We Reason & We Prove for ALL Mathematics (häftad)
Häftad (Paperback)
Antal sidor
Smith, Margaret (Peg) S. / Boyle, Justin D. / Stylianides, Gabriel J. / Steele, Michael D.
229 x 185 x 10 mm
558 g
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We Reason & We Prove for ALL Mathematics (häftad)

We Reason & We Prove for ALL Mathematics

Building Students Critical Thinking, Grades 6-12

Häftad Engelska, 2018-09-18
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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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  3. Inquiry into Mathematics Teacher Education

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  • Inquiry into Mathematics Teacher Education

    Fran Arbaugh, P Mark Taylor

    The 14 chapters in this monograph provide support for mathematics teacher educators in both their Practical Knowledge and their Professional Knowledge. Individually, these articles provide insights into advancing our thinking about professional de...

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"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 sc...

Övrig information

Dr. Fran Arbaugh is an associate professor of mathematics education at Penn State University, having begun her career as a university mathematics teacher educator at the University of Missouri. She is a former high school mathematics teacher, received a M.Ed. in Secondary Mathematics Education from Virginia Commonwealth University and a PhD in Curriculum & Instruction (Mathematics Education) from Indiana University Bloomington. Frans scholarship is in the area of professional learning opportunities for mathematics teachers and mathematics teacher educators, and her work is widely published for both research and practitioner audiences. She is a Past-President of the Association of Mathematics Teacher Educators (ATME) and served as a Co-Editor of the Journal of Teacher Education.

Margaret (Peg) Smith is a Professor Emerita at University of Pittsburgh. Over the past two decades she has been developing research-based materials for use in the professional development of mathematics teachers. She has authored or coauthored over 90 books, edited books or monographs, book chapters, and peer-reviewed articles including the best seller Five Practices for Orchestrating Productive Discussions (co-authored with Mary Kay Stein). She was a member of the writing team for Principles to Actions: Ensuring Mathematical Success for All and she is a co-author of two new books (Taking Action: Implementation Effective Mathematics Teaching Practices Grades 6-8 & 9-12) that provide further explication of the teaching practices first describe in Principles to Actions. She was a member of the Board of Directors of the Association of Mathematics Teacher Educators (2001-2003; 2003 2005), of the National Council of Teachers of Mathematics (2006-2009), and of Teachers Development Group (2009 2017).

Justin Boyle is an assistant professor at the University of Alabama. He is interested in learning how best to develop secondary mathematics teachers, so that they are prepared to engage their future students in becoming intellectually curious about mathematics. In particular, he uses reasoning-and-proving as a way to investigate and discuss the truth of mathematical statements, concepts and objects.

Gabriel J. Stylianides is Professor of Mathematics Education at the University of Oxford (UK) and Fellow of Oxfords Worcester College. A Fulbright scholar, he received MSc degrees in mathematics and mathematics education, and then his PhD in mathematics education, at the University of Michigan. He has conducted extensive research in the area of reasoning-and-proving at all levels of education, including teacher education and professional development. He was an Editor of Research in Mathematics Education and is currently an Editorial Board member of the Elementary School Jou...


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