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Beyond Formulas in Mathematics and Teaching

Author: Daniel Chazan

Publisher: Teachers College Press

Published: 2000-01-01

Total Pages: 222

ISBN-13: 9780807739181

Based on the author’s experience as a researcher and teacher of lower-track students, Beyond Formulas in Mathematics and Teaching illuminates the complex dynamics of the algebra classroom. From within this setting, Daniel Chazan thoughtfully explores topics that concern all dedicated educators, how to really know one’s students, how to find engaging material, and how to inspire meaningful classroom conversations. Throughout, he addresses the predicaments that are central to the lives of teachers who work in standard educational settings. By highlighting teaching dilemmas, Chazan prompts readers to consider what their own responses would be in similar situations. With an eye to ways of restructuring roles and relationships, Beyond Formulas in Mathematics and Teaching is essential reading for educators seeking to enhance their teaching practices and understanding of students who may be estranged from school.

Beyond Formulas in Mathematics and Teaching

Author: Daniel Chazan

Publisher:

Published: 2000

Total Pages: 200

ISBN-13: 9780807770313

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With an eye to ways of restructuring roles and relationships, Beyond Formulas in Mathematics and Teaching is essential reading for educators seeking to enhance their teaching practices and understanding of students who may be estranged from school."--Jacket.

Beyond Constructivism

Author: Richard A. Lesh

Publisher: Routledge

Published: 2003-05-01

Total Pages: 610

ISBN-13: 1317438523

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This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.

Beyond the Quadratic Formula

Author: Ron Irving

Publisher: American Mathematical Soc.

Published: 2020-01-29

Total Pages: 228

ISBN-13: 147045176X

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The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their study forms the heart of this book, as part of the broader theme that a polynomial's coefficients can be used to obtain detailed information on its roots. The book is designed for self-study, with many results presented as exercises and some supplemented by outlines for solution. The intended audience includes in-service and prospective secondary mathematics teachers, high school students eager to go beyond the standard curriculum, undergraduates who desire an in-depth look at a topic they may have unwittingly skipped over, and the mathematically curious who wish to do some work to unlock the mysteries of this beautiful subject.

Teaching Mathematical Reasoning in Secondary School Classrooms

Author: Karin Brodie

Publisher: Springer Science & Business Media

Published: 2009-10-08

Total Pages: 231

ISBN-13: 0387097422

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For too many students, mathematics consists of facts in a vacuum, to be memorized because the instructor says so, and to be forgotten when the course of study is completed. In this all-too-common scenario, young learners often miss the chance to develop skills—specifically, reasoning skills—that can serve them for a lifetime. The elegant pages of Teaching Mathematical Reasoning in Secondary School Classrooms propose a more positive solution by presenting a reasoning- and discussion-based approach to teaching mathematics, emphasizing the connections between ideas, or why math works. The teachers whose work forms the basis of the book create a powerful record of methods, interactions, and decisions (including dealing with challenges and impasses) involving this elusive topic. And because this approach shifts the locus of authority from the instructor to mathematics itself, students gain a system of knowledge that they can apply not only to discrete tasks relating to numbers, but also to the larger world of people and the humanities. A sampling of the topics covered: Whole-class discussion methods for teaching mathematics reasoning. Learning mathematical reasoning through tasks. Teaching mathematics using the five strands. Classroom strategies for promoting mathematical reasoning. Maximizing student contributions in the classroom. Overcoming student resistance to mathematical conversations. Teaching Mathematical Reasoning in Secondary School Classrooms makes a wealth of cutting-edge strategies available to mathematics teachers and teacher educators. This book is an invaluable resource for researchers in mathematics and curriculum reform and of great interest to teacher educators and teachers.

Teaching Mathematics in Grades 6 - 12

Author: Randall E. Groth

Publisher: SAGE Publications

Published: 2012-08-10

Total Pages: 513

ISBN-13: 1452256020

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Teaching Mathematics in Grades 6 - 12 by Randall E. Groth explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows preservice mathematics teachers the value of being a "researcher—constantly experimenting with methods for developing students' mathematical thinking—and connecting this research to practices that enhance students' understanding of the material. Ultimately, preservice teachers will gain a deeper understanding of the types of mathematical knowledge students bring to school, and how students' thinking may develop in response to different teaching strategies.

What Does Understanding Mathematics Mean for Teachers?

Author: Yuichi Handa

Publisher: Taylor & Francis

Published: 2013-05-13

Total Pages: 169

ISBN-13: 1136870539

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This book opens up alternative ways of thinking and talking about ways in which a person can "know" a subject (in this case, mathematics), leading to a reconsideration of what it may mean to be a teacher of that subject. In a number of European languages, a distinction is made in ways of knowing that in the English language is collapsed into the singular word know. In French, for example, to know in the savoir sense is to know things, facts, names, how and why things work, and so on, whereas to know in the connaître sense is to know a person, a place, or even a thing—namely, an other— in such a way that one is familiar with, or in relationship with this other. Primarily through phenomenological reflection with a touch of empirical input, this book fleshes out an image for what a person’s connaître knowing of mathematics might mean, turning to mathematics teachers and teacher educators to help clarify this image.

Learning Through Teaching Mathematics

Author: Roza Leikin

Publisher: Springer Science & Business Media

Published: 2010-04-10

Total Pages: 300

ISBN-13: 9048139902

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The idea of teachers Learning through Teaching (LTT) – when presented to a naïve bystander – appears as an oxymoron. Are we not supposed to learn before we teach? After all, under the usual circumstances, learning is the task for those who are being taught, not of those who teach. However, this book is about the learning of teachers, not the learning of students. It is an ancient wisdom that the best way to “truly learn” something is to teach it to others. Nevertheless, once a teacher has taught a particular topic or concept and, consequently, “truly learned” it, what is left for this teacher to learn? As evident in this book, the experience of teaching presents teachers with an exciting opp- tunity for learning throughout their entire career. This means acquiring a “better” understanding of what is being taught, and, moreover, learning a variety of new things. What these new things may be and how they are learned is addressed in the collection of chapters in this volume. LTT is acknowledged by multiple researchers and mathematics educators. In the rst chapter, Leikin and Zazkis review literature that recognizes this phenomenon and stress that only a small number of studies attend systematically to LTT p- cesses. The authors in this volume purposefully analyze the teaching of mathematics as a source for teachers’ own learning.

Handbook of Research on Teaching

Author: Drew Gitomer

Publisher:

Published: 2016-05-19

Total Pages: 1553

ISBN-13: 0935302484

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The Fifth Edition of the Handbook of Research on Teachingis an essential resource for students and scholars dedicated to the study of teaching and learning. This volume offers a vast array of topics ranging from the history of teaching to technological and literacy issues. In each authoritative chapter, the authors summarize the state of the field while providing conceptual overviews of critical topics related to research on teaching. Each of the volume's 23 chapters is a canonical piece that will serve as a reference tool for the field. The Handbook provides readers with an unaparalleled view of the current state of research on teaching across its multiple facets and related fields.

Handbook of International Research in Mathematics Education

Author: Lyn D. English

Publisher: Routledge

Published: 2010-04-02

Total Pages: 942

ISBN-13: 1135192766

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This book brings together mathematics education research that makes a difference in both theory and practice - research that anticipates problems and needed knowledge before they become impediments to progress.