Knowing And Teaching Elementary Mathematics

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Knowing and Teaching Elementary Mathematics

Author : Liping Ma
Publisher : Routledge
ISBN 13 : 1135149496
Total Pages : 329 pages
Book Rating : 4.1/5 (351 download)

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Book Synopsis Knowing and Teaching Elementary Mathematics by : Liping Ma

Download or read book Knowing and Teaching Elementary Mathematics written by Liping Ma and published by Routledge. This book was released on 2010-03-26 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

Answers to Your Biggest Questions About Teaching Elementary Math

Author : John J. SanGiovanni
Publisher : Corwin Press
ISBN 13 : 1071861220
Total Pages : 233 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Answers to Your Biggest Questions About Teaching Elementary Math by : John J. SanGiovanni

Download or read book Answers to Your Biggest Questions About Teaching Elementary Math written by John J. SanGiovanni and published by Corwin Press. This book was released on 2021-08-31 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Your guide to grow and learn as a math teacher! Let’s face it, teaching elementary math can be hard. So much about how we teach math today may look and feel different from how we learned it. Today, we recognize placing the student at the center of their learning increases engagement, motivation, and academic achievement soars. Teaching math in a student-centered way changes the role of the teacher from one who traditionally “delivers knowledge” to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity. Whether you are a brand new teacher or a veteran, if you find teaching math to be quite the challenge, this is the guide you want by your side. Designed for just-in-time learning and support, this practical resource gives you brief, actionable answers to your most pressing questions about teaching elementary math. Written by four experienced math educators representing diverse experiences, these authors offer the practical advice they wish they received years ago, from lessons they′ve learned over decades of practice, research, coaching, and through collaborating with teams, teachers and colleagues—especially new teachers—every day. Questions and answers are organized into five areas of effort that will help you most thrive in your elementary math classroom: 1. How do I build a positive math community? 2. How do I structure, organize, and manage my math class? 3. How do I engage my students in math? 4. How do I help my students talk about math? 5. How do I know what my students know and move them forward? Woven throughout, you′ll find helpful sidebar notes on fostering identity and agency; access and equity; teaching in different settings; and invaluable resources for deeper learning. The final question—Where do I go from here?— offers guidance for growing your practice over time. Strive to become the best math educator you can be; your students are counting on it! What will be your first step on the journey?

Mathematics Content for Elementary Teachers

Author : Douglas K. Brumbaugh
Publisher : Routledge
ISBN 13 : 1135633800
Total Pages : 314 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Mathematics Content for Elementary Teachers by : Douglas K. Brumbaugh

Download or read book Mathematics Content for Elementary Teachers written by Douglas K. Brumbaugh and published by Routledge. This book was released on 2004-09-22 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: THE book for elementary education mathematics content courses! Designed to help prospective teachers of elementary school mathematics learn content beyond the rote level, this text stimulates readers to think beyond just getting the problem right and fosters their development into thoughtful, reflective, self-motivated, life-long learners. It stresses the what and why of elementary school mathematics content. Hints are provided about how to teach the content but this is mostly left to courses and texts that are dedicated to that purpose. The text is organized around the National Council for Teachers of Mathematics' Principles and Standards for School Mathematics. The Standards dictate the basic sections of the text. Within each section, appropriate specific topics are developed, intertwined with technology, problem solving, assessment, equity issues, planning, teaching skills, use of manipulatives, sequencing, and much more. In addition, major focal points of the Standards are emphasized throughout: effective teachers of mathematics should be able to motivate all students to learn, should understand the developmental levels of how children learn, should concentrate on what children need to become active participants in the learning environment, and should be engaged in ongoing investigations of new mathematical concepts and teaching strategies. Mathematics Content for Elementary Teachers is based on several fundamental premises: *The focus of mathematics education should be on the process, not the answer. *Elementary teachers should know the mathematics content they are teaching, know more than the content they are teaching, and teach from the overflow of knowledge. *It is important for teachers to be flexible in allowing students to use different procedures--teaching from the "overflow of knowledge" implies knowing how to do a given operation more than one way and being willing to examine many different ways. *Teachers need to learn to carefully cover the topics to be taught, to reflect upon them, and to be able to organize them. To help prospective elementary teachers concentrate on the mathematics content they will be expected to teach and begin to build the foundation for the methods they will use, this text includes only elementary mathematics content and does not address middle school concepts. Pedagogical features: *The text is organized according to NCTM Standards. *An informal writing style speaks directly to readers and is geared to pre-service teachers. *Focus is given to multiple methods of problem solving at four developmental levels. *Questions, exercises, and activities are interspersed throughout each section rather than gathered at the end of each chapter. *Complete solutions for exercises are provided.

Elementary Mathematics for Teachers

Author : Thomas H. Parker
Publisher : Ingram
ISBN 13 : 9780974814001
Total Pages : 237 pages
Book Rating : 4.8/5 (14 download)

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Book Synopsis Elementary Mathematics for Teachers by : Thomas H. Parker

Download or read book Elementary Mathematics for Teachers written by Thomas H. Parker and published by Ingram. This book was released on 2004 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Textbook on numbers, arithmetic, and prealgebra for elementary school mathematics teachers. Designed to be used with five Primary Mathematics books (textbooks 3A, 4A, 5A, 6A, and workbook 5A; all U.S. ed.), part of an elementary mathematics curriculum designed by Singapore's Ministry of Education and adapted for use in the U.S.

Knowing and Learning Mathematics for Teaching

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309072522
Total Pages : 233 pages
Book Rating : 4.3/5 (9 download)

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Book Synopsis Knowing and Learning Mathematics for Teaching by : National Research Council

Download or read book Knowing and Learning Mathematics for Teaching written by National Research Council and published by National Academies Press. This book was released on 2001-02-25 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions: What is the mathematical knowledge teachers need to know in order to teach well? How can teachers develop the mathematical knowledge they need to teach well? The Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.

Elementary Mathematics Pedagogical Content Knowledge

Author : James E. Schwartz
Publisher : Allyn & Bacon
ISBN 13 :
Total Pages : 340 pages
Book Rating : 4.X/5 (3 download)

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Book Synopsis Elementary Mathematics Pedagogical Content Knowledge by : James E. Schwartz

Download or read book Elementary Mathematics Pedagogical Content Knowledge written by James E. Schwartz and published by Allyn & Bacon. This book was released on 2008 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schwartz Powerful Ideas in Elementary Mathematics: Pedagogical Content Knowledge for Teachers, 1/e ISBN: 0205493750 "This book would be a great tool for helping [today's future elementary teachers] acquire a 'gut level' understanding of mathematics concepts." - Hester Lewellen, Baldwin-Wallace College, OH "The writing in this text is very clear and would easily be understood by the intended audience. The real-world examples put the various math concepts into a context that is easily understood. The vignettes at the beginning of each chapter are interesting and they get the reader to begin thinking about the math concepts that will follow. Each of the chapters seem to build on one another and the author often refers back to activities and concepts from previous chapters which is meaningful to the reader because it lets the reader know that the information they are learning builds their conceptual understanding of other mathematical concepts. " - Melany L. Rish, University of South Carolina, Aiken Organized around five key concepts or "powerful ideas" in mathematics, this text presents elementary mathematics content in a concise and nonthreatening manner for teachers. Designed to sharpen teachers' mathematics pedagogical content knowledge, the friendly writing style and vignettes relate math concepts to "real life" situations so that they may better present the content to their students. The five "powerful ideas" (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the text thoroughly integrates discussion of the five NCTM process strands. Features: Icons highlighting the NCTM process standards appear throughout the book to indicate where the text relates to each of these. Practice exercises and activities and their explanations reinforce math concepts presented in the text and provide an opportunity for reflection and practice. Concise, conversational chapters and opening vignettes present math contents simply enough for even the most math-anxious pre-service teachers.

Beyond Classical Pedagogy

Author : Terry Wood
Publisher : Routledge
ISBN 13 : 1135658714
Total Pages : 269 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Beyond Classical Pedagogy by : Terry Wood

Download or read book Beyond Classical Pedagogy written by Terry Wood and published by Routledge. This book was released on 2014-04-04 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy. The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching. Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms. The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching. Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.

Improving Instruction in Geometry and Measurement

Author : Margaret Schwan Smith
Publisher : Teachers College Press
ISBN 13 : 9780807745311
Total Pages : 166 pages
Book Rating : 4.7/5 (453 download)

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Book Synopsis Improving Instruction in Geometry and Measurement by : Margaret Schwan Smith

Download or read book Improving Instruction in Geometry and Measurement written by Margaret Schwan Smith and published by Teachers College Press. This book was released on 2005-01-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume One is rational numbers and proportionality. Using materials that were developed under the NSF-funded COMET (Cases of Mathematics to Enhance Teaching) program, each volume in the set features cases from urban, middle school classrooms with ethnically, racially, and linguistically diverse student populations. Each case illustrates an instructional episode in the classroom of a teacher who is implementing standards-based instruction, the teachers' perspective, including their thoughts and actions as they interact with students and with key aspects of mathematical content, cognitively challenging mathematics activities that are built around samples of authentic classroom practice., and facilitation chapters to help professional developers "teach" the cases, including specific guidelines for facilitating discussions and suggestions for connecting the ideas presented in the cases to a teacher's own practice. As a complete set, this resource provides a basis on which to build a comprehensive professional development program to improve mathematics instruction and student learning.

Common Mistakes in Teaching Elementary Math—And How to Avoid Them

Author : Fuchang Liu
Publisher : Routledge
ISBN 13 : 1315511754
Total Pages : 236 pages
Book Rating : 4.3/5 (155 download)

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Book Synopsis Common Mistakes in Teaching Elementary Math—And How to Avoid Them by : Fuchang Liu

Download or read book Common Mistakes in Teaching Elementary Math—And How to Avoid Them written by Fuchang Liu and published by Routledge. This book was released on 2017-03-27 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the most effective ways to teach elementary math, no matter how much experience you have with the subject. In this book, Fuchang Liu takes you through many common mistakes in math instruction and explains the misunderstandings behind them. He points out practices that should be avoided, helping you to adjust your lessons so that all students can achieve success. You’ll discover how to... - Increase your confidence with core math principles and reasoning - Set your students on the path toward eventually developing more complex math skills - Improve student achievement by approaching problems in logical yet creative ways - Overcome common challenges faced by students and teachers - Teach problem solving for different learning styles Every chapter reconsiders well-established ways of teaching all areas of elementary math, from addition and subtraction to statistics and graphs. Helpful examples and tips are scattered throughout the book, offering revisions to the way these topics are often presented in the classroom. Also included are group study ideas for principals and instructional coaches so your school or district can work on the book together. With this practical guide, you’ll be ready to help students truly develop their math understanding.

Strengths-Based Teaching and Learning in Mathematics

Author : Beth McCord Kobett
Publisher : Corwin
ISBN 13 : 1544374909
Total Pages : 273 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Strengths-Based Teaching and Learning in Mathematics by : Beth McCord Kobett

Download or read book Strengths-Based Teaching and Learning in Mathematics written by Beth McCord Kobett and published by Corwin. This book was released on 2020-02-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

Let's Play Math

Author : Denise Gaskins
Publisher : Tabletop Academy Press
ISBN 13 : 1892083248
Total Pages : 288 pages
Book Rating : 4.8/5 (92 download)

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Book Synopsis Let's Play Math by : Denise Gaskins

Download or read book Let's Play Math written by Denise Gaskins and published by Tabletop Academy Press. This book was released on 2012-09-04 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Teaching Elementary Mathematics to Struggling Learners

Author : Bradley S. Witzel
Publisher : Guilford Publications
ISBN 13 : 1462523110
Total Pages : 193 pages
Book Rating : 4.4/5 (625 download)

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Book Synopsis Teaching Elementary Mathematics to Struggling Learners by : Bradley S. Witzel

Download or read book Teaching Elementary Mathematics to Struggling Learners written by Bradley S. Witzel and published by Guilford Publications. This book was released on 2016-01-25 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with effective instructional strategies, this book explores why certain K-5 students struggle with math and provides a framework for helping these learners succeed. The authors present empirically validated practices for supporting students with disabilities and others experiencing difficulties in specific areas of math, including problem solving, early numeracy, whole-number operations, fractions, geometry, and algebra. Concrete examples, easy-to-implement lesson-planning ideas, and connections to state standards, in particular the Common Core standards, enhance the book's utility. Also provided is invaluable guidance on planning and delivering multi-tiered instruction and intervention.

Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8

Author : Jennifer M. Bay-Williams
Publisher : Corwin
ISBN 13 : 1071818430
Total Pages : 265 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 by : Jennifer M. Bay-Williams

Download or read book Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 written by Jennifer M. Bay-Williams and published by Corwin. This book was released on 2021-03-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.

MATHEMATICS FOR ELEMENTARY TEACHERS. (PRODUCT ID 23864410).

Author : MICHELLE. MANES
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (19 download)

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Book Synopsis MATHEMATICS FOR ELEMENTARY TEACHERS. (PRODUCT ID 23864410). by : MICHELLE. MANES

Download or read book MATHEMATICS FOR ELEMENTARY TEACHERS. (PRODUCT ID 23864410). written by MICHELLE. MANES and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Visible Learning for Mathematics, Grades K-12

Author : John Hattie
Publisher : Corwin Press
ISBN 13 : 1506362958
Total Pages : 209 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Visible Learning for Mathematics, Grades K-12 by : John Hattie

Download or read book Visible Learning for Mathematics, Grades K-12 written by John Hattie and published by Corwin Press. This book was released on 2016-09-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

Teaching Mathematics Through Games

Author : Mindy Capaldi
Publisher : American Mathematical Soc.
ISBN 13 : 1470462842
Total Pages : 160 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Teaching Mathematics Through Games by : Mindy Capaldi

Download or read book Teaching Mathematics Through Games written by Mindy Capaldi and published by American Mathematical Soc.. This book was released on 2021-05-18 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Active engagement is the key to learning. You want your students doing something that stimulates them to ask questions and creates a need to know. Teaching Mathematics Through Games presents a variety of classroom-tested exercises and activities that provoke the active learning and curiosity that you hope to promote. These games run the gamut from well-known favorites like SET and Settlers of Catan to original games involving simulating structural inequality in New York or playing Battleship with functions. The book contains activities suitable for a wide variety of college mathematics courses, including general education courses, math for elementary education, probability, calculus, linear algebra, history of math, and proof-based mathematics. Some chapter activities are short term, such as a drop-in lesson for a day, and some are longer, including semester-long projects. All have been tested, refined, and include extensive implementation notes.

The Math Teachers Know

Author : Brent Davis
Publisher : Routledge
ISBN 13 : 1135097860
Total Pages : 141 pages
Book Rating : 4.1/5 (35 download)

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Book Synopsis The Math Teachers Know by : Brent Davis

Download or read book The Math Teachers Know written by Brent Davis and published by Routledge. This book was released on 2013-07-18 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: What sorts of mathematics competencies must teachers have in order to teach the discipline well? This book offers a novel take on the question. Most research is focused on explicit knowledge–that is, on the sorts of insights that might be specified, catalogued, taught, and tested. In contrast, this book focuses on the tacit dimensions of teachers’ mathematics knowledge that precede and enable their competencies with formal mathematics. It highlights the complexity of this knowledge and offers strategies to uncover it, analyze it, and re-synthesize it in ways that will make it more available for teaching. Emerging from 10 years of collaborative inquiry with practicing teachers, it is simultaneously informed by the most recent research and anchored to the realities of teachers’ lives in classrooms.