Teaching Mathematics Conceptually

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Concept-Based Mathematics

Author : Jennifer T.H. Wathall
Publisher : Corwin Press
ISBN 13 : 150633265X
Total Pages : 307 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Concept-Based Mathematics by : Jennifer T.H. Wathall

Download or read book Concept-Based Mathematics written by Jennifer T.H. Wathall and published by Corwin Press. This book was released on 2016-01-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Give math students the connections between what they learn and how they do math—and suddenly math makes sense If your secondary-school students are fearful of or frustrated by math, it’s time for a new approach. When you teach concepts rather than rote processes, you show students math’s essential elegance, as well as its practicality—and help them discover their own natural mathematical abilities. This book is a road map to retooling how you teach math in a deep, clear, and meaningful way —through a conceptual lens—helping students achieve higher-order thinking skills. Jennifer Wathall shows you how to plan units, engage students, assess understanding, incorporate technology, and even guides you through an ideal concept-based classroom. Practical tools include: Examples from arithmetic to calculus Inquiry tasks, unit planners, templates, and activities Sample assessments with examples of student work Vignettes from international educators A dedicated companion website with additional resources, including a study guide, templates, exemplars, discussion questions, and other professional development activities. Everyone has the power to understand math. By extending Erickson and Lanning’s work on Concept-Based Curriculum and Instruction specifically to math, this book helps students achieve the deep understanding and skills called for by global standards and be prepared for the 21st century workplace. "Jennifer Wathall’s book is one of the most forward thinking mathematics resources on the market. While highlighting the essential tenets of Concept-Based Curriculum design, her accessible explanations and clear examples show how to move students to deeper conceptual understandings. This book ignites the mathematical mind!" — Lois A. Lanning, Author of Designing Concept-based Curriculum for English-Language Arts, K-12 "Wathall is a master at covering all the bases here; this book is bursting with engaging assessment examples, discussion questions, research, and resources that apply specifically to mathematical topics. Any math teacher or coach would be hard-pressed to read it and not come away with scores of ideas, assessments, and lessons that she could use instantly in the classroom. As an IB Workshop Leader and instructional coach, I want this book handy on a nearby shelf for regular referral – it′s a boon to any educator who wants to bring math to life for students." — Alexis Wiggins, Instructional Coach, IB Workshop Leader and Consultant

Helping Children Learn Mathematics

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309131987
Total Pages : 53 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Helping Children Learn Mathematics by : National Research Council

Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.

Making Sense of Mathematics for Teaching High School

Author : Edward C. Nolan
Publisher : Solution Tree Press
ISBN 13 : 1942496494
Total Pages : 231 pages
Book Rating : 4.9/5 (424 download)

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Book Synopsis Making Sense of Mathematics for Teaching High School by : Edward C. Nolan

Download or read book Making Sense of Mathematics for Teaching High School written by Edward C. Nolan and published by Solution Tree Press. This book was released on 2016-05-19 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develop a deep understanding of mathematics by grasping the context and purpose behind various strategies. This user-friendly resource presents high school teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Combine student understanding of functions and algebraic concepts so that they can better decipher the world. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, or modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Gain clarity about the most productive progression of mathematical teaching and learning for high school. Watch short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction Equations and Functions Structure of Equations Geometry Types of Functions Function Modeling Statistics and Probability Epilogue: Next Steps Appendix: Weight Loss Study Data References Index

Teaching Mathematics Meaningfully

Author : David H. Allsopp
Publisher : Brookes Publishing Company
ISBN 13 :
Total Pages : 316 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Teaching Mathematics Meaningfully by : David H. Allsopp

Download or read book Teaching Mathematics Meaningfully written by David H. Allsopp and published by Brookes Publishing Company. This book was released on 2007 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making mathematics concepts understandable is a challenge for any teacher--a challenge that's more complex when a classroom includes students with learning difficulties. With this highly practical resource, educators will have just what they need to teach mathematics with confidence: research-based strategies that really work with students who have learning disabilities, ADHD, or mild cognitive disabilities. This urgently needed guidebook helps teachers Understand why students struggle.Teachers will discover how the common learning characteristics of students with learning difficulties create barriers to understanding mathematics. Review the Big Ideas. Are teachers focusing on the right things? A helpful primer on major NCTM-endorsed mathematical concepts and processes helps them be sure. Directly address students' learning barriers. With the lesson plans, practical strategies, photocopiable information-gathering forms, and online strategies in action, teachers will have concrete ways to help students grasp mathematical concepts, improve their proficiency, and generalize knowledge in multiple contexts. Check their own strengths and needs. Educators will reflect critically on their current practices with a thought-provoking questionnaire. With this timely book--filled with invaluable ideas and strategies adaptable for grades K-12--educators will know just what to teach and how to teach it to students with learning difficulties.

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.

The Problem with Math Is English

Author : Concepcion Molina
Publisher : John Wiley & Sons
ISBN 13 : 1118237021
Total Pages : 310 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis The Problem with Math Is English by : Concepcion Molina

Download or read book The Problem with Math Is English written by Concepcion Molina and published by John Wiley & Sons. This book was released on 2012-09-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching K-12 math becomes an easier task when everyone understands the language, symbolism, and representation of math concepts Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at a superficial level. Written to inspire ?aha? moments, this book enables teachers to help students identify and comprehend the nuances and true meaning of math concepts by exploring them through the lenses of language and symbolism, delving into such essential topics as multiplication, division, fractions, place value, proportional reasoning, graphs, slope, order of operations, and the distributive property. Offers a new way to approach teaching math content in a way that will improve how all students, and especially English language learners, understand math Emphasizes major attributes of conceptual understanding in mathematics, including simple yet deep definitions of key terms, connections among key topics, and insightful interpretation This important new book fills a gap in math education by illustrating how a deeper knowledge of math concepts can be developed in all students through a focus on language and symbolism.

Making Sense of Mathematics for Teaching, Grades 3-5

Author : Juli K. Dixon
Publisher : Solution Tree Press
ISBN 13 : 1942496435
Total Pages : 403 pages
Book Rating : 4.9/5 (424 download)

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Book Synopsis Making Sense of Mathematics for Teaching, Grades 3-5 by : Juli K. Dixon

Download or read book Making Sense of Mathematics for Teaching, Grades 3-5 written by Juli K. Dixon and published by Solution Tree Press. This book was released on 2016-04-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develop a deep understanding of mathematics. This user-friendly resource presents grades 3–5 teachers with a logical progression of pedagogical actions, classroom norms, and collaborative teacher team efforts to increase their knowledge and improve mathematics instruction. Focus on an understanding of and procedural fluency with multiplication and division. Address how to learn and teach fraction concepts and operations with depth. Thoroughly teach plane and solid geometry. Explore strategies and techniques to effectively learn and teach significant mathematics concepts and provide all students with the precise, accurate information they need to achieve academic success. Benefits Dig deep into mathematical modeling and reasoning to improve as both a learner and teacher of mathematics. Explore how to develop, select, and modify mathematics tasks in order to balance cognitive demand and engage students. Discover the three important norms to uphold in all mathematics classrooms. Learn to apply the tasks, questioning, and evidence (TQE) process to ensure mathematics instruction is focused, coherent, and rigorous. Use charts and diagrams for classifying shapes, which can engage students in important mathematical practices. Access short videos that show what classrooms that are developing mathematical understanding should look like. Contents Introduction 1 Place Value, Addition, and Subtraction 2 Multiplication and Division 3 Fraction Concepts 4 Fraction Operations 5 Geometry 6 Measurement Epilogue Next Steps Appendix A Completed Classification of Triangles Chart Appendix B Completed Diagram for Classifying Quadrilaterals

Strengths-Based Teaching and Learning in Mathematics

Author : Beth McCord Kobett
Publisher : Corwin Press
ISBN 13 : 1544374925
Total Pages : 189 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 Press. This book was released on 2020-02-27 with total page 189 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.

Teacher Learning of Ambitious and Equitable Mathematics Instruction

Author : Ilana Horn
Publisher : Routledge
ISBN 13 : 1000556387
Total Pages : 284 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Teacher Learning of Ambitious and Equitable Mathematics Instruction by : Ilana Horn

Download or read book Teacher Learning of Ambitious and Equitable Mathematics Instruction written by Ilana Horn and published by Routledge. This book was released on 2022-03-17 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing on sociocultural learning theory, this book offers a groundbreaking theory of secondary mathematics teacher learning in schools, focusing on the transformation of instruction as a conceptual change project to achieve ambitious and equitable mathematics teaching. Despite decades of research showing the importance of ambitious and equitable teaching, few inroads have been made in most U.S. classrooms, and teacher learning in general remains undertheorized in most educational research. Illustrating their theory through closely documented case studies of secondary mathematics teachers’ learning and instructional practices, authors Horn and Garner explore the key conceptual issues teachers are required to work through in order to more fully realize ambitious and equitable teaching in their classrooms. By theorizing teacher learning from a sociocultural perspective and focusing on instructional practice, the authors make a unique contribution to the field of teacher learning. This book offers researchers, scholars, and teacher educators new theoretical and methodological tools for the elusive phenomenon of teacher learning, and provides instructional leaders and coaches with practical examples of how teachers shift their thinking and practice.

Principles to Actions

Author : National Council of Teachers of Mathematics
Publisher : National Council of Teachers of Mathematics, Incorporated
ISBN 13 : 9780873537742
Total Pages : 139 pages
Book Rating : 4.5/5 (377 download)

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Book Synopsis Principles to Actions by : National Council of Teachers of Mathematics

Download or read book Principles to Actions written by National Council of Teachers of Mathematics and published by National Council of Teachers of Mathematics, Incorporated. This book was released on 2014-02 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning.

Concept-rich Mathematics Instruction

Author : Meir Ben-Hur
Publisher : ASCD
ISBN 13 : 141660359X
Total Pages : 162 pages
Book Rating : 4.4/5 (166 download)

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Book Synopsis Concept-rich Mathematics Instruction by : Meir Ben-Hur

Download or read book Concept-rich Mathematics Instruction written by Meir Ben-Hur and published by ASCD. This book was released on 2006 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an instructional approach that helps students in every grade level understand math concepts so they can apply them on assessments, across the curriculum, and outside of school. Provides teaching practices and lesson ideas that give students a stronger foundation for reasoning and problem solving.

Teaching and Learning Mathematics Online

Author : James P. Howard, II
Publisher : CRC Press
ISBN 13 : 1351245562
Total Pages : 358 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Teaching and Learning Mathematics Online by : James P. Howard, II

Download or read book Teaching and Learning Mathematics Online written by James P. Howard, II and published by CRC Press. This book was released on 2020-05-10 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Online education has become a major component of higher education worldwide. In mathematics and statistics courses, there exists a number of challenges that are unique to the teaching and learning of mathematics and statistics in an online environment. These challenges are deeply connected to already existing difficulties related to math anxiety, conceptual understanding of mathematical ideas, communicating mathematically, and the appropriate use of technology. Teaching and Learning Mathematics Online bridges these issues by presenting meaningful and practical solutions for teaching mathematics and statistics online. It focuses on the problems observed by mathematics instructors currently working in the field who strive to hone their craft and share best practices with our professional community. The book provides a set of standard practices, improving the quality of online teaching and the learning of mathematics. Instructors will benefit from learning new techniques and approaches to delivering content. Features Based on the experiences of working educators in the field Assimilates the latest technology developments for interactive distance education Focuses on mathematical education for developing early mathematics courses

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.

Teaching Mathematics Conceptually

Author : Beth L. MacDonald
Publisher : Sage Publications UK
ISBN 13 : 1529618177
Total Pages : 268 pages
Book Rating : 4.5/5 (296 download)

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Book Synopsis Teaching Mathematics Conceptually by : Beth L. MacDonald

Download or read book Teaching Mathematics Conceptually written by Beth L. MacDonald and published by Sage Publications UK. This book was released on 2023-04-08 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book expands upon the guiding principles at the heart of Math Recovery® instruction, exploring their connections with learning theory, practical application in the classroom and their wider links to agreed concepts of high-quality mathematics teaching. It provides a well-rounded overview of all major aspects of mathematics teaching including inquiry-based and constructivist approaches, planning and assessment, and strategies that offer children opportunities for reflection, satisfaction and increasing challenge. Particular focus is placed on equitable and inclusive practices in mathematics and how we can develop teaching that connects with the abilities, cultures, and lived experiences of all children. This is essential reading for all teachers familiar with the Math Recovery® approach and classroom mathematics teachers in elementary and primary schools everywhere seeking to enhance their own professional knowledge and understanding. Beth L. MacDonald is an associate professor in Early Childhood Mathematics Education in the School of Teaching and Learning at Illinois State University. Jonathan N. Thomas is an associate professor of mathematics education and the chairperson of the Department of STEM Education at the University of Kentucky.

Conceptual Mathematics

Author : F. William Lawvere
Publisher : Cambridge University Press
ISBN 13 : 0521894859
Total Pages : 409 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Conceptual Mathematics by : F. William Lawvere

Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

Tools for Teaching Conceptual Understanding, Secondary

Author : Julie Stern
Publisher : Corwin Press
ISBN 13 : 1506355722
Total Pages : 142 pages
Book Rating : 4.5/5 (63 download)

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Book Synopsis Tools for Teaching Conceptual Understanding, Secondary by : Julie Stern

Download or read book Tools for Teaching Conceptual Understanding, Secondary written by Julie Stern and published by Corwin Press. This book was released on 2017-02-02 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students become experts and innovators through Concept-Based teaching Innovators don’t invent without a deep understanding of how the world works. With this foundation, they apply conceptual understanding to solve new problems. We want our students to not only retain ideas, but relate them to other things they encounter, using each new situation to add nuance and sophistication to their thinking. To do this, they need conceptual understanding. This book serves as a road map for Concept-Based teaching. Discover how to help students uncover conceptual relationships and transfer them to new situations. Specifically, teachers will learn: Strategies for introducing conceptual learning to students Four lesson frameworks to help students uncover conceptual relationships How to assess conceptual understanding, and How to differentiate concept-based instruction Look no further. For deep learning and innovative thinking, this book is the place to start. "The authors tear down the false dichotomies of traditional vs innovative education and provide a practical toolkit for developing creativity and applying knowledge through Concept-Based learning. Every practitioner needs this book to juxtapose what worked well in the 20th Century with what is essential in the 21st Century and beyond." Michael McDowell, Superintendent Ross School District, Ross, CA "While most good educators recognise the incredible value of teaching conceptually, it is challenging. The authors have created accessible, practical baby steps for every teacher to use." Dr. Vincent Chan, principal Fairview International School, Kuala Lumpur, Malaysia

Rigorous Mathematical Thinking

Author : James T. Kinard
Publisher : Cambridge University Press
ISBN 13 : 1139472399
Total Pages : 210 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Rigorous Mathematical Thinking by : James T. Kinard

Download or read book Rigorous Mathematical Thinking written by James T. Kinard and published by Cambridge University Press. This book was released on 2008-06-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.