Mathematics Teacher Education in the Public Interest

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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.

Mathematics for Human Flourishing

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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.

Rethinking Mathematics

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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.

Excursions in Geometry

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Publisher : Courier Corporation
ISBN 13 : 0486265307
Total Pages : 191 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Excursions in Geometry by : Charles Stanley Ogilvy

Download or read book Excursions in Geometry written by Charles Stanley Ogilvy and published by Courier Corporation. This book was released on 1990-01-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.

Mindset Mathematics

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Publisher : John Wiley & Sons
ISBN 13 : 1119358809
Total Pages : 288 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Mindset Mathematics by : Jo Boaler

Download or read book Mindset Mathematics written by Jo Boaler and published by John Wiley & Sons. This book was released on 2017-08-28 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the first-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning

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Publisher : American Mathematical Soc.
ISBN 13 : 1470463776
Total Pages : 348 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning by : Wendy M. Smith

Download or read book Transformational Change Efforts: Student Engagement in Mathematics through an Institutional Network for Active Learning written by Wendy M. Smith and published by American Mathematical Soc.. This book was released on 2021-05-05 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this handbook is to help launch institutional transformations in mathematics departments to improve student success. We report findings from the Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) study. SEMINAL's purpose is to help change agents, those looking to (or currently attempting to) enact change within mathematics departments and beyond—trying to reform the instruction of their lower division mathematics courses in order to promote high achievement for all students. SEMINAL specifically studies the change mechanisms that allow postsecondary institutions to incorporate and sustain active learning in Precalculus to Calculus 2 learning environments. Out of the approximately 2.5 million students enrolled in collegiate mathematics courses each year, over 90% are enrolled in Precalculus to Calculus 2 courses. Forty-four percent of mathematics departments think active learning mathematics strategies are important for Precalculus to Calculus 2 courses, but only 15 percnt state that they are very successful at implementing them. Therefore, insights into the following research question will help with institutional transformations: What conditions, strategies, interventions and actions at the departmental and classroom levels contribute to the initiation, implementation, and institutional sustainability of active learning in the undergraduate calculus sequence (Precalculus to Calculus 2) across varied institutions?

Living Culturally Responsive Mathematics Education with/in Indigenous Communities

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Author :
Publisher : BRILL
ISBN 13 : 9004415769
Total Pages : 291 pages
Book Rating : 4.0/5 (44 download)

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Book Synopsis Living Culturally Responsive Mathematics Education with/in Indigenous Communities by :

Download or read book Living Culturally Responsive Mathematics Education with/in Indigenous Communities written by and published by BRILL. This book was released on 2019-11-26 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: Living Culturally Responsive Mathematics Education with/in Indigenous Communities explores challenges and possibilities across international contexts, involving Indigenous and non-Indigenous scholars, teachers and Elders responding to calls for improved education for all Indigenous students. Authors from Australia, New Zealand, United States, Micronesia, and Canada explore the nature of culturally responsive mathematics education. Chapters highlight the importance of relationships with communities and the land, each engaging critically with ideas of culturally responsive education, exploring what this stance might mean and how it is lived in local contexts within global conversations. Education researchers and teacher educators will find a living pathway where scholars, educators, youth and community members critically take-up culturally responsive teachings and the possibilities and challenges that arise along the journey. Contributors are: Dayle Anderson, Dora Andre-Ihrke, Jo-ann Archibald Q'um Q'um Xiiem, Maria Jose Athie-Martinez, Robin Averill, Trevor Bills, Beatriz A. Camacho, A. J. (Sandy) Dawson, Dwayne Donald, Herewini Easton, Tauvela Fale, Amanda Fritzlan, Florence Glanfield, Jodie Hunter, Roberta Hunter, Newell Margaret Johnson, Julie Kaomea, Robyn Jorgensen, Jerry Lipka, Lisa Lunney Borden, Dora Miura, Sharon Nelson-Barber, Cynthia Nicol, Gladys Sterenberg, Marama Taiwhati, Pania Te Maro, Jennifer S. Thom, David Wagner, Evelyn Yanez, and Joanne Yovanovich.

Mathematics Curriculum in School Education

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Publisher : Springer Science & Business Media
ISBN 13 : 9400775601
Total Pages : 651 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Mathematics Curriculum in School Education by : Yeping Li

Download or read book Mathematics Curriculum in School Education written by Yeping Li and published by Springer Science & Business Media. This book was released on 2013-11-19 with total page 651 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics curriculum, which is often a focus in education reforms, has not received extensive research attention until recently. Ongoing mathematics curriculum changes in many education systems call for further research and sharing of effective curriculum policies and practices that can help lead to the improvement of school education. This book provides a unique international perspective on diverse curriculum issues and practices in different education systems, offering a comprehensive picture of various stages along curriculum transformation from the intended to the achieved, and showing how curriculum changes in various stages contribute to mathematics teaching and learning in different educational systems and cultural contexts. The book is organized to help readers learn not only from reading individual chapters, but also from reading across chapters and sections to explore broader themes, including: Identifying what is important in mathematics for teaching and learning in different education systems; Understanding mathematics curriculum and its changes that are valued over time in different education systems; Identifying and analyzing effective curriculum practices; Probing effective infrastructure for curriculum development and implementation. Mathematics Curriculum in School Education brings new insights into curriculum policies and practices to the international community of mathematics education, with 29 chapters and four section prefaces contributed by 56 scholars from 14 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, curriculum developers, and graduate students interested in learning about recent curriculum development, research, and practices in different education systems. It will help readers to reflect on curriculum policies and practices in their own education systems, and also inspire them to identify and further explore new areas of curriculum research for improving mathematics teaching and learning.

Research Trends in Mathematics Teacher Education

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Author :
Publisher : Springer
ISBN 13 : 3319025627
Total Pages : 321 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Research Trends in Mathematics Teacher Education by : Jane-Jane Lo

Download or read book Research Trends in Mathematics Teacher Education written by Jane-Jane Lo and published by Springer. This book was released on 2014-05-28 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on the preparation and continued development of mathematics teachers is becoming an increasingly important subset of mathematics education research. Such research explores the attributes, knowledge, skills and beliefs of mathematics teachers as well as methods for assessing and developing these critical aspects of teachers and influences on teaching. Research Trends in Mathematics Teacher Education focuses on three major themes in current mathematics teacher education research: mathematical knowledge for teaching, teacher beliefs and identities, and tools and techniques to support teacher learning. Through careful reports of individual research studies and cross-study syntheses of the state of research in these areas, the book provides insights into teachers’ learning processes and how these processes can be harnessed to develop effective teachers. Chapters investigate bedrock skills needed for working with primary and secondary learners (writing relevant problems, planning lessons, being attentive to student learning) and illustrate how knowledge can be accessed, assessed, and nurtured over the course of a teaching career. Commentaries provide context for current research while identifying areas deserving future study. Included among the topics: Teachers’ curricular knowledge Teachers’ personal and classroom mathematics Teachers’ learning journeys toward reasoning and sense-making Teachers’ transitions in noticing Teachers’ uses of a learning trajectory as a tool for mathematics lesson planning A unique and timely set of perspectives on the professional development of mathematics teachers at all stages of their careers, Research Trends in Mathematics Teacher Education brings clarity and practical advice to researchers as well as practitioners in this increasingly critical arena.

Research in Mathematics Education in Australasia 2016–2019

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Publisher : Springer Nature
ISBN 13 : 9811542694
Total Pages : 383 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Research in Mathematics Education in Australasia 2016–2019 by : Jennifer Way

Download or read book Research in Mathematics Education in Australasia 2016–2019 written by Jennifer Way and published by Springer Nature. This book was released on 2020-04-20 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: The tenth edition of the four-yearly review of mathematics education research in Australasia, compiled by the Mathematics Education Research Group of Australasia (MERGA), critically reviews research in mathematics education in the four years from 2016 to 2019. Its goals are to provide a reference guide for researchers, and to promote further quality research in Australasia.

Borders in Mathematics Pre-Service Teacher Education

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Publisher : Springer Nature
ISBN 13 : 3030442926
Total Pages : 292 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Borders in Mathematics Pre-Service Teacher Education by : Nenad Radakovic

Download or read book Borders in Mathematics Pre-Service Teacher Education written by Nenad Radakovic and published by Springer Nature. This book was released on 2020-05-22 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the current state of the field of mathematics pre-service teacher education through the theme of borders. Borders are ubiquitous; they can be used to define, classify, organize, make sense of, and/or group. There are many ways that the concept of a border illuminates the field of mathematics pre-service teacher education. Consequently, there are a multitude of responses to these borders: researchers and practitioners question, challenge, cross, blur, and erase them. Chapters include the following topics: explorations of mathematics across topics (e.g., geometry, algebra, probability) and with other disciplines (e.g., science, the arts, social sciences); challenging gender, cultural, and racial borders; exploring the structure and curriculum of teacher education programs; spaces inhabited by teacher education programs (e.g., university, community); and international collaborations and programs to promote cross-cultural sharing and learning. The book targets a readership of researchers and graduate students in integrated education studies, teacher education, practitioners of mathematics education, curriculum developers, and educational administrators and policy makers. ​

Handbook on the History of Mathematics Education

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Publisher : Springer Science & Business Media
ISBN 13 : 146149155X
Total Pages : 627 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Handbook on the History of Mathematics Education by : Alexander Karp

Download or read book Handbook on the History of Mathematics Education written by Alexander Karp and published by Springer Science & Business Media. This book was released on 2014-01-25 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive International Handbook on the History of Mathematics Education, covering a wide spectrum of epochs and civilizations, countries and cultures. Until now, much of the research into the rich and varied history of mathematics education has remained inaccessible to the vast majority of scholars, not least because it has been written in the language, and for readers, of an individual country. And yet a historical overview, however brief, has become an indispensable element of nearly every dissertation and scholarly article. This handbook provides, for the first time, a comprehensive and systematic aid for researchers around the world in finding the information they need about historical developments in mathematics education, not only in their own countries, but globally as well. Although written primarily for mathematics educators, this handbook will also be of interest to researchers of the history of education in general, as well as specialists in cultural and even social history.

The Effectiveness of Mathematics Teaching in Primary Schools

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Author :
Publisher : Taylor & Francis
ISBN 13 : 1317191072
Total Pages : 196 pages
Book Rating : 4.3/5 (171 download)

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Book Synopsis The Effectiveness of Mathematics Teaching in Primary Schools by : Zhenzhen Miao

Download or read book The Effectiveness of Mathematics Teaching in Primary Schools written by Zhenzhen Miao and published by Taylor & Francis. This book was released on 2017-07-06 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Effectiveness of Mathematics Teaching in Primary Schools: Lessons from England and China provides a unique insight into the mathematics classrooms of these two countries and arrives at a time when the world is eager to know how Chinese learners consistently excel at learning mathematics and other core subjects. Showcasing the kinds of teaching methods that work within and across countries, this book presents a rich collection of views, including those from teachers, their native colleagues, their foreign colleagues and the researcher, regarding the quality of mathematics teaching today. Interweaving scientific results about teaching and learning evaluations with multiple perspectives of various roles in and out of the classroom, Miao and Reynolds offer insights into how and why different approaches of teaching have led to different learning outcomes in mathematics internationally. Building on rigid and robust analyses of the most up-to-date data in England and China, the book indicates that it is through changing teaching rather than changing teachers that mathematics learning can be improved, because it is what teachers do in the classroom that really makes a big difference. Containing four decades of wisdom from the field of teaching effectiveness research, this book is essential reading for all who want to improve the quality of mathematics teaching worldwide. This book is particularly relevant for educational researchers, postgraduate students and teachers, as well as school leaders, policymakers and parents.

Teaching Secondary and Middle School Mathematics

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Publisher : Taylor & Francis
ISBN 13 : 1003820042
Total Pages : 540 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Teaching Secondary and Middle School Mathematics by : Daniel J. Brahier

Download or read book Teaching Secondary and Middle School Mathematics written by Daniel J. Brahier and published by Taylor & Francis. This book was released on 2024-01-22 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching Secondary and Middle School Mathematics combines the latest developments in research, technology, and standards with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics. The book explores the mathematics teaching profession by examining the processes of planning, teaching, and assessing student progress through practical examples and recommendations. Beginning with an examination of what it means to teach and learn mathematics, the reader is led through the essential components of teaching, concluding with an examination of how teachers continue with professional development throughout their careers. Hundreds of citations are used to support the ideas presented in the text, and specific websites and other resources are presented for future study by the reader. Classroom scenarios are presented to engage the reader in thinking through specific challenges that are common in mathematics classrooms. The seventh edition has been updated and expanded with particular emphasis on the latest technology, standards, and other resources. The reader is introduced to the ways that students think and how to best meet their needs through planning that involves attention to differentiation, as well as how to manage a classroom for success. Features include: • Following on from the sixth edition, assessment takes a central role in planning and teaching. Unit 3 (of 5) addresses the use of summative and formative assessments to inform classroom teaching practices. • A new appendix is included that lists websites that can be used in a methods class to view other teachers interacting with students for discussion of effective teaching practices. • The feature entitled “Links and Resources” has been updated in each of the 13 chapters. Five strongly recommended and practical resources are spotlighted at the end of each chapter as an easy reference to some of the most important materials on the topic. • Approximately 150 new citations have either replaced or been added to the text to reflect the latest in research, materials, and resources that support the teaching of mathematics. • Significant revisions have been made to Chapter 12, which now includes updated research and practices as well as a discussion on culturally responsive pedagogy. Likewise, Chapter 8 now includes a description of best and high-leverage teaching practices, and a discussion in Chapter 11 on alternative high school mathematics electives for students has been added. • Chapter 9, on the practical use of classroom technology, has again been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld personal devices, in light of changes in education resulting from the global pandemic. An updated Instructor’s Manual features a test bank, sample classroom activities, PowerPoint slide content, chapter summaries, and learning outcomes for each chapter, and can be accessed by instructors online at www.routledge.com/9781032472867.

The Mathematics Teacher Education Partnership

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Author :
Publisher : IAP
ISBN 13 : 1641139331
Total Pages : 432 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis The Mathematics Teacher Education Partnership by : W. Gary Martin

Download or read book The Mathematics Teacher Education Partnership written by W. Gary Martin and published by IAP. This book was released on 2020-01-01 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of a body of work conducted over the past seven years related to the preparation of secondary mathematics teachers by the Mathematics Teacher Education Partnership (MTE-Partnership), a national consortium of more than 90 universities and 100 school systems. The MTE-Partnership is organized as a Networked Improvement Community (NIC), which combines the disciplined inquiry of improvement science with the power of networking to accelerate improvement by engaging a broad set of participants. The MTE-Partnership is addressing key challenges in secondary mathematics teacher preparation, including: • Supporting the development of content knowledge relevant to teaching secondary mathematics; • Providing effective clinical experiences to teacher candidates; • Recruiting secondary mathematics teacher candidates, ensuring program completion and their subsequent retention in the field as early career teachers; • Supporting overall transformation of secondary mathematics teacher preparation in alignment with these challenges; • Ensuring a focus on equity and social justice in secondary mathematics teacher recruitment, preparation, and induction. This book outlines existing knowledge related to each of these key challenges, as well as the work of Research Action Clusters (RACs) formed to address the challenges. Each RAC includes participants from multiple institutions who work collaboratively to iteratively develop, test, and refine processes and products that can help programs more effectively prepare secondary mathematics teacher candidates. The book describes promising approaches to improving aspects of secondary mathematics teacher preparation developed by the RACs, including specific products that have been developed, which will inform the work of others involved in secondary mathematics teacher preparation. In addition, reflections on the use of the NIC model provides insights for others considering this research design. Particular references to the Standards for Preparing Teachers of Mathematics (Association of Mathematics Teacher Educators, 2017) are included throughout the book.

Let's Play Math

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Author :
Publisher : Tabletop Academy Press
ISBN 13 : 1892083248
Total Pages : 288 pages
Book Rating : 4.8/5 (92 download)

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Book Synopsis Let's Play Math by : Denise Gaskins

Download or read book Let's Play Math written by Denise Gaskins and published by Tabletop Academy Press. This book was released on 2012-09-04 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematics, Affect and Learning

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Author :
Publisher : Springer
ISBN 13 : 9812876790
Total Pages : 145 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Mathematics, Affect and Learning by : Peter Grootenboer

Download or read book Mathematics, Affect and Learning written by Peter Grootenboer and published by Springer. This book was released on 2015-10-17 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the beliefs, attitudes, values and emotions of students in Years 5 to 8 (aged 10 to 14 years) about mathematics and mathematics education. Fundamentally, this book focuses on the development of affective views and responses towards mathematics and mathematics learning. Furthermore, it seems that students develop their more negative views of mathematics during the middle school years (Years 5 to 8), and so here we concentrate on students in this critical period. The book is based on a number of empirical studies, including an enquiry undertaken with 45 children in Years 5 and 6 in one school; a large-scale quantitative study undertaken with students from a range of schools across diverse communities in New Zealand; and two related small-scale studies with junior secondary students in Australia. This book brings substantial, empirically-based evidence to the widely held perception that many students have negative views of mathematics, and these affective responses develop during the middle years of school. The data for this book were collected with school students, and students who were actually engaged in learning mathematics in their crucial middle school years. The findings reported and discussed here are relevant for researchers and mathematics educators, policy makers and curriculum developers, and teachers and school principals engaged in the teaching of mathematics.