The Proceedings of the 12th International Congress on Mathematical Education

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Publisher : Springer
ISBN 13 : 3319126881
Total Pages : 617 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis The Proceedings of the 12th International Congress on Mathematical Education by : Sung Je Cho

Download or read book The Proceedings of the 12th International Congress on Mathematical Education written by Sung Je Cho and published by Springer. This book was released on 2015-02-10 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.

The Proceedings of the 12th International Congress on Mathematical Education

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Publisher : Springer
ISBN 13 : 9783319126890
Total Pages : 648 pages
Book Rating : 4.1/5 (268 download)

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Book Synopsis The Proceedings of the 12th International Congress on Mathematical Education by : Sung Je Cho

Download or read book The Proceedings of the 12th International Congress on Mathematical Education written by Sung Je Cho and published by Springer. This book was released on 2015-02-22 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.

Selected Regular Lectures from the 12th International Congress on Mathematical Education

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Publisher : Springer
ISBN 13 : 3319171879
Total Pages : 932 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Selected Regular Lectures from the 12th International Congress on Mathematical Education by : Sung Je Cho

Download or read book Selected Regular Lectures from the 12th International Congress on Mathematical Education written by Sung Je Cho and published by Springer. This book was released on 2015-07-16 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises the full selected Regular Lectures from the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 4700 experts from 100 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. These selected Regular Lectures present the work of fifty-one prominent mathematics educators from all over the globe. The Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Proceedings of the 13th International Congress on Mathematical Education

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Publisher : Springer
ISBN 13 : 3319625977
Total Pages : 766 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Proceedings of the 13th International Congress on Mathematical Education by : Gabriele Kaiser

Download or read book Proceedings of the 13th International Congress on Mathematical Education written by Gabriele Kaiser and published by Springer. This book was released on 2017-10-31 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current state-of-the-art of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teaching-and-learning processes. The book introduces the major activities of ICME-13, namely articles from the four plenary lecturers and two plenary panels, articles from the five ICMI awardees, reports from six national presentations, three reports from the thematic afternoon devoted to specific features of ICME-13. Furthermore, the proceedings contain descriptions of the 54 Topic Study Groups, which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME-13, namely papers from the invited lecturers, will be presented in the second volume of the proceedings.

Proceedings of the Ninth International Congress on Mathematical Education

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Publisher :
ISBN 13 : 9781402079023
Total Pages : 430 pages
Book Rating : 4.0/5 (79 download)

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Book Synopsis Proceedings of the Ninth International Congress on Mathematical Education by : Hiroshi Fujita

Download or read book Proceedings of the Ninth International Congress on Mathematical Education written by Hiroshi Fujita and published by . This book was released on 2004 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among organizations devoted to mathematics education, The International Commission on Mathematical Instruction (ICMI) is distinctive because of its close ties to the mathematics community. The great challenges now facing mathematics education around the world demand a deeper and more sensitive involvement of disciplinary mathematicians than we now have, both in the work of educational improvements and in research on the nature of teaching and learning. This book constitutes the Proceedings of the Ninth International Conference on Mathematical Education (ICME9), which was held in Tokyo/Makuhari Japan, in July and August 2000. ICME9 brought together experts from 70 countries, working to understand the challenges of mathematics education including boundary crossing and collaboration, such as the need to reconcile language, epistemology, norms of evidence and, in general, all of the intellectual and attitudinal challenges that face multidisciplinary research and development.

Proceedings of the Fourth International Congress on Mathematical Education

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Publisher : Springer Science & Business Media
ISBN 13 : 1468482238
Total Pages : 740 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Proceedings of the Fourth International Congress on Mathematical Education by : M. Zweng

Download or read book Proceedings of the Fourth International Congress on Mathematical Education written by M. Zweng and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: Henry O. Pollak Chairman of the International Program Committee Bell Laboratories Murray Hill, New Jersey, USA The Fourth International Congress on Mathematics Education was held in Berkeley, California, USA, August 10-16, 1980. Previous Congresses were held in Lyons in 1969, Exeter in 1972, and Karlsruhe in 1976. Attendance at Berkeley was about 1800 full and 500 associate members from about 90 countries; at least half of these come from outside of North America. About 450 persons participated in the program either as speakers or as presiders; approximately 40 percent of these came from the U.S. or Canada. There were four plenary addresses; they were delivered by Hans Freudenthal on major problems of mathematics education, Hermina Sinclair on the relationship between the learning of language and of mathematics, Seymour Papert on the computer as carrier of mathematical culture, and Hua Loo-Keng on popularising and applying mathematical methods. Gearge Polya was the honorary president of the Congress; illness prevented his planned attendence but he sent a brief presentation entitled, "Mathematics Improves the Mind". There was a full program of speakers, panelists, debates, miniconferences, and meetings of working and study groups. In addition, 18 major projects from around the world were invited to make presentations, and various groups representing special areas of concern had the opportunity to meet and to plan their future activities.

Proceedings of the 14th International Congress on Mathematical Education (Icme-14) (in 2 Volumes)

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Publisher :
ISBN 13 : 9789811289378
Total Pages : 0 pages
Book Rating : 4.2/5 (893 download)

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Book Synopsis Proceedings of the 14th International Congress on Mathematical Education (Icme-14) (in 2 Volumes) by : Jianpan Wang

Download or read book Proceedings of the 14th International Congress on Mathematical Education (Icme-14) (in 2 Volumes) written by Jianpan Wang and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings of the 14th International Congress on Mathematical Education. Presents the latest trends in mathematics education research and mathematics teaching practices at all levels"--

Invited Lectures from the 13th International Congress on Mathematical Education

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Publisher : Springer
ISBN 13 : 3319721704
Total Pages : 786 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Invited Lectures from the 13th International Congress on Mathematical Education by : Gabriele Kaiser

Download or read book Invited Lectures from the 13th International Congress on Mathematical Education written by Gabriele Kaiser and published by Springer. This book was released on 2018-02-05 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Proceedings of the Fifth International Congress on Mathematical Education

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Publisher : Springer Science & Business Media
ISBN 13 : 147574238X
Total Pages : 411 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Proceedings of the Fifth International Congress on Mathematical Education by : CARASS

Download or read book Proceedings of the Fifth International Congress on Mathematical Education written by CARASS and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Congresses on Mathematical Education (ICMEs), under the auspices of the International Commission on Mathematical Instruction, are held every four years. Previous Congresses have been held in France (Lyons), England (Exeter), the Federal Republic of Germany (Karlsruhe), and the United States of America (Berkeley). The Fifth International Congress on Mathematical Education (lCME 5) was held in Adelaide, Australia, from August 24-30, 1984. More than 1800 participants from over 70 countries participated in the Congress, while some additional 200 people attended social functions and excursions. The program for ICME 5 was planned and structured by an International Program Committee, and implemented by the National Program Committee in Australia. For the main body of the program, Chief Organisers, assisted by Australian Coordinators, were invited to plan and prepare the individual components of the program which addressed a wide range of topics and interest areas. Each of these teams involved many individuals from around the world in the detailed planning and preparation of the working sessions for their area of program responsibility. For the actual working sessions at the Congress, the smallest group had some 60 members, while the largest had well over 300. In addition to the working sessions, there were three major plenary addresses, several specially invited presentations, and over 420 individual papers in the form of short communications, either as posters or brief talks.

Proceedings of the 13th International Congress on Mathematical Education

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Publisher :
ISBN 13 : 9781013268649
Total Pages : 734 pages
Book Rating : 4.2/5 (686 download)

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Book Synopsis Proceedings of the 13th International Congress on Mathematical Education by : Gabriele Kaiser

Download or read book Proceedings of the 13th International Congress on Mathematical Education written by Gabriele Kaiser and published by . This book was released on 2020-10-08 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current state-of-the-art of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teaching-and-learning processes.The book introduces the major activities of ICME-13, namely articles from the four plenary lecturers and two plenary panels, articles from the five ICMI awardees, reports from six national presentations, three reports from the thematic afternoon devoted to specific features of ICME-13. Furthermore, the proceedings contain descriptions of the 54 Topic Study Groups, which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME-13, namely papers from the invited lecturers, will be presented in the second volume of the proceedings. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

School Mathematics Curricula

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Publisher : Springer
ISBN 13 : 9811363129
Total Pages : 237 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis School Mathematics Curricula by : Catherine P. Vistro-Yu

Download or read book School Mathematics Curricula written by Catherine P. Vistro-Yu and published by Springer. This book was released on 2019-04-26 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book sheds light on school mathematics curricula in Asian countries, including their design and the recent reforms that have been initiated. By discussing and analyzing various problematic aspects of curriculum development and implementation in a number of East and South Asian countries and offering insights into these countries’ unique approaches to supplementing school mathematics curricula, it contributes to shaping effective policies for implementation, assessment and monitoring of curricula. The book covers a wide range of issues: curriculum design, localization of curricula, directions of curricular reforms, mathematics textbooks, assessment within the curriculum and teachers’ professional development, which are of interest to a wide international audience.

K-12 Mathematics Education In Israel: Issues And Innovations

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Publisher : World Scientific
ISBN 13 : 9813231203
Total Pages : 460 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis K-12 Mathematics Education In Israel: Issues And Innovations by : Movshovitz-hadar Nitsa

Download or read book K-12 Mathematics Education In Israel: Issues And Innovations written by Movshovitz-hadar Nitsa and published by World Scientific. This book was released on 2018-02-27 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides the reader with a multifaceted picture of mathematics education in Israel, put into an international perspective where relevant. It is intended to give an overview of a wide range of topics covering issues such as raising and maintaining motivation, search for excellence, treatment of difficulties, teacher education, language issues, minorities issues, curriculum changes over the first 70 years of the state of Israel, and many more. This includes aspects of research and practice into the teaching and learning of mathematics, innovation, developments, policy, achievements, and implementation with some international comparison as well. Contents: Issues and Innovations Related to the Structure of Mathematics Education in Israel: Highlights in the Development of Education and Mathematics Education in the State of Israel: A Timeline (Michael N Fried, Hannah Perl and Abraham Arcavi) How Did a Crisis in Mathematics Education Lead to a Positive Reform? (Muhana Fares) A Start-Up Nation at Risk: Israel's Quest for Excellence (Eli Hurvitz) Supervision of Mathematics Teaching by the Ministry of Education (Hannah Perl, Dorit Neria, Ruth Segal and Niza Sion) Mathematics Education in Israeli Religious High-Schools (Thierry (Noah) Dana-Picard and Sara Hershkovitz) Excellence in Mathematics in the Ultra-Orthodox Community: Fantasy or Reality? (Reuven Gal, Yehuda Morgenstern and Yael Elimelech) Mathematics Education in the Arabic-Speaking Sectors in Israel (Shaker A Rasslan and Amal Sharif-Rasslan) Issues and Innovations Related to Mathematics Education at Preschool and Primary School (Grades K-6) in Israel: New Developments and Trends in Preschool Mathematics Education in Israel (Ornit Spektor-Levy and Taly Shechter) Origametria — Paper Folding for Teaching Geometry in Preschool and Primary School (John Oberman) Educating the Eye: The Agam Program for Visual Thinking (Rina Hershkowitz, Zvia Markovits, Sherman Rosenfeld, Lea Ilani and Bat-Sheva Eylon) Professional Development for Preschool Teachers: The CAMTE Framework and Repeating Patterns (Dina Tirosh, Pessia Tsamir, Esther Levenson and Ruthi Barkai) Time to Know — A Socio-constructivist Initiative to Integrate Computers in the Teaching and Learning of Primary Mathematics (Dovi Weiss and Tali Wallach) Issues and Innovations Related to Mathematics Education at Middle and High School (Grades 7–12) in Israel: Exhausting Students' Potential in Mathematics: A Comprehensive Approach to Promoting Both Struggling and Promising Students (Orit Zaslavsky, Liora Linchevski, Noga Hermon, Drora Livneh and Iris Zodik) Middle School Mathematics Curriculum Based on the Power of Open Technological Tools: The Case of CompuMath Project (Rina Hershkowitz and Michal Tabach) Mathematics at the Virtual School: Why? Why not? Who? What? And So What? (Yaniv Biton, Osnat Fellus, Dafna Raviv, David Feilchenfeld and Boris Koichu) Nurturing Students with High Mathematical Potential (Abraham (Avi) Berman and Roza Leikin) The Bar-Ilan University — ICAMS Program for the Advancement of Mathematically Talented Youth (Zvi Arad and Elisheva (Gerstein) Fridman) Mathematical Excellence: The Mofet Way (Tamara Avissar-Zeldis) The Advancement of Mathematics Studies in the ORT Israel Educational Network — Policy and Implementation (Lea Dolev and Eli Eisenberg) Promoting Advanced-Level Mathematics in Diverse Populations in the Amal Educational Network (Ronit Ashkenazy and Anna Vaknin) Problem-Solving Forums on Social Networks that Accompany

Assessment in Mathematics Education

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Publisher : Springer
ISBN 13 : 3319323946
Total Pages : 38 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Assessment in Mathematics Education by : Christine Suurtamm

Download or read book Assessment in Mathematics Education written by Christine Suurtamm and published by Springer. This book was released on 2016-07-07 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of current research on a variety of topics related to both large-scale and classroom assessment. First, the purposes, traditions and principles of assessment are considered, with particular attention to those common to all levels of assessment and those more connected with either classroom or large-scale assessment. Assessment design based on sound assessment principles is discussed, differentiating between large-scale and classroom assessment, but also examining how the design principles overlap. The focus then shifts to classroom assessment and provides specific examples of assessment strategies, before examining the impact of large-scale assessment on curriculum, policy, instruction, and classroom assessment. The book concludes by discussing the challenges that teachers currently face, as well as ways to support them. The book offers a common language for researchers in assessment, as well as a primer for those interested in understanding current work in the area of assessment. In summary, it provides the opportunity to discuss large-scale and classroom assessment by addressing the following main themes: ·Purposes, Traditions and Principles of Assessment ·Design of Assessment Tasks ·Classroom Assessment in Action ·Interactions of Large-Scale and Classroom Assessment ·Enhancing Sound Assessment Knowledge and Practices It also suggests areas for future research in assessment in mathematics education.

On the Road to Mathematical Expertise and Innovation

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Publisher :
ISBN 13 : 9783959872263
Total Pages : 0 pages
Book Rating : 4.8/5 (722 download)

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Book Synopsis On the Road to Mathematical Expertise and Innovation by : Scott A. Chamberlin

Download or read book On the Road to Mathematical Expertise and Innovation written by Scott A. Chamberlin and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

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Publisher : Springer
ISBN 13 : 3319683519
Total Pages : 443 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds by : Carolyn Kieran

Download or read book Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds written by Carolyn Kieran and published by Springer. This book was released on 2017-12-04 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Research in Mathematics Education in Australasia 2012-2015

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Publisher : Springer
ISBN 13 : 9811014191
Total Pages : 378 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Research in Mathematics Education in Australasia 2012-2015 by : Katie Makar

Download or read book Research in Mathematics Education in Australasia 2012-2015 written by Katie Makar and published by Springer. This book was released on 2016-06-02 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the ninth edition of the four-yearly review of mathematics education research in Australasia, the Mathematics Education Research Group of Australasia (MERGA) discusses the Australasian research in mathematics education in the four years from 2012-2015. This review aims to critically promote quality research and focus on the building of research capacity in Australasia.

Handbook of International Research in Mathematics Education

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Author :
Publisher : Routledge
ISBN 13 : 1134626711
Total Pages : 1064 pages
Book Rating : 4.1/5 (346 download)

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Book Synopsis Handbook of International Research in Mathematics Education by : Lyn D. English

Download or read book Handbook of International Research in Mathematics Education written by Lyn D. English and published by Routledge. This book was released on 2015-07-30 with total page 1064 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition of the Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field.