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We Reason & We Prove for ALL Mathematics

We Reason & We Prove for ALL Mathematics PDF Author: Fran Arbaugh
Publisher: Corwin Press
ISBN: 150637820X
Category : Education
Languages : en
Pages : 273

Book Description
Sharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, 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 No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.

We Reason & We Prove for ALL Mathematics

We Reason & We Prove for ALL Mathematics PDF Author: Fran Arbaugh
Publisher: Corwin Press
ISBN: 150637820X
Category : Education
Languages : en
Pages : 273

Book Description
Sharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, 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 No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.

We Reason & We Prove for ALL Mathematics

We Reason & We Prove for ALL Mathematics PDF Author: Fran Arbaugh
Publisher:
ISBN: 9781071800812
Category :
Languages : en
Pages : 250

Book Description
Sharpen concrete teaching strategies that empower students to reason-and-prove How do teachers and students benefit from engaging in reasoning-and-proving? What strategies can teachers use to support students' capacity to reason-and-prove? What does reasoning-and-proving instruction look like? We Reason & We Prove for ALL Mathematics helps mathematics teachers in grades 6--12 engage in the critical practice of reasoning-and-proving and support the development of reasoning-and-proving in their students. The phrase "reasoning-and-proving" describes the processes of identifying patterns, making conjectures, and providing arguments that may or may not qualify as proofs-processes that reflect the work of mathematicians. Going beyond the idea of "formal proof" traditionally relegated only to geometry, this book transcends all mathematical content areas with a variety of activities for teachers to learn more about reasoning-and-proving and about how to support students' capacities to engage in this mathematical thinking through: Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work that features a range of solution strategies, representations, and misconceptions Modifying tasks from curriculum materials so that they better support students to reason-and-prove Evaluating learning environments and making connections between key ideas about reasoning-and-proving and teaching strategies We Reason & We Prove for ALL Mathematics is designed as a learning tool for practicing and pre-service mathematics teachers and can be used individually or in a group. No other book tackles reasoning-and-proving with such breadth, depth, and practical applicability. Classroom examples, case studies, and sample problems help to sharpen concrete teaching strategies that empower students to reason-and-prove!

Principia Mathematica

Principia Mathematica PDF Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 696

Book Description


All the Mathematics You Missed

All the Mathematics You Missed PDF Author: Thomas A. Garrity
Publisher: 清华大学出版社有限公司
ISBN: 9787302090854
Category : Mathematics
Languages : en
Pages : 380

Book Description


Proofs from THE BOOK

Proofs from THE BOOK PDF Author: Martin Aigner
Publisher: Springer Science & Business Media
ISBN: 3662223430
Category : Mathematics
Languages : en
Pages : 194

Book Description
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.

Why Prove it Again?

Why Prove it Again? PDF Author: John W. Dawson, Jr.
Publisher: Birkhäuser
ISBN: 3319173685
Category : Mathematics
Languages : en
Pages : 204

Book Description
This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

The Five Practices in Practice [High School]

The Five Practices in Practice [High School] PDF Author: Margaret (Peg) Smith
Publisher: Corwin
ISBN: 1544321244
Category : Education
Languages : en
Pages : 281

Book Description
Take a deep dive into the five practices for faciliting productive mathematical discussons Enhance your fluency in the five practices—anticipating, monitoring, selecting, sequencing, and connecting—to bring powerful discussions of mathematical concepts to life in your high school classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively. · Video excerpts vividly illustrate the five practices in action in real high school classrooms · Key questions help you set learning goals, identify high-level tasks, and jumpstart discussion · Prompts guide you to be prepared for and overcome common challenges Includes planning templates, sample lesson plans, completed monitoring tools, and mathematical tasks.

Reading, Writing, and Proving

Reading, Writing, and Proving PDF Author: Ulrich Daepp
Publisher: Springer Science & Business Media
ISBN: 0387215603
Category : Mathematics
Languages : en
Pages : 395

Book Description
This book, based on Pólya's method of problem solving, aids students in their transition to higher-level mathematics. It begins by providing a great deal of guidance on how to approach definitions, examples, and theorems in mathematics and ends by providing projects for independent study. Students will follow Pólya's four step process: learn to understand the problem; devise a plan to solve the problem; carry out that plan; and look back and check what the results told them.

How to Prove It

How to Prove It PDF Author: Daniel J. Velleman
Publisher: Cambridge University Press
ISBN: 0521861241
Category : Mathematics
Languages : en
Pages : 401

Book Description
This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

Yes, But Why? Teaching for Understanding in Mathematics

Yes, But Why? Teaching for Understanding in Mathematics PDF Author: Ed Southall
Publisher: SAGE
ISBN: 152973648X
Category : Education
Languages : en
Pages : 401

Book Description
The bestselling essential guide for mathematics teachers and those training to teach, Yes, but why? answers all your questions, and sheds light on the hidden connections between everything in mathematics at school. The new edition includes a new ′Test Yourself′ feature, additional coverage on fractions and much more!