What Is Mathematics School Guide To Conceptual Understanding Of Mathematics

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What is Mathematics: School Guide to Conceptual Understanding of Mathematics

Catalin Barboianu

Author : Catalin Barboianu
Publisher : PhilScience Press
Page : 315 pages
File Size : 45,9 Mb
Release : 2021-01-18
Category : Education
ISBN : 9789731991986

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What is Mathematics: School Guide to Conceptual Understanding of Mathematics by Catalin Barboianu Pdf

This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student's full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students' distorted vision of mathematics as a merely formal, instrumental, and calculatory discipline. Without the conceptual base of mathematics, students develop over time a "mathematical anxiety" and abandon any effort to understand mathematics, which becomes their "traditional enemy" in school. This work materializes the results of the inter- and trans-disciplinary research aimed toward the understanding of mathematics, which concluded that the fields with the potential to contribute to mathematics education in this respect, by unifying the procedural and conceptual approaches, are epistemology and philosophy of mathematics and science, as well as fundamentals and history of mathematics. These results argue that students' fear of mathematics can be annulled through a conceptual approach, and a student with a good conceptual understanding will be a better problem solver. The author has identified those zones and concepts from the above disciplines that can be adapted and processed for familiarizing the student with this type of knowledge, which should accompany the traditional content of school mathematics. The work was organized so as to create for the reader a unificatory image of the complex nature of mathematics, as well as a conceptual perspective ultimately necessary to the holistic understanding of school mathematics. The author talks about mathematics to convince readers that to understand mathematics means first to understand it as a whole, but also as part of a whole. The nature of mathematics, its primary concepts (like numbers and sets), its structures, language, methods, roles, and applicability, are all presented in their essential content, and the explanation of non-mathematical concepts is done in an accessible language and with many relevant examples.

Concept-Based Mathematics

Jennifer T.H. Wathall

Author : Jennifer T.H. Wathall
Publisher : Corwin Press
Page : 307 pages
File Size : 44,9 Mb
Release : 2016-01-14
Category : Education
ISBN : 9781506332659

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Concept-Based Mathematics by Jennifer T.H. Wathall Pdf

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

Concept-rich Mathematics Instruction

Meir Ben-Hur

Author : Meir Ben-Hur
Publisher : ASCD
Page : 162 pages
File Size : 42,8 Mb
Release : 2006
Category : Education
ISBN : 9781416603597

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Concept-rich Mathematics Instruction by Meir Ben-Hur Pdf

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.

Key Concepts in Mathematics

Timothy J. McNamara

Author : Timothy J. McNamara
Publisher : Corwin Press
Page : 265 pages
File Size : 53,7 Mb
Release : 2007
Category : Education
ISBN : 9781412938426

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Key Concepts in Mathematics by Timothy J. McNamara Pdf

"Includes a large number of user-friendly examples that integrate mathematics content and process standards. The step-by-step guidance and explanations in each chapter are beneficial."-Melissa Miller, TeacherRandall G. Lynch Middle School, Farmington, AR "Great activities that are exploratory in nature. A valuable resource."-Carol Amos, Teacher Leader and Mathematics CoordinatorTwinfield Union School, Plainfield, VT Increase students' mathematics achievement with rich problem-solving lessons and activities that are aligned with NCTM standards! Helping teachers envision how math standards can be integrated into the secondary classroom, Key Concepts in Mathematics, Second Edition presents engaging activities and ready-to-use lessons aligned with NCTM content and process standards. This user-friendly book by mathematics educator Timothy J. McNamara is filled with a generous collection of lessons for each of the ten NCTM standards, with many activities that address multiple standards, and numerous practical suggestions for extending the lessons beyond the curriculum. In addition, this updated resource combines standards-based mathematics and technology by incorporating TI-73 Explorer(tm) and TI-83 Plus graphing calculator applications and programs. Each chapter offers: Ready-to-use lessons, hands-on activities, practical suggestions, and an abundance of "good problems" Suggestions for integrating multiple topics and concepts in each lesson Strategies to strengthen student engagement, understanding, and retention by building connections among mathematics topics This exciting guide delivers exactly what is needed for today's standards-based math classroom!

Conceptual Understanding in Mathematics

Brian R. Evans

Author : Brian R. Evans
Publisher : Unknown
Page : 188 pages
File Size : 42,7 Mb
Release : 2015-08-06
Category : Electronic
ISBN : 1515378020

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Conceptual Understanding in Mathematics by Brian R. Evans Pdf

This brief handbook is intended for educators, parents/guardians, students, or anyone simply interested in understanding the reasoning behind selected basic, and not so basic, mathematical topics. Another intention of the handbook is to present the reader with a selected group of counterintuitive results found in mathematics, which would prove interesting for the reader and for students in mathematics. Despite the emphasis on understanding in the educational research literature and teacher education programs, many students continue to learn mathematics procedurally with a lack of real conceptual understanding. Research shows that many new teachers revert to teaching the way they were taught when they were in school, and not the way they were taught to teach in their teacher education programs. Moreover, teachers often claim that they believe in teaching for understanding and through problem solving, but continue to teach their students procedural knowledge only. Perhaps for some teachers it can be a lack of understanding in their own mathematical background that prevents them from teaching from an understanding perspective. When a person learns mathematics procedurally without real understanding, he or she is more likely to later forget what was learned rather than if the mathematics if fully understood initially. This handbook is intended for those interested in knowing the "why" behind selected mathematical concepts. Further, this book presents mathematics in a motivating way to make the subject more interesting. There is a reciprocal relationship between understanding and enjoying mathematics because people generally find mathematics more interesting when they truly understand what they are learning.The contents of this book begin with the basics structure of the number system and then progresses through basic operations, exponents, logarithms, compound interest, fractions, decimals, percentages, area of selected shapes, counting techniques, and calculus. As the book progresses, the mathematics becomes more sophisticated. The author recommends the reader attempt to understand the content of the entire book, but acknowledges that some readers may wish to stop at a certain point or ask someone for more assistance. In some cases, skipping to other sections of the book may prove useful. For example, it might make sense to skip the sections on exponents, logarithms, and compound interest in order to get to the section on fractions after the reader read about basic operations. The book is meant to be an overview of important topics, but some readers may focus on one or more sections only. Mathematics is a fascinating subject and hopefully this brief handbook will be a start for further mathematical explorations. If approached from the right perspective, mathematics can be enjoyable and engaging, and understanding the deep mathematical ideas behind the basic concepts will motivate a person to want to learn more. This is a major shift in the way in which mathematics can be viewed.

Developing Mathematical Thinking

Jonathan D. Katz

Author : Jonathan D. Katz
Publisher : Rowman & Littlefield
Page : 145 pages
File Size : 40,8 Mb
Release : 2014-07-07
Category : Education
ISBN : 9781475810585

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Developing Mathematical Thinking by Jonathan D. Katz Pdf

In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.

Vital Directions for Mathematics Education Research

Keith R Leatham

Author : Keith R Leatham
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 55,8 Mb
Release : 2014-07-08
Category : Education
ISBN : 9781461469773

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Vital Directions for Mathematics Education Research by Keith R Leatham Pdf

This book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical “research agenda projects,” which seek to outline specific research questions that the field should address around a central topic.

Mathematics for Elementary Teachers

Albert B. Bennett,Laurie J. Burton,Leonard T. Nelson

Author : Albert B. Bennett,Laurie J. Burton,Leonard T. Nelson
Publisher : McGraw-Hill Europe
Page : 128 pages
File Size : 44,8 Mb
Release : 2009
Category : Mathematics
ISBN : 0071310029

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Mathematics for Elementary Teachers by Albert B. Bennett,Laurie J. Burton,Leonard T. Nelson Pdf

Overview: Albert B. Bennett, Jr. and L. Ted Nelson have presented hundreds of workshops on how to give future teachers the conceptual understanding and procedural fluency they will need in order to successfully teach elementary-school mathematics. The Eighth Edition of Mathematics for Elementary Teachers: A Conceptual Approach continues their innovative, time-tested approach: an emphasis on learning via specific, realistic examples and the extensive use of visual aids, hands-on activities, problem-solving strategies and active classroom participation. Special features in the text ensure that prospective teachers will gain not only a deeper understanding of the mathematical concepts, but also a better sense of the connections between their college math courses and their future teaching experiences, along with helpful ideas for presenting math to their students in a way that will generate interest and enthusiasm. The text draws heavily on NCTM Standards and contains many pedagogical elements designed to foster reasoning, problem-solving and communication skills. The text also incorporates references to the virtual manipulative kit and other online resources that enhance the authors' explanations and examples.

Mathematical Argumentation in Middle School-The What, Why, and How

Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nikki Schechtman,Nicole Shechtman

Author : Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nikki Schechtman,Nicole Shechtman
Publisher : Corwin Press
Page : 185 pages
File Size : 47,6 Mb
Release : 2017-09-21
Category : Education
ISBN : 9781506394237

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Mathematical Argumentation in Middle School-The What, Why, and How by Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nikki Schechtman,Nicole Shechtman Pdf

This research-based book brings tough Standards for Mathematical Practice 3 standards for mathematical argumentation and critical reasoning alive - all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding.

How Math Works

G. Arnell Williams

Author : G. Arnell Williams
Publisher : Rowman & Littlefield Publishers
Page : 347 pages
File Size : 55,8 Mb
Release : 2013-04-04
Category : Education
ISBN : 9781442218765

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How Math Works by G. Arnell Williams Pdf

We hear all the time how American children are falling behind their global peers in various basic subjects, but particularly in math. Is it our fear of math that constrains us? Or our inability to understand math’s place in relation to our everyday lives? How can we help our children better understand the basics of arithmetic if we’re not really sure we understand them ourselves? Here, G. Arnell Williams helps parents and teachers explore the world of math that their elementary school children are learning. Taking readers on a tour of the history of arithmetic, and its growth into the subject we know it to be today, Williams explores the beauty and relevance of mathematics by focusing on the great conceptual depth and genius already inherent in the elementary mathematics familiar to us all, and by connecting it to other well-known areas such as language and the conceptual aspects of everyday life. The result is a book that will help you to better explain mathematics to your children. For those already well versed in these areas, the book offers a tour of the great conceptual and historical facts and assumptions that most simply take for granted. If you are someone who has always struggled with mathematics either because you couldn’t do it or because you never really understood why the rules are the way they are, if you were irritated with the way it was taught to you with the emphasis being only on learning the rules and “recipes” by rote as opposed to obtaining a good conceptual understanding, then How Math Works is for you!

Guided Math: A Framework for Mathematics Instruction

Sammons, Laney

Author : Sammons, Laney
Publisher : Shell Education
Page : 266 pages
File Size : 47,7 Mb
Release : 2017-03-01
Category : Education
ISBN : 9781618137951

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Guided Math: A Framework for Mathematics Instruction by Sammons, Laney Pdf

Use a practical approach to teaching mathematics that integrates proven literacy strategies for effective instruction. This professional resource will help to maximize the impact of instruction through the use of whole-class instruction, small-group instruction, and Math Workshop. Incorporate ideas for using ongoing assessment to guide your instruction and increase student learning, and use hands-on, problem-solving experiences with small groups to encourage mathematical communication and discussion. Guided Math supports the College and Career Readiness and other state standards.

Measuring What Counts

National Research Council,Mathematical Sciences Education Board

Author : National Research Council,Mathematical Sciences Education Board
Publisher : National Academies Press
Page : 240 pages
File Size : 48,5 Mb
Release : 1993-02-01
Category : Education
ISBN : 9780309049818

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Measuring What Counts by National Research Council,Mathematical Sciences Education Board Pdf

To achieve national goals for education, we must measure the things that really count. Measuring What Counts establishes crucial research- based connections between standards and assessment. Arguing for a better balance between educational and measurement concerns in the development and use of mathematics assessment, this book sets forth three principlesâ€"related to content, learning, and equityâ€"that can form the basis for new assessments that support emerging national standards in mathematics education.

Conceptual Mathematics

F. William Lawvere,Stephen H. Schanuel

Author : F. William Lawvere,Stephen H. Schanuel
Publisher : Cambridge University Press
Page : 409 pages
File Size : 55,5 Mb
Release : 2009-07-30
Category : Mathematics
ISBN : 9780521894852

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Conceptual Mathematics by F. William Lawvere,Stephen H. Schanuel Pdf

This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

IP Mathematics Book 2 Answers Booklet

Wong-Ng Siew Hiong

Author : Wong-Ng Siew Hiong
Publisher : Shing Lee Publishers Pte Ltd
Page : 52 pages
File Size : 53,8 Mb
Release : 2013-01-01
Category : Juvenile Nonfiction
ISBN : 9789812376947

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IP Mathematics Book 2 Answers Booklet by Wong-Ng Siew Hiong Pdf

Mathematics in schools offering the Integrated Programme is usually taught as an integrated subject, so that students will be able to better relate learnt knowledge to new knowledge and transfer conceptual understanding to application, as many mathematical concepts are interconnected. One driving force to write the series is to provide a guidebook especially for students in the Integrated Programme. The other is to share teaching ideas with other Mathematics teachers who love the subject as much as I do. Features: � Each topic begins with a recap of key mathematical concepts to help students consolidate learning. � Worked examples are included to enhance understanding and application of key concepts, with side notes explaining some of the working. � Practice questions are tiered into three levels of difficulty. Level 1 aims to provide students with the necessary practice; Level 2 to further build the confidence and test students� understanding; Level 3 to challenge students with higher order thinking questions. � �Math Wonderland� is one highlight of the book. Activities include extension of the topic, suggested alternative assessment and questions to stretch mathematical thinking. The primary purpose of the Wonderland is to allow students to think deeply about what they have learnt and to appreciate the learning of Mathematics beyond classroom. � Step-by-step solutions to all questions are provided as an additional resource to students� problem solving process. I hope this book will benefit students studying Integrated Mathematics, as well as those with aptitude for the subject who are preparing for the GCE O Level Mathematics and Additional Mathematics examinations.

The Role of Language in Teaching Children Math

Bernice Kastner

Author : Bernice Kastner
Publisher : Austin Macauley Publishers
Page : 73 pages
File Size : 41,5 Mb
Release : 2019-02-28
Category : Education
ISBN : 9781645369486

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The Role of Language in Teaching Children Math by Bernice Kastner Pdf

It can be difficult to recognize that in spite of the precision and power of mathematics, both the verbal and symbolic language it uses have the same qualities of ambiguity as every other human language. In The Role of Language in Teaching Children Math, Dr. Kastner reveals strategies to overcome the fact that traditional and current mathematics curricula, beginning in the early grades, fail to provide students with the conceptual understanding required to advance to levels where the delight of geometry and calculus become accessible. Kastner's clear prose and organic organization assists teachers, parents, and students to untangle abstract meanings required for mastery in the field of mathematics. "As teachers of mathematics, it is critical that we continually foster meaningful mathematical conversations with children in order for them to develop a deep understanding of the math. Bernice's extraordinary, thought-provoking book is a primer on how the language we use to teach and talk about mathematics can either obscure or illuminate the profound beauty of mathematics. The Role of Language in Teaching Children Math should be read by any serious teacher of mathematics." --Debby Halperin, Recipient of the Presidential Award for Excellence in Mathematics Teaching 2014

What Is Mathematics School Guide To Conceptual Understanding Of Mathematics

What is Mathematics: School Guide to Conceptual Understanding of Mathematics by Catalin Barboianu Pdf

Concept-Based Mathematics by Jennifer T.H. Wathall Pdf

Concept-rich Mathematics Instruction by Meir Ben-Hur Pdf

Key Concepts in Mathematics by Timothy J. McNamara Pdf

Conceptual Understanding in Mathematics by Brian R. Evans Pdf

Developing Mathematical Thinking by Jonathan D. Katz Pdf

Vital Directions for Mathematics Education Research by Keith R Leatham Pdf

Mathematics for Elementary Teachers by Albert B. Bennett,Laurie J. Burton,Leonard T. Nelson Pdf

Mathematical Argumentation in Middle School-The What, Why, and How by Jennifer Knudsen,Harriette S. Stevens,Teresa Lara-Meloy,Hee-Joon Kim,Nikki Schechtman,Nicole Shechtman Pdf

How Math Works by G. Arnell Williams Pdf

Guided Math: A Framework for Mathematics Instruction by Sammons, Laney Pdf

Measuring What Counts by National Research Council,Mathematical Sciences Education Board Pdf

Conceptual Mathematics by F. William Lawvere,Stephen H. Schanuel Pdf

IP Mathematics Book 2 Answers Booklet by Wong-Ng Siew Hiong Pdf

The Role of Language in Teaching Children Math by Bernice Kastner Pdf

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