We Reason We Prove For All Mathematics
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We Reason We Prove For All Mathematics
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Author : Fran Arbaugh
language : en
Publisher: Corwin Press
Release Date : 2018-08-08
We Reason We Prove For All Mathematics written by Fran Arbaugh and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-08 with Education categories.
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!
We Reason We Prove For All Mathematics
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Author : Fran Arbaugh
language : en
Publisher:
Release Date : 2018
We Reason We Prove For All Mathematics written by Fran Arbaugh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
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!
We Reason We Prove For All Mathematics
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Author : Fran Arbaugh
language : en
Publisher: Corwin Press
Release Date : 2018-08-08
We Reason We Prove For All Mathematics written by Fran Arbaugh and has been published by Corwin Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-08 with Education categories.
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.
The Five Practices In Practice High School
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Author : Margaret (Peg) Smith
language : en
Publisher: Corwin
Release Date : 2020-02-26
The Five Practices In Practice High School written by Margaret (Peg) Smith and has been published by Corwin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Education categories.
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.
On Your Feet Guide Modifying Mathematical Tasks
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Author : Margaret (Peg) S Smith
language : en
Publisher: Corwin Publishers
Release Date : 2020-03-24
On Your Feet Guide Modifying Mathematical Tasks written by Margaret (Peg) S Smith and has been published by Corwin Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-24 with categories.
All On-Your-Feet Guide orders receive FREE SHIPPING! Use code SHIPOYFG at check out. Students learn what mathematics is and how one does it through their classroom instruction and the mathematical tasks they explore. Student learning is greatest when students have regular opportunities to engage with high-level or cognitively challenging tasks that engage students in thinking, reasoning, and problem solving and are essential to developing students' conceptual understanding of mathematics. How do you help students develop the capacity to think, reason, and problem solve, but your curricular resources don't have many high-level, cognitively demanding tasks? Learn to modify existing tasks for higher-level thinking! This On-Your-Feet-Guide provides: - 8 Key Strategies for modifying low-level procedural tasks and transforming them into high-level thinking tasks. - Examples across grades K-12 - Opportunities to practice modifying tasks and reflect on how the modified versions better meet students' learning needs - Helpful hints to set your tasks up for ultimate success. On-Your-Feet Guides (OYFGs) provide you with the ultimate "cheat sheet" to implement effective change in your classroom while in the moment of teaching. Designed for accessibility, and providing step-by-step guidance, the OYFGs are written by experts who take research-based practices and make them doable for the busy teacher. Each On-Your-Feet Guide is laminated, 8.5"x11" tri-fold (6 pages), and 3-hole punched. Use On-Your-Feet Guides - When you know the "what" but need help with the "how" - As a quick reference to support a practice you learned in a PD workshop or book - To learn how to implement foundational practices - When you want to help your students learn a specific strategy, routine, or approach, but aren't sure how to do it yourself
Why Prove It Again
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Author : John W. Dawson, Jr.
language : en
Publisher: Birkhäuser
Release Date : 2015-07-15
Why Prove It Again written by John W. Dawson, Jr. and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-15 with Mathematics categories.
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.
Proof Technology In Mathematics Research And Teaching
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Author : Gila Hanna
language : en
Publisher: Springer Nature
Release Date : 2019-10-02
Proof Technology In Mathematics Research And Teaching written by Gila Hanna and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-02 with Education categories.
This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field.
How To Prove It
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Author : Daniel J. Velleman
language : en
Publisher: Cambridge University Press
Release Date : 2006-01-16
How To Prove It written by Daniel J. Velleman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Transform Your Math Class Using Asset Based Teaching For Grades 6 12
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Author : Michael D Steele
language : en
Publisher: Corwin Publishers
Release Date : 2024-08-13
Transform Your Math Class Using Asset Based Teaching For Grades 6 12 written by Michael D Steele and has been published by Corwin Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-13 with Education categories.
Foster a love of mathematics by creating a more inclusive and empowering learning environment through asset-based teaching! An asset-based perspective on math education means starting with what students already know instead of focusing on what's missing. This approach elevates student thinking and reasoning skills. In this way, educators acknowledge that all students bring prior experiences, strengths, talents, and resources to the learning process and can contribute meaningfully in an authentic learning environment. Transform Your Math Class Using Asset-Based Teaching for Grades 6-12 provides insight into asset-based perspectives in mathematics education to create an environment where all students feel valued and capable of being doers of mathematics. In the book, Michael Steele and Joleigh Honey highlight the importance of using language, instructional routines, and systemic structure that positively impact student engagement, their math identity, and ultimately their outcomes. Providing a wealth of knowledge and practical strategies that can be used to transform math classrooms into inclusive, supportive, and empowering learning environments, this book: Introduces an asset-based perspective that focuses on students′ strengths, assets, and potential to learn mathematics Includes a variety of frameworks and tools that teachers can use to build and grow their sense of asset-based perspectives Offers strategies for promoting a growth mindset in mathematics, encouraging productive struggle in math, and promoting equitable math instruction Supports teachers in reflecting on their decisions, self-awareness, and self-management Includes a companion online study guide to support teachers individually or as part of a professional learning community Adopting asset-based perspectives is about movement over time, not about flipping a switch. This book paves the path for an asset-based journey that ultimately helps to transform our math classrooms and advance all students' learning and development.
Explanation And Proof In Mathematics
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Author : Gila Hanna
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-04
Explanation And Proof In Mathematics written by Gila Hanna and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-04 with Education categories.
In the four decades since Imre Lakatos declared mathematics a "quasi-empirical science," increasing attention has been paid to the process of proof and argumentation in the field -- a development paralleled by the rise of computer technology and the mounting interest in the logical underpinnings of mathematics. Explanantion and Proof in Mathematics assembles perspectives from mathematics education and from the philosophy and history of mathematics to strengthen mutual awareness and share recent findings and advances in their interrelated fields. With examples ranging from the geometrists of the 17th century and ancient Chinese algorithms to cognitive psychology and current educational practice, contributors explore the role of refutation in generating proofs, the varied links between experiment and deduction, the use of diagrammatic thinking in addition to pure logic, and the uses of proof in mathematics education (including a critique of "authoritative" versus "authoritarian" teaching styles). A sampling of the coverage: The conjoint origins of proof and theoretical physics in ancient Greece. Proof as bearers of mathematical knowledge. Bridging knowing and proving in mathematical reasoning. The role of mathematics in long-term cognitive development of reasoning. Proof as experiment in the work of Wittgenstein. Relationships between mathematical proof, problem-solving, and explanation. Explanation and Proof in Mathematics is certain to attract a wide range of readers, including mathematicians, mathematics education professionals, researchers, students, and philosophers and historians of mathematics.