Mathematics In Service To The Community

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Mathematics in Service to the Community

Author : Charles Robert Hadlock
Publisher : Mathematical Association of America (MAA)
ISBN 13 :
Total Pages : 284 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Mathematics in Service to the Community by : Charles Robert Hadlock

Download or read book Mathematics in Service to the Community written by Charles Robert Hadlock and published by Mathematical Association of America (MAA). This book was released on 2005 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description: This book looks at the wide variety of ways in which math, statistics, and math education teachers have incorporated service-learning into their courses. These projects are not just stand-alone community service initiatives, but rather they specifically target the improvement of mathematics skills and insights of the college students in the courses with which they are associated. In some cases, the projects are the major focus of the courses. In others, they may range from an essential component to one of several options. The book also speculates about heretofore untapped possibilities for service-learning, even including courses in pure mathematics. College faculty often may not fully appreciate the wide range of support mechanisms for such ventures even within their own institutions, so the book includes a lengthy chapter on the details of converting a rough idea to a solid action plan, sometimes even picking up financial support and other often unexpected benefits along the way. Creative teachers rarely implement a project in exactly the same way as a colleague might have, so the emphasis here is to display a wide range of successful projects in order to encourage readers to develop some of their own.

Mathematics for Social Justice: Resources for the College Classroom

Author : Gizem Karaali
Publisher : American Mathematical Soc.
ISBN 13 : 1470449269
Total Pages : 288 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mathematics for Social Justice: Resources for the College Classroom by : Gizem Karaali

Download or read book Mathematics for Social Justice: Resources for the College Classroom written by Gizem Karaali and published by American Mathematical Soc.. This book was released on 2019-07-09 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics for Social Justice offers a collection of resources for mathematics faculty interested in incorporating questions of social justice into their classrooms. The book begins with a series of essays from instructors experienced in integrating social justice themes into their pedagogy; these essays contain political and pedagogical motivations as well as nuts-and-bolts teaching advice. The heart of the book is a collection of fourteen classroom-tested modules featuring ready-to-use activities and investigations for the college mathematics classroom. The mathematical tools and techniques used are relevant to a wide variety of courses including college algebra, math for the liberal arts, calculus, differential equations, discrete mathematics, geometry, financial mathematics, and combinatorics. The social justice themes include human trafficking, income inequality, environmental justice, gerrymandering, voting methods, and access to education. The volume editors are leaders of the national movement to include social justice material into mathematics teaching. Gizem Karaali is Associate Professor of Mathematics at Pomona College. She is one of the founding editors of The Journal of Humanistic Mathematics, and an associate editor for The Mathematical Intelligencer and Numeracy ; she also serves on the editorial board of the MAA's Carus Mathematical Monographs. Lily Khadjavi is Associate Professor of Mathematics at Loyola Marymount University and is a past co-chair of the Infinite Possibilities Conference. She has served on the boards of Building Diversity in Science, the Barbara Jordan-Bayard Rustin Coalition, and the Harvard Gender and Sexuality Caucus.

High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice

Author : Robert Q. Berry III
Publisher : Corwin Press
ISBN 13 : 1071806467
Total Pages : 328 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice by : Robert Q. Berry III

Download or read book High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice written by Robert Q. Berry III and published by Corwin Press. This book was released on 2020-03-09 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students have —through various media and their lived experiences— a more visceral experience of social, economic, and environmental injustices. However, when people think of social justice, mathematics is rarely the first thing that comes to mind. Through model lessons developed by over 30 diverse contributors, this book brings seemingly abstract high school mathematics content to life by connecting it to the issues students see and want to change in the world. Along with expert guidance from the lead authors, the lessons in this book explain how to teach mathematics for self- and community-empowerment. It walks teachers step-by-step through the process of using mathematics—across all high school content domains—as a tool to explore, understand, and respond to issues of social injustice including: environmental injustice; wealth inequality; food insecurity; and gender, LGBTQ, and racial discrimination. This book features: Content cross-referenced by mathematical concept and social issues Downloadable instructional materials for student use User-friendly and logical interior design for daily use Guidance for designing and implementing social justice lessons driven by your own students’ unique passions and challenges Timelier than ever, teaching mathematics through the lens of social justice will connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will make them responsive citizens and leaders in the future.

Mathematics Teacher Education in the Public Interest

Author : Bharath Sriraman
Publisher : IAP
ISBN 13 : 161735970X
Total Pages : 302 pages
Book Rating : 4.6/5 (173 download)

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Book Synopsis Mathematics Teacher Education in the Public Interest by : Bharath Sriraman

Download or read book Mathematics Teacher Education in the Public Interest written by Bharath Sriraman and published by IAP. This book was released on 2013-02-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics teacher education has a critical role to play in preparing teachers to put at center stage goals to support equity in mathematics education and to diversify student interest and participation in mathematics. These goals must also resonate with broader public interest goals to improve educational and social conditions both in the U.S. and abroad. The Mathematics Teacher Education in the Public Interest book aims to support mathematics teacher educators to prepare teachers with new knowledge and skills to support all students to learn mathematics and to become informed, engaged, and critical citizens within their community, nation, and world. While internationally there is considerable interest among mathematics educators in issues of equity and social justice, the literature on mathematics teacher education for equity and social justice thus far has been very limited.The book provides theoretical discussions on the need for equity and social justice emphases in mathematics teacher education, as well as practical examples from mathematics teacher educators, documenting their own professional efforts to center practices on equity and social justice. Section emphases include critical perspectives on mathematics teacher education, the use of equity and social justice-themed activities in mathematics teacher preparation courses, and issues of identity and community and cultural contexts in mathematics teacher education. In addition syntheses of major ideas of the book are offered by experienced researchers.

Building Support for Scholarly Practices in Mathematics Methods

Author : Signe E. Kastberg
Publisher : IAP
ISBN 13 : 164113027X
Total Pages : 375 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis Building Support for Scholarly Practices in Mathematics Methods by : Signe E. Kastberg

Download or read book Building Support for Scholarly Practices in Mathematics Methods written by Signe E. Kastberg and published by IAP. This book was released on 2017-09-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building Support for Scholarly Practices in Mathematics Methods is the product of collaborations among over 40 mathematics teacher educators (MTEs) who teach mathematics methods courses for prospective PreK?12 teachers in many different institutional contexts and structures. Each chapter unpacks ways in which MTEs use theoretical perspectives to inform their construction of goals, activities designed to address those goals, facilitation of activities, and ways in which MTEs make sense of experiences prospective teachers have as a result. The book is organized in seven sections that highlight how the theoretical perspective of the instructor impacts scholarly inquiry and practice. The final section provides insight as we look backward to reflect, and forward with excitement, moving with the strength of the variation we found in our stories and the feeling of solidarity that results in our understandings of purposes for and insight into teaching mathematics methods. This book can serve as a resource for MTEs as they discuss and construct scholarly practices and as they undertake scholarly inquiry as a means to systematically examine their practice.

Strengths-Based Teaching and Learning in Mathematics

Author : Beth McCord Kobett
Publisher : Corwin
ISBN 13 : 1544374909
Total Pages : 273 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Strengths-Based Teaching and Learning in Mathematics by : Beth McCord Kobett

Download or read book Strengths-Based Teaching and Learning in Mathematics written by Beth McCord Kobett and published by Corwin. This book was released on 2020-02-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

Activating Math Talk

Author : Paola Sztajn
Publisher : Corwin Press
ISBN 13 : 1071821571
Total Pages : 225 pages
Book Rating : 4.0/5 (718 download)

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Book Synopsis Activating Math Talk by : Paola Sztajn

Download or read book Activating Math Talk written by Paola Sztajn and published by Corwin Press. This book was released on 2020-09-24 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Achieve High-Quality Mathematics Discourse With Purposeful Talk Techniques Many mathematics teachers agree that engaging students in high quality discourse is important for their conceptual learning, but successfully promoting such discourse in elementary classrooms—with attention to the needs of every learner—can be a challenge. Activating Math Talk tackles this challenge by bringing practical, math-specific, productive discourse techniques that are applicable to any lesson or curriculum. Framed around 11 student-centered discourse techniques, this research-based book connects purposeful instructional techniques to specific lesson goals and includes a focus on supporting emergent multilingual learners. You will be guided through each technique with Classroom examples of tasks and techniques spanning grades K–5 Reflection moments to help you consider how key ideas relate to your own instruction Classroom vignettes that illustrate the techniques in action and provide opportunities to analyze and prepare for your own implementation Group discussion questions for engaging with colleagues in your professional community Achieving high-quality mathematics discourse is within your reach using the clear-cut techniques that activates your math talk efforts to promote every student’s conceptual learning.

Research in Collegiate Mathematics Education III

Author : James J. Kaput
Publisher : American Mathematical Soc.
ISBN 13 : 0821808826
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Research in Collegiate Mathematics Education III by : James J. Kaput

Download or read book Research in Collegiate Mathematics Education III written by James J. Kaput and published by American Mathematical Soc.. This book was released on 1998 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs.

Mathematics Education

Author : Jacqueline Dewar
Publisher : Springer
ISBN 13 : 3319449508
Total Pages : 382 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Mathematics Education by : Jacqueline Dewar

Download or read book Mathematics Education written by Jacqueline Dewar and published by Springer. This book was released on 2016-11-26 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

Rethinking Mathematics

Author : Eric Gutstein
Publisher : Rethinking Schools
ISBN 13 : 0942961544
Total Pages : 192 pages
Book Rating : 4.9/5 (429 download)

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Book Synopsis Rethinking Mathematics by : Eric Gutstein

Download or read book Rethinking Mathematics written by Eric Gutstein and published by Rethinking Schools. This book was released on 2005 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this unique collection, more than 30 articles show how to weave social justice issues throughout the mathematics curriculum, as well as how to integrate mathematics into other curricular areas. Rethinking Mathematics offers teaching ideas, lesson plans, and reflections by practitioners and mathematics educators. This is real-world math-math that helps students analyze problems as they gain essential academic skills. This book offers hope and guidance for teachers to enliven and strengthen their math teaching. It will deepen students' understanding of society and help prepare them to be critical, active participants in a democracy. Blending theory and practice, this is the only resource of its kind.

Standards for Preparing Teachers of Mathematics

Author : Nadine Bezuk
Publisher :
ISBN 13 : 9781641139960
Total Pages : 200 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Standards for Preparing Teachers of Mathematics by : Nadine Bezuk

Download or read book Standards for Preparing Teachers of Mathematics written by Nadine Bezuk and published by . This book was released on 2020 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: AMTE, in the Standards for Preparing Teachers of Mathematics, puts forward a national vision of initial preparation for all Pre-K-12 teachers who teach mathematics. SPTM pertains not only to middle and high school mathematics teachers who may teach mathematics exclusively but also to elementary school teachers teaching all disciplines, special education teachers, teachers of emergent multilingual students, and all other teaching professionals and administrators who have responsibility for students' mathematical learning. SPTM has broad implications for teacher preparation programs, in which stakeholders include faculty and administrators in both education and mathematics at the university level; teachers, principals, and district leaders in the schools with which preparation programs partner; and the communities in which preparation programs and their school partners are situated. SPTM is intended as a national guide that articulates a vision for mathematics teacher preparation and supports the continuous improvement of teacher preparation programs. Such continuous improvement includes changes to preparation program courses and structures, partnerships involving schools and universities and their leaders, the ongoing accreditation of such programs regionally and nationally, and the shaping of state and national mathematics teacher preparation policy. SPTM is also designed to inform accreditation processes for mathematics teacher preparation programs, to influence policies related to preparation of teachers of mathematics, and to promote national dialogue around preparing teachers of mathematics. The vision articulated in SPTM is aspirational in that it describes a set of high expectations for developing a well-prepared beginning mathematics teacher who can support meaningful student learning. The vision is research-based and establishes a set of goals for the continued development and refinement of a mathematics teacher preparation program and a research agenda for the study of the effects of such a program. SPTM contains detailed depictions of what a well-prepared beginning teacher knows and is able to do related to content, pedagogy, and disposition, and what a strong preparation program entails with respect to learning experiences, assessments, and partnerships. Stakeholders in mathematics teacher preparation will find messages related to their roles. Standards for Preparing Teachers of Mathematics includes standards and indicators for teacher candidates and for the design of teacher preparation programs. SPTM outlines assessment practices related to overall quality, program effectiveness, and candidate performance. SPTM describes specific focal practices by grade band and provides guidance to stakeholders regarding processes for productive change.

The Professional Education and Development of Teachers of Mathematics

Author : Ruhama Even
Publisher : Springer Science & Business Media
ISBN 13 : 0387096019
Total Pages : 271 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis The Professional Education and Development of Teachers of Mathematics by : Ruhama Even

Download or read book The Professional Education and Development of Teachers of Mathematics written by Ruhama Even and published by Springer Science & Business Media. This book was released on 2008-11-16 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The premise of the 15th ICMI Study is that teachers are key to students' opportunities to learn mathematics. What teachers of mathematics know, care about, and do is a product of their experiences and socialization, together with the impact of their professional education. The Professional Education and Development of Teachers of Mathematics assembles important new international work- development, research, theory and practice - concerning the professional education of teachers of mathematics. As it examines critical areas to reveal what is known and what significant questions and problems warrant collective attention, the volume also contributes to the strengthening of the international community of mathematics educators. The Professional Education and Development of Teachers of Mathematics is of interest to the mathematics education community as well as to other researchers, practitioners and policy makers concerned with the professional education of teachers.

The Science of Effective Mentorship in STEMM

Author : National Academies of Sciences, Engineering, and Medicine
Publisher : National Academies Press
ISBN 13 : 0309497299
Total Pages : 307 pages
Book Rating : 4.3/5 (94 download)

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Book Synopsis The Science of Effective Mentorship in STEMM by : National Academies of Sciences, Engineering, and Medicine

Download or read book The Science of Effective Mentorship in STEMM written by National Academies of Sciences, Engineering, and Medicine and published by National Academies Press. This book was released on 2020-01-24 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mentorship is a catalyst capable of unleashing one's potential for discovery, curiosity, and participation in STEMM and subsequently improving the training environment in which that STEMM potential is fostered. Mentoring relationships provide developmental spaces in which students' STEMM skills are honed and pathways into STEMM fields can be discovered. Because mentorship can be so influential in shaping the future STEMM workforce, its occurrence should not be left to chance or idiosyncratic implementation. There is a gap between what we know about effective mentoring and how it is practiced in higher education. The Science of Effective Mentorship in STEMM studies mentoring programs and practices at the undergraduate and graduate levels. It explores the importance of mentorship, the science of mentoring relationships, mentorship of underrepresented students in STEMM, mentorship structures and behaviors, and institutional cultures that support mentorship. This report and its complementary interactive guide present insights on effective programs and practices that can be adopted and adapted by institutions, departments, and individual faculty members.

Reading and Writing the World with Mathematics

Author : Eric Gutstein
Publisher : Routledge
ISBN 13 : 1136284656
Total Pages : 274 pages
Book Rating : 4.1/5 (362 download)

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Book Synopsis Reading and Writing the World with Mathematics by : Eric Gutstein

Download or read book Reading and Writing the World with Mathematics written by Eric Gutstein and published by Routledge. This book was released on 2012-09-10 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics education in the United States can reproduce social inequalities whether schools use either "basic-skills" curricula to prepare mainly low-income students of color for low-skilled service jobs or "standards-based" curricula to ready students for knowledge-intensive positions. And working for fundamental social change and rectifying injustice are rarely included in any mathematics curriculum. Reading and Writing the World with Mathematics argues that mathematics education should prepare students to investigate and critique injustice, and to challenge, in words and actions, oppressive structures and acts. Based on teacher-research, the book provides a theoretical framework and practical examples for how mathematics educators can connect schooling to a larger sociopolitical context and concretely teach mathematics for social justice.

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Mathematics Success and Failure Among African-American Youth

Author : Danny Bernard Martin
Publisher : Routledge
ISBN 13 : 1135676224
Total Pages : 231 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Mathematics Success and Failure Among African-American Youth by : Danny Bernard Martin

Download or read book Mathematics Success and Failure Among African-American Youth written by Danny Bernard Martin and published by Routledge. This book was released on 2000 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings together theory & methods from cultural & cog. perspectives to examine forces contributing to why a dispropriate no. of African-Amer. students don't reach their potential in math & are then underrepresented in professions requiring math skills.

Proceedings of the 13th International Congress on Mathematical Education

Author : Gabriele Kaiser
Publisher : Springer
ISBN 13 : 3319625977
Total Pages : 735 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 735 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.