Learning And Teaching Number Theory

Author : Rina Zazkis,Stephen R. Campbell
Publisher : Routledge
Page : 305 pages
File Size : 47,7 Mb
Release : 2012-10-12
Category : Education
ISBN : 9781136501364

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Number Theory in Mathematics Education by Rina Zazkis,Stephen R. Campbell Pdf

This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education. Topics variously engaged include: *understanding particular concepts related to numerical structure and number theory; *elaborating on the historical and psychological relevance of number theory in concept development; *attaining a smooth transition and extension from pattern recognition to formative principles; *appreciating the aesthetics of number structure; *exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; *reexamining previously constructed knowledge from a novel angle; *investigating connections between technique and theory; *utilizing computers and calculators as pedagogical tools; and *generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs. Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.

Author : Rina Zazkis,Stephen R. Campbell
Publisher : Routledge
Page : 306 pages
File Size : 43,6 Mb
Release : 2012-10-12
Category : Education
ISBN : 9781136501432

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Number Theory in Mathematics Education by Rina Zazkis,Stephen R. Campbell Pdf

This book offers multiple interconnected perspectives on the largely untapped potential of elementary number theory for mathematics education: its formal and cognitive nature, its relation to arithmetic and algebra, its accessibility, its utility and intrinsic merits, to name just a few. Its purpose is to promote explication and critical dialogue about these issues within the international mathematics education community. The studies comprise a variety of pedagogical and research orientations by an international group of researchers that, collectively, make a compelling case for the relevance and importance of number theory in mathematics education in both pre K-16 settings and mathematics teacher education. Topics variously engaged include: *understanding particular concepts related to numerical structure and number theory; *elaborating on the historical and psychological relevance of number theory in concept development; *attaining a smooth transition and extension from pattern recognition to formative principles; *appreciating the aesthetics of number structure; *exploring its suitability in terms of making connections leading to aha! insights and reaching toward the learner's affective domain; *reexamining previously constructed knowledge from a novel angle; *investigating connections between technique and theory; *utilizing computers and calculators as pedagogical tools; and *generally illuminating the role number theory concepts could play in developing mathematical knowledge and reasoning in students and teachers. Overall, the chapters of this book highlight number theory-related topics as a stepping-stone from arithmetic toward generalization and algebraic formalism, and as a means for providing intuitively grounded meanings of numbers, variables, functions, and proofs. Number Theory in Mathematics Education: Perspectives and Prospects is of interest to researchers, teacher educators, and students in the field of mathematics education, and is well suited as a text for upper-level mathematics education courses.

Author : Rina Zazkis,John Mason,Igor' Kontorovich
Publisher : Taylor & Francis
Page : 229 pages
File Size : 42,7 Mb
Release : 2021-05-23
Category : Education
ISBN : 9780429757969

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The Learning and Teaching of Number by Rina Zazkis,John Mason,Igor' Kontorovich Pdf

Numbers are the backbones of mathematics. From 1 to infinity, numbers accompany and underlie the learning of mathematics and research. While perceived as familiar and understood, numbers present fascinating and often mysterious patterns, relationships and pedagogical issues. The Learning and Teaching of Number explores how mathematics education research has addressed issues related to the structure of numbers and number operations and provides a classroom context. It invites readers to explore less-travelled paths through a well-trodden terrain of number. This fascinating book combines mathematical content with pedagogical ideas and research results. Focusing on number, the book illustrates central ideas related to numbers via a variety of tasks at different levels of complexity. The Learning and Teaching of Number will allow the reader to examine and develop personal understanding of number sets and the relationships among them; enhance personal understanding of familiar topics associated with number operations; engage in a variety of tasks and strengthen personal problem-solving skills; enrich their repertoire of mathematical tasks and pedagogical actions; and consider research ideas and results related to teaching numbers, number operations and number relationships. This is a valuable resource for teacher education courses, graduate programs in mathematics education and professional development programs. Teacher trainers and maths teachers will find their personal understanding of numbers and relationships enriched and will draw connections between research and classroom pedagogy which will extend and enhance their teaching.

Author : Calvin T. Long
Publisher : D.C. Heath
Page : 264 pages
File Size : 42,5 Mb
Release : 1972
Category : Mathematics
ISBN : CORNELL:31924001582521

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Elementary Introduction to Number Theory by Calvin T. Long Pdf

Author : Stephen R. Campbell,Rina Zazkis
Publisher : Praeger
Page : 0 pages
File Size : 51,9 Mb
Release : 2002
Category : Education
ISBN : 9781567506525

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Learning and Teaching Number Theory by Stephen R. Campbell,Rina Zazkis Pdf

Annotation Essential to developing deeper understandings of mathematics, number theory has received scant attention in mathematics education research. This volume redresses this matter and serves as a launch point for further research in this important area.

Author : William Stein
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 43,6 Mb
Release : 2008-10-28
Category : Mathematics
ISBN : 9780387855257

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Elementary Number Theory: Primes, Congruences, and Secrets by William Stein Pdf

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

Author : Edward Wall
Publisher : McGraw-Hill Humanities/Social Sciences/Languages
Page : 0 pages
File Size : 50,5 Mb
Release : 2009-02-13
Category : Education
ISBN : 007337847X

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Number Theory for Elementary School Teachers by Edward Wall Pdf

In response to concerns about teacher retention, especially among teachers in their first to fourth year in the classroom, we offer future teachers a series of brief guides full of practical advice that they can refer to in both their student teaching and in their first years on the job. Number Theory for Elementary School Teachers is designed for preservice candidates in early and/or elementary education. The text complements traditional Math Methods courses and provides deep content knowledge for prospective and first year teachers.

Author : Bowen Kerins, Darryl Yong,Al Cuoco,Glenn Stevens
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 52,6 Mb
Release : 2015-10-15
Category : Education
ISBN : 9781470421953

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Famous Functions in Number Theory by Bowen Kerins, Darryl Yong,Al Cuoco,Glenn Stevens Pdf

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares. Famous Functions in Number Theory is a volume of the book series "IAS/PCMI-The Teacher Program Series" published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Author : Kathryn B. Chval,Erin Smith,Lina Trigos-Carrillo,Rachel J. Pinnow
Publisher : Corwin Press
Page : 317 pages
File Size : 55,8 Mb
Release : 2021-01-07
Category : Education
ISBN : 9781071810835

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Teaching Math to Multilingual Students, Grades K-8 by Kathryn B. Chval,Erin Smith,Lina Trigos-Carrillo,Rachel J. Pinnow Pdf

Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction.

Author : Robert J Wright,Garry Stanger,Ann K. Stafford,James Martland
Publisher : SAGE
Page : 256 pages
File Size : 54,9 Mb
Release : 2014-10-17
Category : Education
ISBN : 9781473908741

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Teaching Number in the Classroom with 4-8 Year Olds by Robert J Wright,Garry Stanger,Ann K. Stafford,James Martland Pdf

Bring the principles and practice of the acclaimed Mathematics Recovery Programme to whole-class teaching! WHY INVEST IN THE NEW EDITION? In full-colour with a revised layout for clearer navigation More up-to-date tasks, activities and real classroom examples Learning trajectories for guiding instruction and tracking progress on key topics Extra resources online on the companion website Part of the best-selling Maths Recovery series, this practical, step-by-step guide to classroom instruction takes an inquiry-based approach to assess children's knowledge and build on this to develop a firm foundation of understanding and confidence in mathematics. Topics covered range from beginning number and early counting strategies to multi-digit addition and subtraction right through to multiplication and division. An invaluable resource for use on pre-service teacher training courses and for all primary classroom teachers and assistants, including experienced Mathematics Recovery instructors, as well as learning support personnel, primary mathematics advisors, numeracy consultants and educational psychologists. WHAT EXTRAS ARE ON THE COMPANION WEBSITE? Downloadable extra chapter resources like print-out grids, worksheets, cards and much more A Facilitator’s Guide that can be used either individually or in group study to help you get the most out of the material In-class video demonstrations to clearly show how the instructional activities in the book are used in the classroom Webinar discussing the key points in the book and how it supports your teaching Visit the companion website at https://study.sagepub.com/wrighttnc "Research informs practice in this easy to access resource. Each chapter gives educators practical, bite-sized assessments, linked to a host of activities that helps them target teaching and develop the firm foundations which are so vital for confident and competent mathematicians." - Jill Piotrowski, Numeracy Consultant, Wigan Local Authority, UK "'The Classroom Instructional Framework in Early Number is research-based and provides a roadmap of not only the what, but the when and the how to teach all aspects of early number." - Vicki Nally, Mathematics Consultant at Catholic Education Office, Melbourne "The structured approach offers a wealth of rich and easily implemented classroom-based activities that work - thousands of teachers in Ireland attest to this!" - Noreen O'Loughlin, Director Maths Recovery and Maths Education Lecturer, Mary Immaculate College, Limerick, Ireland

Author : Charles Stanley Ogilvy,John Timothy Anderson
Publisher : Courier Corporation
Page : 196 pages
File Size : 43,7 Mb
Release : 1988-01-01
Category : Mathematics
ISBN : 0486257789

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Excursions in Number Theory by Charles Stanley Ogilvy,John Timothy Anderson Pdf

Challenging, accessible mathematical adventures involving prime numbers, number patterns, irrationals and iterations, calculating prodigies, and more. No special training is needed, just high school mathematics and an inquisitive mind. "A splendidly written, well selected and presented collection. I recommend the book unreservedly to all readers." — Martin Gardner.

Author : Robert J Wright,Garry Stanger,Ann K Stafford,James Martland
Publisher : SAGE
Page : 265 pages
File Size : 53,5 Mb
Release : 2006-08-30
Category : Education
ISBN : 9781446237571

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Teaching Number by Robert J Wright,Garry Stanger,Ann K Stafford,James Martland Pdf

The book lets teachers identify where their students are in terms of number skills, and sets out a strategy for developing their knowledge. The authors show how to advance children′s learning across five stages of early arithmetical learning - emergent, perceptual, figurative, initial number, and facile number. This provides for increasingly sophisticated number strategies across addition, subtraction, multiplication and division, as well as developing children′s number word and numeral knowledge, and their ability to structure number and have grouping strategies. The approach used nine guiding principles for teaching. Each chapter has clearly defined teaching procedures which show how to take the children onto the next more sophisticated stage. The teaching procedures are organized into key teaching topics, and each includes: a clearly defined purpose detailed instructions, activities, learning tasks and reinforcing games lists of responses which children may make application in whole class, small group and individualised settings a link to the Learning Framework in Number (see Early Numeracy- second edition, 2005) how the guiding principles for teaching can be used to allow teachers to evaluate and reflect upon their practice Primary practitioners in Australia, the United States, the United Kingdom and Canada have tested the teaching procedures which can be used in conjunction with each country′s numeracy strategy. Primary teachers, especially of the early years, mathematics co-ordinators, heads of school, mathematics advisers, special educationalists, learning support personnel, teacher assistants, lecturers in initial teacher training and educational psychologists will all find this book invaluable.

Author : Keith J. Devlin
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 2012
Category : Mathematics
ISBN : 0615653634

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Introduction to Mathematical Thinking by Keith J. Devlin Pdf

"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.

Author : Joseph Silverman
Publisher : Unknown
Page : 0 pages
File Size : 45,9 Mb
Release : 2017-02-13
Category : Number theory
ISBN : 0134689461

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Friendly Introduction to Number Theory, a (Classic Version) by Joseph Silverman Pdf

For one-semester undergraduate courses in Elementary Number Theory This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. A Friendly Introduction to Number Theory, 4th Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

Author : Elliot Benjamin
Publisher : Unknown
Page : 162 pages
File Size : 53,6 Mb
Release : 2017-06-23
Category : Electronic
ISBN : 1681085135

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Numberama by Elliot Benjamin Pdf

Numberama: Recreational Number Theory in the School System presents number patterns and mathematical formulas that can be taught to children in schools. The number theories and problems are reinforced by enjoyable games that children can play to enhance their learning in a fun-loving way. Key features of the book include: information about a number of well-known number theory problems such as Fibonaccci numbers, triangular numbers, perfect numbers, sums of squares, and Diophantine equations organized presentation based on skill level for easy understanding all basic mathematical operations for elementary school children a range of algebraic formulae for middle school students descriptions of positive feedback and testimonials where recreational number theory has been effective in schools and education programs This book is a useful handbook for elementary and middle-school teachers, students, and parents who will be able to experience the inherent joys brought by teaching number theory to children in a recreational way.