Transforming Mathematics Teacher Education

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Author :
Publisher : Springer
ISBN 13 : 3030210170
Total Pages : 181 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Transforming Mathematics Teacher Education by : Tonya Gau Bartell

Download or read book Transforming Mathematics Teacher Education written by Tonya Gau Bartell and published by Springer. This book was released on 2019-08-01 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book builds on the Teachers Empowered to Advance Change in Mathematics (TEACH Math) project, which was an initiative that sought to develop a new generation of preK-8 mathematics teachers to connect mathematics, children’s mathematical thinking, and community and family knowledge in mathematics instruction – or what we have come to call children’s multiple mathematical knowledge bases in mathematics instruction, with an explicit focus on equity. Much of the work involved in the TEACH Math project included the development of three instructional modules for preK-8 mathematics methods courses to support the project’s goals. These activities were used and refined over eight semesters, and in Fall 2014 shared at a dissemination conference with other mathematics teacher educators from a variety of universities across the United States. Chapter contributions represent diverse program and geographical contexts and teach prospective and practicing teachers from a variety of socioeconomic and ethnic backgrounds, in particular providing accounts of supports, challenges, and tensions in implementing equity-based mathematics teacher education. The chapters supply rich evidence and illustrative examples of how other mathematics teacher educators and professional developers might make the modules work for their unique practices, courses, workshops, and prospective teachers/teachers. It promises to be an important resource for offering guidance and examples to those working with prospective teachers of mathematics who want to create positive, culturally responsive, and equity-based mathematics experiences for our nation’s youth.

Handbook of Research on Transforming Mathematics Teacher Education in the Digital Age

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Author :
Publisher : IGI Global
ISBN 13 : 1522501215
Total Pages : 679 pages
Book Rating : 4.5/5 (225 download)

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Book Synopsis Handbook of Research on Transforming Mathematics Teacher Education in the Digital Age by : Niess, Margaret

Download or read book Handbook of Research on Transforming Mathematics Teacher Education in the Digital Age written by Niess, Margaret and published by IGI Global. This book was released on 2016-04-22 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: The digital age provides ample opportunities for enhanced learning experiences for students; however, it can also present challenges for educators who must adapt to and implement new technologies in the classroom. The Handbook of Research on Transforming Mathematics Teacher Education in the Digital Age is a critical reference source featuring the latest research on the development of educators’ knowledge for the integration of technologies to improve classroom instruction. Investigating emerging pedagogies for preservice and in-service teachers, this publication is ideal for professionals, researchers, and educational designers interested in the implementation of technology in the mathematics classroom.

The Mathematics Teacher Education Partnership

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Author :
Publisher : Association of Mathematics Teacher Educators (
ISBN 13 : 9781641139328
Total Pages : 0 pages
Book Rating : 4.1/5 (393 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 Association of Mathematics Teacher Educators (. This book was released on 2019-12-31 with total page 0 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.

Transforming Mathematics Instruction

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Author :
Publisher : Springer
ISBN 13 : 3319049933
Total Pages : 586 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Transforming Mathematics Instruction by : Yeping Li

Download or read book Transforming Mathematics Instruction written by Yeping Li and published by Springer. This book was released on 2014-07-05 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys and examines different approaches and practices that contribute to the changes in mathematics instruction, including (1) innovative approaches that bring direct changes in classroom instructional practices, (2) curriculum reforms that introduce changes in content and requirements in classroom instruction, and (3) approaches in mathematics teacher education that aim to improve teachers’ expertise and practices. It also surveys relevant theory and methodology development in studying and assessing mathematics instruction. Classroom instruction is commonly seen as one of the key factors contributing to students’ learning of mathematics, but much remains to be understood about teachers’ instructional practices that lead to the development and enactment of effective classroom instruction, and approaches and practices developed and used to transform classroom instruction in different education systems. Transforming Mathematics Instruction 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 emphasized in different approaches; - Exploring how students’ learning is considered and facilitated through different approaches and practices; - Understanding the nature of various approaches that are valued in different systems and cultural contexts; - Probing culturally valued approaches in identifying and evaluating effective instructional practices. The book brings new research and insights into multiple approaches and practices for transforming mathematics instruction to the international community of mathematics education, with 25 chapters and four section prefaces contributed by 56 scholars from 10 different education systems. This rich collection is indispensable reading for mathematics educators, researchers, teacher educators, curriculum developers, and graduate students interested in learning about different instructional practices, approaches for instructional transformation, and research in different education systems. It will help readers to reflect on approaches and practices that are useful for instructional changes in their own education systems, and also inspire them to identify and further explore new areas of research and program development in improving mathematics teaching and learning.

The Mathematics Teacher Education Partnership

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Author :
Publisher : IAP
ISBN 13 : 1641139331
Total Pages : 433 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 433 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.

Improving Instruction in Geometry and Measurement

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Publisher : Teachers College Press
ISBN 13 : 9780807745311
Total Pages : 166 pages
Book Rating : 4.7/5 (453 download)

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Book Synopsis Improving Instruction in Geometry and Measurement by : Margaret Schwan Smith

Download or read book Improving Instruction in Geometry and Measurement written by Margaret Schwan Smith and published by Teachers College Press. This book was released on 2005-01-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Helping students develop an understanding of important mathematical ideas is a persistent challenge for teachers. In this book, one of a three-volume set, well-known mathematics educators Margaret Smith, Edward A. Silver, and Mary Kay Stein provide teachers of mathematics the support they need to improve their instruction. They focus on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency. The content focus of Volume One is rational numbers and proportionality. Using materials that were developed under the NSF-funded COMET (Cases of Mathematics to Enhance Teaching) program, each volume in the set features cases from urban, middle school classrooms with ethnically, racially, and linguistically diverse student populations. Each case illustrates an instructional episode in the classroom of a teacher who is implementing standards-based instruction, the teachers' perspective, including their thoughts and actions as they interact with students and with key aspects of mathematical content, cognitively challenging mathematics activities that are built around samples of authentic classroom practice., and facilitation chapters to help professional developers "teach" the cases, including specific guidelines for facilitating discussions and suggestions for connecting the ideas presented in the cases to a teacher's own practice. As a complete set, this resource provides a basis on which to build a comprehensive professional development program to improve mathematics instruction and student learning.

Cases for Mathematics Teacher Educators

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Author :
Publisher : IAP
ISBN 13 : 1681236273
Total Pages : 511 pages
Book Rating : 4.6/5 (812 download)

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Book Synopsis Cases for Mathematics Teacher Educators by : Dorothy Y. White

Download or read book Cases for Mathematics Teacher Educators written by Dorothy Y. White and published by IAP. This book was released on 2016-10-01 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Association of Mathematics Teacher Educators (AMTE) in its 2015 position paper on Equity in Mathematics Teacher Education provides a list of actions for mathematics teacher educators (MTE’s) to help them develop and implement equitable practices. The position paper states it is critical that mathematics teacher educators: “Model equity?based pedagogy that emphasizes rich and rigorous mathematics; elicit and build on children’s and young adults’ mathematical thinking; connect to P?12 students’ cultural/linguistic knowledge and backgrounds as well as individual interests; facilitate mathematical discourse; minimize status issues by expanding broader participation and engagement where varied mathematical strengths are valued; and promote positive mathematical identity and agency (p. 2)”. Cases for Mathematics Teacher Educators: Facilitating Conversations about Inequities in Mathematics Classrooms provides an excellent resource to start conversations describing the enactment of these actions. The book is organized into three main sections: (1) Conversations About Inequities in Mathematics Methods Courses, (2) Conversations About Inequities in Mathematics Content Courses, and (3) Conversations about Inequities in Graduate and Professional Development Contexts. Across these sections there are 19 cases and 57 corresponding commentaries focused on dilemmas that arise when mathematics teacher educators foreground equity in their work. This book of cases provides a needed resource for MTEs to engage prospective teachers, practicing teachers, and future teacher educators in discussions about inequities, privilege, and oppression in society, in schools, and in the mathematics classroom. It is the product of the thinking and experiences of 87 authors who are committed to the improvement of mathematics teacher education.

Transforming Teacher Education

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Author :
Publisher : DIANE Publishing
ISBN 13 : 0788185934
Total Pages : 102 pages
Book Rating : 4.7/5 (881 download)

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Book Synopsis Transforming Teacher Education by : Patricia Simpson

Download or read book Transforming Teacher Education written by Patricia Simpson and published by DIANE Publishing. This book was released on 2000 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a vision for what teacher education could be. It is intended as a guide for Minnesota post-secondary institutions as they consider the implications of national and state K-12 reform recommendations for teacher education (TE) programs. Chapters: transforming TE; context for change; standards for the education of teachers of math. and science; recommendations for transforming the education of teachers of math. and science; transforming policy to practices; references; national standards for math. and science teaching and TE and for curriculum, instruction, and assessment in math. and science; and the history of transforming TE. Math. and science bibliographies.

Making Sense of Mathematics Teacher Education

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 0792369866
Total Pages : 346 pages
Book Rating : 4.7/5 (923 download)

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Book Synopsis Making Sense of Mathematics Teacher Education by : Fou-Lai Lin

Download or read book Making Sense of Mathematics Teacher Education written by Fou-Lai Lin and published by Springer Science & Business Media. This book was released on 2001-07-31 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a research-based book that deals with a broad range of issues about mathematics teacher education. It examines teacher education programs from different societies and cultures as it develops an international perspective on mathematics teacher education. Practical situations that are associated with related theories are studied critically. It is intended for teacher educators, mathematics educators, graduate students in mathematics education, and mathematics teachers.

The Work of Mathematics Teacher Educators

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Author :
Publisher : IAP
ISBN 13 : 1623969468
Total Pages : 172 pages
Book Rating : 4.6/5 (239 download)

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Book Synopsis The Work of Mathematics Teacher Educators by : Kathleen Lynch-Davis

Download or read book The Work of Mathematics Teacher Educators written by Kathleen Lynch-Davis and published by IAP. This book was released on 2015-10-01 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: (Orginally published in 2005) A major focus of teacher education is the development of preservice teachers. However, it should not be the only focus of those who work in teacher education. Educating inservice teachers in equally important, and the conversation among those involved in mathematics teacher education needs to include discussion of this group as well. This conversation also highlights a need for professional development for teacher educators and research on the development of teacher educators. This monograph discusses issues in educating all of these groups of individuals in an effort to continue the conversation among those involded in mathematics teacher education.

Research for Educational Change

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Author :
Publisher : Routledge
ISBN 13 : 1317285409
Total Pages : 293 pages
Book Rating : 4.3/5 (172 download)

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Book Synopsis Research for Educational Change by : Jill Adler

Download or read book Research for Educational Change written by Jill Adler and published by Routledge. This book was released on 2016-06-17 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research for Educational Change presents ways in which educational research can fulfil its commitments to educational practice. Focussing its discussion within the context of mathematics education, it argues that while research-generated insights can have beneficial effects on learning and teaching, the question of how these effects are to be generated and sustained is far from evident. The question of how to turn research into educational improvement is discussed here in the context of learning and teaching hindered by poverty and social injustice. In the first part of the book, four teams of researchers use different methodologies while analysing the same corpus of data, collected in a South African mathematics classroom. In the second part, each of these teams makes a specific proposal about what can be done and how so that its research-generated insights have a tangible, beneficial impact on what is happening in mathematical classrooms. Combining two discourses – that of researchers speaking to one another, and that of researchers communicating their insights to those responsible for educational practice – the book deals with the perenial question of communication between those who study educational processes and those who are directly responsible for teacher education, educational research and classroom practices. This book will be key reading for postgraduates, researchers and academics in education and particularly in the areas of mathematics education, education research, teacher education and classroom practice. It will also appeal to teacher educators, practitioners and undergraduate students interested in educational research.

The Learning and Development of Mathematics Teacher Educators

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Author :
Publisher : Springer Nature
ISBN 13 : 3030624080
Total Pages : 472 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis The Learning and Development of Mathematics Teacher Educators by : Merrilyn Goos

Download or read book The Learning and Development of Mathematics Teacher Educators written by Merrilyn Goos and published by Springer Nature. This book was released on 2021-04-07 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in mathematics teacher education as a distinctive field of inquiry has grown substantially over the past 10-15 years. Within this field there is emerging interest in how mathematics teacher educators (MTEs) themselves learn and develop. Until recently there were few published studies on this topic, and the processes by which mathematics teacher educators learn, and the forms of knowledge they require for effective practice, had not been systematically investigated. However, researchers in mathematics education are now beginning to investigate the development of MTE expertise and associated issues. This volume draws on the latest research and thinking in this area is therefore timely to stimulate future development and directions. It will survey the emerging field of inquiry in mathematics education, combining the work of established scholars with perspectives of newcomers to the field, with the aim of influencing development of the field, invite cross-cultural comparisons in becoming a mathematics teacher educator by highlighting issues in the development of MTEs in different countries, and examine the roles of both mathematics educators and mathematicians in preparing future teachers of mathematics. The primary audience will be university-based mathematics teacher educators and MTE researchers, and postgraduate research students who are seeking academic careers as MTEs. Additional interest may come from teacher educators in disciplines other than mathematics, and education policy makers responsible for accreditation and quality control of initial teacher education programs.

Building Support for Scholarly Practices in Mathematics Methods

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Author :
Publisher : IAP
ISBN 13 : 164113027X
Total Pages : 373 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 373 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.

Research Trends in Mathematics Teacher Education

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Author :
Publisher : Springer
ISBN 13 : 3319025627
Total Pages : 320 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 320 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.

International Handbook of Mathematics Teacher Education: Volume 3

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Author :
Publisher : BRILL
ISBN 13 : 9004419233
Total Pages : 427 pages
Book Rating : 4.0/5 (44 download)

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Book Synopsis International Handbook of Mathematics Teacher Education: Volume 3 by :

Download or read book International Handbook of Mathematics Teacher Education: Volume 3 written by and published by BRILL. This book was released on 2019-12-09 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of the International Handbook of Mathematics Teacher Education focuses on teachers, teacher educators, researchers, and others who work to provide effective learning opportunities for teachers, with emphasis on describing and analysing their engagement in mathematics teacher education collaborations and contexts from various perspectives.

Re-Imagining Transformative Leadership in Teacher Education

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Author :
Publisher : IAP
ISBN 13 : 1648024556
Total Pages : 263 pages
Book Rating : 4.6/5 (48 download)

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Book Synopsis Re-Imagining Transformative Leadership in Teacher Education by : Ann E. Lopez

Download or read book Re-Imagining Transformative Leadership in Teacher Education written by Ann E. Lopez and published by IAP. This book was released on 2021-05-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third and final book in the series Transformative Pedagogies in Teacher Education. Like the first two books in the series it is geared towards practitioners in the field of teacher education. This third book focuses on transformative leadership in teacher education. In other words, the kind of leadership and practices that will be important and necessary to bring about the kind of changes that both teachers and students seek to improve educational outcomes for all students, but in particular Black, Indigenous and racialized students who have been traditionally underserved by the education system. Teacher leadership plays an important role in transformative educational change that challenges all forms of oppression and white supremacy. This book features chapters by a collection of scholars, teacher educators, researchers, teacher advocates and practitioners drawing on their research and experiences to explore critical issues in teacher education. The book will be useful to teacher educators working with teacher candidates in different contexts, experienced teachers and school leaders. Given demographic shifts and the need for educators to respond to growing diversity in schools, educators will find valuable strategies in Transformative Pedagogies in Teacher Education: Re-Imagining Transformative Leadership in Teacher Education they can employ in their own practice. In addition to valuable strategies, authors explore different approaches and perspectives critical in these changing and challenging times. Critical notions of education are posited from different perspectives and contexts. This book will be useful for teacher education programs, principal preparation programs, in-service teachers, school boards and districts engaging in ongoing professional development of teachers and school leaders.

Problem Solving in Mathematics Instruction and Teacher Professional Development

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Author :
Publisher : Springer Nature
ISBN 13 : 3030292150
Total Pages : 418 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Problem Solving in Mathematics Instruction and Teacher Professional Development by : Patricio Felmer

Download or read book Problem Solving in Mathematics Instruction and Teacher Professional Development written by Patricio Felmer and published by Springer Nature. This book was released on 2019-11-22 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the role of teachers in problem-solving classrooms and their professional development, moving onto—secondly—the role of students when solving problems, with particular consideration of factors like group work, discussion, role of students in discussions and the effect of students’ engagement on their self-perception and their view of mathematics. Finally, the book considers the question of problem solving in mathematics instruction as it overlaps with problem design, problem-solving situations, and actual classroom implementation. The volume brings together diverse contributors from a variety of countries and with wide and varied experiences, combining the voices of leading and developing researchers. The book will be of interest to any reader keeping on the frontiers of research in problem solving, more specifically researchers and graduate students in mathematics education, researchers in problem solving, as well as teachers and practitioners.