Students Connect Pictorial and Symbolic Representations: The Case of Natalie Boyer
References

Notă biografică

Descriere

Develop concrete instructional strategies that support students' capacity to reason-and-prove across all mathematical content areas in 6-12 classrooms, while becoming adept at reasoning-and-proving.

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