The Learning And Teaching Of Algebra

Author : Abraham Arcavi,Paul Drijvers,Kaye Stacey
Publisher : Routledge
Page : 159 pages
File Size : 50,6 Mb
Release : 2016-06-23
Category : Education
ISBN : 9781134820702

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The Learning and Teaching of Algebra by Abraham Arcavi,Paul Drijvers,Kaye Stacey Pdf

IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include: • Algebra: Setting the Scene • Some Lessons From History • Seeing Algebra Through the Eyes of a Learner • Emphases in Algebra Teaching • Algebra Education in the Digital Era This guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides.

Author : Kaye Stacey,Helen Chick,Margaret Kendal
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 52,8 Mb
Release : 2006-04-11
Category : Education
ISBN : 9781402081316

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The Future of the Teaching and Learning of Algebra by Kaye Stacey,Helen Chick,Margaret Kendal Pdf

Kaye Stacey‚ Helen Chick‚ and Margaret Kendal The University of Melbourne‚ Australia Abstract: This section reports on the organisation‚ procedures‚ and publications of the ICMI Study‚ The Future of the Teaching and Learning of Algebra. Key words: Study Conference‚ organisation‚ procedures‚ publications The International Commission on Mathematical Instruction (ICMI) has‚ since the 1980s‚ conducted a series of studies into topics of particular significance to the theory and practice of contemporary mathematics education. Each ICMI Study involves an international seminar‚ the “Study Conference”‚ and culminates in a published volume intended to promote and assist discussion and action at the international‚ national‚ regional‚ and institutional levels. The ICMI Study running from 2000 to 2004 was on The Future of the Teaching and Learning of Algebra‚ and its Study Conference was held at The University of Melbourne‚ Australia fromDecember to 2001. It was the first study held in the Southern Hemisphere. There are several reasons why the future of the teaching and learning of algebra was a timely focus at the beginning of the twenty first century. The strong research base developed over recent decades enabled us to take stock of what has been achieved and also to look forward to what should be done and what might be achieved in the future. In addition‚ trends evident over recent years have intensified. Those particularly affecting school mathematics are the “massification” of education—continuing in some countries whilst beginning in others—and the advance of technology.

Author : Heidi Strømskag Måsøval,Yves Chevallard
Publisher : Springer
Page : 166 pages
File Size : 52,6 Mb
Release : 2016-05-04
Category : Education
ISBN : 3319030108

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Teaching and Learning Algebra by Heidi Strømskag Måsøval,Yves Chevallard Pdf

The book is based on a longitudinal study of beginning teachers' struggles with algebra, with strong foundation in the theory of didactical situations (Brousseau, 1997). The focus is on factors that constrain students’ engagement with algebraic generality in shape patterns. Participants in the study are six student teachers and two teacher educators of mathematics. The empirical material consists of videotaped classroom observations and the mathematical tasks with which the students engaged. Three analytic categories emerged from an open coding process which show that the students’ algebraic generalization is constrained by: 1) a limited feedback potential in situations where the students are supposed to solve the mathematical tasks without teacher intervention; 2) obstacles the students face when they shall transform into algebraic notation formulae they have expressed informally in natural language; and, 3) challenges with justification of formulae and mathematical statements that the students have proposed. This book provides many practical and concrete examples to guide mathematics education researchers, mathematics teacher educators, and mathematics educators in teaching algebra in a variety of contexts and environments.

Author : Sigrid Wagner,Carolyn Kieran
Publisher : Routledge
Page : 128 pages
File Size : 51,9 Mb
Release : 2016-11-30
Category : Electronic
ISBN : 1138985244

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Research Issues in the Learning and Teaching of Algebra by Sigrid Wagner,Carolyn Kieran Pdf

First Published in 1989. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng
Publisher : Springer
Page : 48 pages
File Size : 51,8 Mb
Release : 2016-07-11
Category : Education
ISBN : 9783319322582

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Early Algebra by Carolyn Kieran,JeongSuk Pang,Deborah Schifter,Swee Fong Ng Pdf

This survey of the state of the art on research in early algebra traces the evolution of a relatively new field of research and teaching practice. With its focus on the younger student, aged from about 6 years up to 12 years, this volume reveals the nature of the research that has been carried out in early algebra and how it has shaped the growth of the field. The survey, in presenting examples drawn from the steadily growing research base, highlights both the nature of algebraic thinking and the ways in which this thinking is being developed in the primary and early middle school student. Mathematical relations, patterns, and arithmetical structures lie at the heart of early algebraic activity, with processes such as noticing, conjecturing, generalizing, representing, justifying, and communicating being central to students’ engagement.

Author : Carolyn Kieran
Publisher : Springer
Page : 443 pages
File Size : 51,6 Mb
Release : 2017-12-04
Category : Education
ISBN : 9783319683515

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Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds by Carolyn Kieran Pdf

This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.

Author : Alex Friedlander,Abraham Arcavi
Publisher : National Council of Teachers of English
Page : 260 pages
File Size : 49,6 Mb
Release : 2018-02-28
Category : Algebra
ISBN : 0873537599

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Tasks and Competencies in the Teaching and Learning of Algebra by Alex Friedlander,Abraham Arcavi Pdf

Tasks and Competencies in the Teaching and Learning of Algebra provides a conceptual approach that will encourage students learning algebra to employ a variety of thinking processes and strategies and, most importantly, will enable them to truly understand the concepts that underlie the problems they are solving. The authors' framework develops those skills and competencies, aligned with the goals of the Common Core State Standards, that are necessary for an integrated, conceptual learning of algebra. The book's four chapters include tasks focusing on algebraic expressions, equations, and functions, followed by tasks that integrate several mathematical concepts. Each of the 48 tasks in this book contains: a classroom-ready task, with items arranged by increasing order of complexity a discussion of the task's main ideas and objectives solutions for each item in the task, with suggestions of various methods that students might use; and a listing of the essential competencies that students can develop by working on the task. All 48 tasks are also available at NCTM's More4U website as downloadable and printable worksheets to hand out to students. With its strong conceptual framework, Tasks and Competencies in the Teaching and Learning of Algebra is designed to enable teachers, teacher educators, and curriculum designers to help students at all levels master the ideas and practices found in algebra and to develop skills they can use throughout their mathematics education.

Author : Sepideh Stewart,Christine Andrews-Larson,Avi Berman,Michelle Zandieh
Publisher : Springer
Page : 382 pages
File Size : 49,7 Mb
Release : 2018-02-01
Category : Education
ISBN : 9783319668116

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Challenges and Strategies in Teaching Linear Algebra by Sepideh Stewart,Christine Andrews-Larson,Avi Berman,Michelle Zandieh Pdf

This book originated from a Discussion Group (Teaching Linear Algebra) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning. The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks. Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.

Author : J.-L. Dorier
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 51,9 Mb
Release : 2005-12-27
Category : Education
ISBN : 9780306472244

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On the Teaching of Linear Algebra by J.-L. Dorier Pdf

This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It provides university teachers in charge of linear algebra courses with a wide range of information from works including theoretical and experimental issues.

Author : Sigrid Wagner
Publisher : Unknown
Page : 128 pages
File Size : 54,7 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 0873532686

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Research agenda for mathematics education by Sigrid Wagner Pdf

Author : Sigrid Wagner,Carolyn Kieran
Publisher : Routledge
Page : 307 pages
File Size : 54,8 Mb
Release : 2018-12-07
Category : Education
ISBN : 9781135434212

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Research Issues in the Learning and Teaching of Algebra by Sigrid Wagner,Carolyn Kieran Pdf

First Published in 1989. Routledge is an imprint of Taylor & Francis, an informa company.

Author : Douglas H. Clements,Julie Sarama
Publisher : Routledge
Page : 552 pages
File Size : 55,5 Mb
Release : 2009-04-01
Category : Education
ISBN : 9781135843793

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Learning and Teaching Early Math by Douglas H. Clements,Julie Sarama Pdf

In this important new book for pre- and in-service teachers, early math experts Douglas Clements and Julie Sarama show how "learning trajectories" help teachers become more effective professionals. By opening up new windows to seeing young children and the inherent delight and curiosity behind their mathematical reasoning, learning trajectories ultimately make teaching more joyous. They help teachers understand the varying level of knowledge and thinking of their classes and the individuals within them as key in serving the needs of all children. In straightforward, no-nonsense language, this book summarizes what is known about how children learn mathematics, and how to build on what they know to realize more effective teaching practice. It will help teachers understand the learning trajectories of early mathematics and become quintessential professionals.

Author : Meixia Ding
Publisher : Routledge
Page : 0 pages
File Size : 50,5 Mb
Release : 2023-01-09
Category : Electronic
ISBN : 0367750821

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Teaching Early Algebra Through Example-Based Problem Solving by Meixia Ding Pdf

Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS). Recognizing young children's particular cognitive and developmental capabilities, this book powerfully argues for the importance of infusing algebraic thinking into early grade mathematics teaching and illustrates how this has been achieved by teachers in U.S. and Chinese contexts. Documenting best practice and students' responses to example-based instruction, the text demonstrates that this TEPS approach - which involves the use of worked examples, representations, and deep questions - helps students learn and master fundamental mathematical ideas, making it highly effective in developing algebraic readiness and mathematical understanding. This text will benefit post-graduate students, researchers, and academics in the fields of mathematics, STEM, and elementary education, as well as algebra research more broadly. Those interested in teacher education, classroom practice, and developmental and cognitive psychology will also find this volume of interest.

Author : N. Bednarz,C. Kieran,L. Lee
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789400917323

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Approaches to Algebra by N. Bednarz,C. Kieran,L. Lee Pdf

In Greek geometry, there is an arithmetic of magnitudes in which, in terms of numbers, only integers are involved. This theory of measure is limited to exact measure. Operations on magnitudes cannot be actually numerically calculated, except if those magnitudes are exactly measured by a certain unit. The theory of proportions does not have access to such operations. It cannot be seen as an "arithmetic" of ratios. Even if Euclidean geometry is done in a highly theoretical context, its axioms are essentially semantic. This is contrary to Mahoney's second characteristic. This cannot be said of the theory of proportions, which is less semantic. Only synthetic proofs are considered rigorous in Greek geometry. Arithmetic reasoning is also synthetic, going from the known to the unknown. Finally, analysis is an approach to geometrical problems that has some algebraic characteristics and involves a method for solving problems that is different from the arithmetical approach. 3. GEOMETRIC PROOFS OF ALGEBRAIC RULES Until the second half of the 19th century, Euclid's Elements was considered a model of a mathematical theory. This may be one reason why geometry was used by algebraists as a tool to demonstrate the accuracy of rules otherwise given as numerical algorithms. It may also be that geometry was one way to represent general reasoning without involving specific magnitudes. To go a bit deeper into this, here are three geometric proofs of algebraic rules, the frrst by Al-Khwarizmi, the other two by Cardano.

Author : Andrew Hacker
Publisher : New Press, The
Page : 257 pages
File Size : 47,5 Mb
Release : 2010-05-25
Category : Education
ISBN : 9781620970690

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The Math Myth by Andrew Hacker Pdf

A New York Times–bestselling author looks at mathematics education in America—when it’s worthwhile, and when it’s not. Why do we inflict a full menu of mathematics—algebra, geometry, trigonometry, even calculus—on all young Americans, regardless of their interests or aptitudes? While Andrew Hacker has been a professor of mathematics himself, and extols the glories of the subject, he also questions some widely held assumptions in this thought-provoking and practical-minded book. Does advanced math really broaden our minds? Is mastery of azimuths and asymptotes needed for success in most jobs? Should the entire Common Core syllabus be required of every student? Hacker worries that our nation’s current frenzied emphasis on STEM is diverting attention from other pursuits and even subverting the spirit of the country. Here, he shows how mandating math for everyone prevents other talents from being developed and acts as an irrational barrier to graduation and careers. He proposes alternatives, including teaching facility with figures, quantitative reasoning, and understanding statistics. Expanding upon the author’s viral New York Times op-ed, The Math Myth is sure to spark a heated and needed national conversation—not just about mathematics but about the kind of people and society we want to be. “Hacker’s accessible arguments offer plenty to think about and should serve as a clarion call to students, parents, and educators who decry the one-size-fits-all approach to schooling.” —Publishers Weekly, starred review