Elementary Mathematics Pedagogical Content Knowledge

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Elementary Mathematics Pedagogical Content Knowledge

James E. Schwartz
Elementary Mathematics Pedagogical Content Knowledge Book PDF

Author : James E. Schwartz
Publisher : Allyn & Bacon
Page : 340 pages
File Size : 52,5 Mb
Release : 2008
Category : Education
ISBN : UVA:X030261052

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Elementary Mathematics Pedagogical Content Knowledge by James E. Schwartz Pdf

Schwartz Powerful Ideas in Elementary Mathematics: Pedagogical Content Knowledge for Teachers, 1/e ISBN: 0205493750 "This book would be a great tool for helping [today's future elementary teachers] acquire a 'gut level' understanding of mathematics concepts." - Hester Lewellen, Baldwin-Wallace College, OH "The writing in this text is very clear and would easily be understood by the intended audience. The real-world examples put the various math concepts into a context that is easily understood. The vignettes at the beginning of each chapter are interesting and they get the reader to begin thinking about the math concepts that will follow. Each of the chapters seem to build on one another and the author often refers back to activities and concepts from previous chapters which is meaningful to the reader because it lets the reader know that the information they are learning builds their conceptual understanding of other mathematical concepts. " - Melany L. Rish, University of South Carolina, Aiken Organized around five key concepts or "powerful ideas" in mathematics, this text presents elementary mathematics content in a concise and nonthreatening manner for teachers. Designed to sharpen teachers' mathematics pedagogical content knowledge, the friendly writing style and vignettes relate math concepts to "real life" situations so that they may better present the content to their students. The five "powerful ideas" (composition, decomposition, relationships, representation, and context) provide an organizing framework and highlight the interconnections between mathematics topics. In addition, the text thoroughly integrates discussion of the five NCTM process strands. Features: Icons highlighting the NCTM process standards appear throughout the book to indicate where the text relates to each of these. Practice exercises and activities and their explanations reinforce math concepts presented in the text and provide an opportunity for reflection and practice. Concise, conversational chapters and opening vignettes present math contents simply enough for even the most math-anxious pre-service teachers.

The Language of Mathematics

Patrick M. Jenlink
The Language of Mathematics Book PDF

Author : Patrick M. Jenlink
Publisher : Rowman & Littlefield
Page : 221 pages
File Size : 42,9 Mb
Release : 2020-02-04
Category : Education
ISBN : 9781475854817

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The Language of Mathematics by Patrick M. Jenlink Pdf

The Language of Mathematics: How the Teacher’s Knowledge of Mathematics Affects Instruction introduces the reader to a collection of thoughtful works by authors that represent current thinking about mathematics teacher preparation. The book provides the reader with current and relevant knowledge concerning preparation of mathematics teachers. The complexity of teaching mathematics is undeniable and all too often ignored in the preparation of teachers with substantive mathematical content knowledge and mathematical teaching knowledge. That said, this book has a focus on the substantive knowledge and the relevant pedagogy required for preparing teachings to enter classrooms to teach mathematics in K-12 school settings. Each chapter focuses on the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. Chapter One opens the book with a focus on the language and knowledge of mathematics teaching. The authors of Chapters Two-Nine present field-based research that examines the complexities of content and pedagogical knowledge as well as knowledge for teaching. Each chapter offers the reader an examination of mathematics teacher preparation and practice based on formal research that provides the reader with insight into how the research study was conducted as well as providing the findings and conclusions drawn with respect to mathematics teacher preparation and practice. Finally, Chapter 10 presents an epilogue that focuses on the future of mathematics teacher preparation.

Beyond Classical Pedagogy

Terry Wood,Barbara Scott Nelson,Janet E. Warfield
Beyond Classical Pedagogy Book PDF

Author : Terry Wood,Barbara Scott Nelson,Janet E. Warfield
Publisher : Routledge
Page : 324 pages
File Size : 55,9 Mb
Release : 2014-04-04
Category : Education
ISBN : 9781135658724

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Beyond Classical Pedagogy by Terry Wood,Barbara Scott Nelson,Janet E. Warfield Pdf

The emergence of the National Council of Teachers of Mathematics Standards in 1989 sparked a sea change in thinking about the nature and quality of mathematics instruction in U.S. schools. Much is known about transmission forms of mathematics teaching and the influence of this teaching on students' learning, but there is still little knowledge about the alternative forms of instruction that have evolved from the recent widespread efforts to reform mathematics education. Beyond Classical Pedagogy: Teaching Elementary School Mathematics reports on the current state of knowledge about these new instructional practices, which differ in significant ways from the traditional pedagogy that has permeated mathematics education in the past. This book provides a research-based view of the nature of facilitative teaching in its relatively mature form, along with opposing views and critique of this form of pedagogy. The focus is on elementary school mathematics classrooms, where the majority of the reform-based efforts have occurred, and on the micro level of teaching (classroom interaction) as a source for revealing the complexity involved in teaching, teachers' learning, and the impact of both on children's learning. The work in elementary mathematics teaching is situated in the larger context of research on teaching. Research and insights from three disciplinary perspectives are presented: the psychological perspective centers on facilitative teaching as a process of teachers' learning; the mathematical perspective focuses on the nature of the mathematical knowledge teachers need in order to engage in this form of teaching; the sociological perspective attends to the interactive process of meaning construction as teachers and students create intellectual communities in their classrooms. The multidisciplinary perspectives presented provide the editors with the necessary triangulation to provide confirming evidence and rich detail about the nature of facilitative teaching. Audiences for this book include scholars in mathematics education and teacher education, teacher educators, staff developers, and classroom teachers. It is also appropriate as a text for graduate courses in mathematics education, teacher education, elementary mathematics teaching methods, and methods of research in mathematics education.

Mathematics Teaching and Learning

Rina Kim,Lillie R. Albert
Mathematics Teaching and Learning Book PDF

Author : Rina Kim,Lillie R. Albert
Publisher : Springer
Page : 160 pages
File Size : 49,6 Mb
Release : 2015-03-24
Category : Education
ISBN : 9783319135427

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Mathematics Teaching and Learning by Rina Kim,Lillie R. Albert Pdf

The purpose of this research is to identify the categories of South Korean elementary teachers’ knowledge for teaching mathematics. Emerging from the data collected and the subsequent analysis are five categories of South Korean elementary teachers’ knowledge for teaching mathematics: Mathematics Curriculum Knowledge, Mathematics Learner Knowledge, Fundamental Mathematics Conceptual Knowledge, Mathematics Pedagogical Content Knowledge, and Mathematics Pedagogical Procedural Knowledge. The first three categories of knowledge play a significant role in mathematics instruction as an integrated form within Mathematics Pedagogical Content Knowledge. This study also demonstrated that Mathematics Pedagogical Procedural Knowledge might play a pivotal role in constructing Mathematics Pedagogical Content Knowledge. These findings are connected to results from relevant studies in terms of the significant role of teachers’ knowledge in mathematics instruction.

Knowing and Teaching Elementary Mathematics

Liping Ma
Knowing and Teaching Elementary Mathematics Book PDF

Author : Liping Ma
Publisher : Routledge
Page : 290 pages
File Size : 43,6 Mb
Release : 2010-03-26
Category : Education
ISBN : 9781135149499

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Knowing and Teaching Elementary Mathematics by Liping Ma Pdf

Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

Research Advances in the Mathematical Education of Pre-service Elementary Teachers

Gabriel J. Stylianides,Keiko Hino
Research Advances in the Mathematical Education of Pre service Elementary Teachers Book PDF

Author : Gabriel J. Stylianides,Keiko Hino
Publisher : Springer
Page : 304 pages
File Size : 47,6 Mb
Release : 2017-11-16
Category : Education
ISBN : 9783319683423

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Research Advances in the Mathematical Education of Pre-service Elementary Teachers by Gabriel J. Stylianides,Keiko Hino Pdf

This book examines new trends and developments in research related to the mathematical education of pre-service elementary teachers, and explores the implications of these research advances for theory and practice in teacher education. The book is organized around the following four overarching themes: pre-service teachers’ mathematics content and mathematics-specific pedagogical preparation; professional growth through activities and assessment tools used in mathematics teacher preparation programs; pre-service mathematics teachers’ knowledge and beliefs; and perspectives on noticing in the preparation of elementary mathematics teachers. Including contributions from researchers working in 11 different countries, the book offers a forum for discussing and debating the state of the art regarding the mathematical preparation of pre-service elementary teachers. By presenting and discussing the findings of research conducted in different countries, the book offers also opportunities to readers to learn about varying teacher education practices around the world, such as: innovative practices in advancing or assessing teachers’ knowledge and beliefs, similarities and differences in the formal mathematics education of teachers, types of and routes in teacher education, and factors that can influence similarities or differences.

Diversifying Mathematics Teaching: Advanced Educational Content And Methods For Prospective Elementary Teachers

Abramovich Sergei
Diversifying Mathematics Teaching Advanced Educational Content And Methods For Prospective Elementary Teachers Book PDF

Author : Abramovich Sergei
Publisher : World Scientific
Page : 284 pages
File Size : 48,7 Mb
Release : 2017-02-24
Category : Education
ISBN : 9789813206892

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Diversifying Mathematics Teaching: Advanced Educational Content And Methods For Prospective Elementary Teachers by Abramovich Sergei Pdf

The book is written to enhance the preparation of elementary teacher candidates by offering teaching ideas conducive to the development of deep understanding of concepts fundamental to the mathematics curriculum they are to teach. It intends to show how the diversity of teaching methods stems from the knowledge of mathematics content and how the appreciation of this diversity opens a window to the teaching of extended content. The book includes material that the author would have shared with teacher candidates should there have been more instructional time than a 3 credit hour master's level course, "Elementary Mathematics: Content and Methods", provides. Thus the book can supplement a basic textbook for such a course by extending content and diversifying methods. Also, the book can support graduate level mathematics education programs which have problem-solving seminars/courses in their curriculum. The book is well-informed with (available in English) the mathematical standards and recommendations for teachers from Australia, Canada, Chile, England, Japan, Korea, Singapore, and the United States.

Elementary School Mathematics for Parents and Teachers

Raz Kupferman
Elementary School Mathematics for Parents and Teachers Book PDF

Author : Raz Kupferman
Publisher : World Scientific Publishing Company
Page : 304 pages
File Size : 52,9 Mb
Release : 2017-03-17
Category : Electronic
ISBN : 9789813108950

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Elementary School Mathematics for Parents and Teachers by Raz Kupferman Pdf

This book covers the elementary school mathematics curriculum common in most parts of the world. Its aim is to serve educators (teachers and parents) as a guide for teaching mathematics at elementary school level. The book focuses both on content knowledge and on pedagogical content knowledge. It bridges the gap between fundamental mathematical principles and good teaching practices. It also offers the reader a glimpse on how mathematicians perceive elementary mathematics and presents ideas for specific mathematical activities. Volume 2 focuses on content taught in the higher grades of elementary school. It covers the following topics: multiplication and division of multi-digit numbers, divisibility and primality, divisibility signs, sequences, fractions and their representations, and fraction arithmetic. Request Inspection Copy

Mathematics as the Science of Patterns

Patrick M. Jenlink
Mathematics as the Science of Patterns Book PDF

Author : Patrick M. Jenlink
Publisher : IAP
Page : 265 pages
File Size : 51,9 Mb
Release : 2022-02-01
Category : Education
ISBN : 9781648027468

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Mathematics as the Science of Patterns by Patrick M. Jenlink Pdf

Mathematics as the Science of Patterns: Making the Invisible Visible to Students through Teaching introduces the reader to a collection of thoughtful, research-based works by authors that represent current thinking about mathematics, mathematics education, and the preparation of mathematics teachers. Each chapter focuses on mathematics teaching and the preparation of teachers who will enter classrooms to instruct the next generation of students in mathematics. The value of patterns to the teaching and learning of mathematics is well understood, both in terms of research and application. When we involve or appeal to pattern in teaching mathematics, it is usually because we are trying to help students to extract greater meaning, or enjoyment, or both, from the experience of learning environments within which they are occupied, and perhaps also to facilitate remembering. As a general skill it is thought that the ability to discern a pattern is a precursor to the ability to generalize and abstract, a skill essential in the early years of learning and beyond. Research indicates that the larger problem in teaching mathematics does not lie primarily with students; rather it is with the teachers themselves. In order to make changes for students there first needs to be a process of change for teachers. Understanding the place of patterns in learning mathematics is a predicate to understanding how to teach mathematics and how to use pedagogical reasoning necessary in teaching mathematics. Importantly, the lack of distinction created by the pedagogical use of patterns is not immediately problematic to the student or the teacher. The deep-seated cognitive patterns that both teachers and students bring to the classroom require change. Chapter 1 opens the book with a focus on mathematics as the science of patterns and the importance of patterns in mathematical problem solving, providing the reader with an introduction. The authors of Chapter 2 revisit the work of Po lya and the development and implementation of problem solving in mathematics. In Chapter 3, the authors present an argument for core pedagogical content knowledge in mathematics teacher preparation. The authors of Chapter 4 focus on preservice teachers’ patterns of conception as related to understanding number and operation. In Chapter 5 the authors examine the role of visual representation in exploring proportional reasoning, denoting the importance of helping learners make their thinking visible. The authors of Chapter 6 examine patterns and relationships, and the importance of each in assisting students’ learning and development in mathematical understanding. The authors of Chapter 7 examine the use of worked examples as a scalable practice, with emphasis on the importance of worked examples in teaching fraction magnitude and computation is discussed. In Chapter 8, the authors expand on the zone of proximal development to investigate the potential of Zankov’s Lesson in terms of students analyzing numerical equalities. The authors of Chapter 9 focus on high leverage mathematical practices in elementary pre-service teacher preparation, drawing into specific relief the APEX cycle to develop deep thinking. In Chapter 10, the author focuses on number talks and the engagement of students in mathematical reasoning, which provides opportunities for students to be sensemakers of mathematics. Chapter 11 presents an epilogue, focusing on the importance of recognizing the special nature of mathematics knowledge for teaching.

Examining Pedagogical Content Knowledge

Julie Gess-Newsome,Norman G. Lederman
Examining Pedagogical Content Knowledge Book PDF

Author : Julie Gess-Newsome,Norman G. Lederman
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 48,8 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306472176

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Examining Pedagogical Content Knowledge by Julie Gess-Newsome,Norman G. Lederman Pdf

This ambitious text is the first of its kind to summarize the theory, research, and practice related to pedagogical content knowledge. The audience is provided with a functional understanding of the basic tenets of the construct as well as its applications to research on science teacher education and the development of science teacher education programs.

Teachers' Professional Development and the Elementary Mathematics Classroom

Sophia Cohen
Teachers Professional Development and the Elementary Mathematics Classroom Book PDF

Author : Sophia Cohen
Publisher : Routledge
Page : 208 pages
File Size : 50,5 Mb
Release : 2004-07-13
Category : Education
ISBN : 9781135632267

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Teachers' Professional Development and the Elementary Mathematics Classroom by Sophia Cohen Pdf

This book illustrates the experiences of elementary school teachers across one year's time as they participated in a teacher development seminar focused on mathematics, and as a result changed their beliefs, their knowledge, and their practices. It explores these experiences as a means of understanding the learning that takes a teacher from a more traditional teaching practice to one that is focused on the ideas and understandings that students and teachers have of the subject matter. The work emerges from and reports on a unique data set from a two-year study of teacher learning that was funded by the Spencer and MacArthur foundations. The teachers, whose work is at the center of this study, were participants in the Developing Mathematical Ideas seminar (DMI), a mathematics teacher development seminar for elementary school teachers. This seminar is one example of intensive, domain-specific professional development. In this seminar teachers study elementary mathematics content to deepen their own understanding of it, they study the development among children of the ideas central to elementary mathematics, and they experience a teaching and learning environment consistent with the pedagogy envisioned by the National Council for Teachers of Mathematics' Principles and Standards for School Mathematics. The seminar is a nationally available teacher development curriculum, thus interested educators can gain access to the resources necessary to offer similar seminars in their own communities. Teachers' Professional Development and the Elementary Mathematics Classroom: Bringing Understandings to Light will be widely interesting to a broad audience, including mathematics teacher educators, teacher education researchers, policymakers, and classroom teachers. It will serve well as a text in a range of graduate courses dealing with teacher cognition/knowledge for teaching, mathematics methods, psychology of learning, and pedagogical theory.

The Handbook of Mathematics Teacher Education: Volume 1

Anonim
The Handbook of Mathematics Teacher Education Volume 1 Book PDF

Author : Anonim
Publisher : BRILL
Page : 330 pages
File Size : 55,5 Mb
Release : 2008-01-01
Category : Education
ISBN : 9789087905439

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The Handbook of Mathematics Teacher Education: Volume 1 by Anonim Pdf

Knowledge and Beliefs in Mathematics Teaching and Teaching Development addresses the “what” of mathematics teacher education, meaning knowledge for mathematics teaching and teaching development and consideration of associated beliefs.

Elementary Mathematics Curriculum Materials

Janine T. Remillard,Ok-Kyeong Kim
Elementary Mathematics Curriculum Materials Book PDF

Author : Janine T. Remillard,Ok-Kyeong Kim
Publisher : Springer Nature
Page : 329 pages
File Size : 49,8 Mb
Release : 2020-03-16
Category : Education
ISBN : 9783030385880

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Elementary Mathematics Curriculum Materials by Janine T. Remillard,Ok-Kyeong Kim Pdf

The book presents comparative analyses of five elementary mathematics curriculum programs used in the U.S. from three different perspectives: the mathematical emphasis, the pedagogical approaches, and how authors communicate with teachers. These perspectives comprise a framework for examining what curriculum materials are comprised of, what is involved in reading and interpreting them, and how curriculum authors can and do support teachers in this process. Although the focus of the analysis is 5 programs used at a particular point in time, this framework extends beyond these specific programs and illuminates the complexity of curriculum materials and their role in teaching in general. Our analysis of the mathematical emphasis considers how the mathematics content is presented in each program, in terms of sequencing, the nature of mathematical tasks (cognitive demand and ongoing practice), and the way representations are used. Our analysis of the pedagogical approach examines explicit and implicit messages about how students should interact with mathematics, one another, the teacher, and the textbook around these mathematical ideas, as well as the role of the teacher. In order to examine how curriculum authors support teachers, we analyze how they communicate with teachers and what they communicate about, including the underlying mathematics, noticing student thinking, and rationale for design elements. The volume includes a chapter on curriculum design decisions based on interviews with curriculum authors.

Mathematics Matters in Education

Yeping Li,W. James Lewis,James J. Madden
Mathematics Matters in Education Book PDF

Author : Yeping Li,W. James Lewis,James J. Madden
Publisher : Springer
Page : 303 pages
File Size : 47,7 Mb
Release : 2017-10-03
Category : Education
ISBN : 9783319614342

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Mathematics Matters in Education by Yeping Li,W. James Lewis,James J. Madden Pdf

This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics taught in the early school grades and has challenged and stimulated mathematicians and mathematics educators to work together to examine this part of the mathematical universe more critically and in imaginative new ways. This volume will help summarize and highlight Howe's contributions to several topic areas in mathematics education, demonstrating the possibility and importance of engaging mathematicians in high-impact research in mathematics education, and showcasing the importance of cross-disciplinary collaboration and exchange.

Cases in Mathematics Teacher Education

Margaret S. Smith,Susan N. Friel
Cases in Mathematics Teacher Education Book PDF

Author : Margaret S. Smith,Susan N. Friel
Publisher : IAP
Page : 156 pages
File Size : 49,5 Mb
Release : 2015-10-01
Category : Mathematics
ISBN : 9781623969486

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Cases in Mathematics Teacher Education by Margaret S. Smith,Susan N. Friel Pdf

(Orginally published in 2008) The goal of AMTE Monograph 4, "Cases in Mathematics Teacher Education: Tools for Developing Knowledge Needed for Teaching", is to provide detailed accounts of case use that will inform the mathematics teacher education community on the range of ways in which cases can be used to foster teacher learning and the capacity to reflect on and learn from teaching. The chapters in this monograph describe the use of cases with preservice and practicing teachers at all levels K - 12, in content and methods courses as well as professional development settings, and focus on developing various aspects of teachers' knowledge base (i.e., content, pedagogy, and students as learners). Hence, Monograph 4 should prove to be a superb resource for mathematics teacher educators.