Beyond Formulas In Mathematics And Teaching
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Beyond Formulas In Mathematics And Teaching
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Author : Daniel Chazan
language : en
Publisher: Teachers College Press
Release Date : 2000-01-01
Beyond Formulas In Mathematics And Teaching written by Daniel Chazan and has been published by Teachers College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-01 with Education categories.
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
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Author : Daniel Chazan
language : en
Publisher:
Release Date : 2000
Beyond Formulas In Mathematics And Teaching written by Daniel Chazan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Algebra categories.
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
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Author : Richard A. Lesh
language : en
Publisher: Routledge
Release Date : 2003-05-01
Beyond Constructivism written by Richard A. Lesh and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-01 with Education categories.
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.
Teaching Mathematics In Grades 6 12
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Author : Randall E. Groth
language : en
Publisher: SAGE Publications
Release Date : 2012-08-10
Teaching Mathematics In Grades 6 12 written by Randall E. Groth and has been published by SAGE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-10 with Education categories.
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.
Mathematics As The Science Of Patterns
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Author : Patrick M. Jenlink
language : en
Publisher: IAP
Release Date : 2022-02-01
Mathematics As The Science Of Patterns written by Patrick M. Jenlink and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-01 with Education categories.
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.
Learning Through Teaching Mathematics
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Author : Roza Leikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-10
Learning Through Teaching Mathematics written by Roza Leikin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-10 with Science categories.
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.
Teaching Mathematical Reasoning In Secondary School Classrooms
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Author : Karin Brodie
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-08
Teaching Mathematical Reasoning In Secondary School Classrooms written by Karin Brodie and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-08 with Education categories.
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.
Theorizing Teaching
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Author : Anna-Katharina Praetorius
language : en
Publisher: Springer Nature
Release Date : 2023-03-11
Theorizing Teaching written by Anna-Katharina Praetorius and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-11 with Education categories.
This open access book seeks to create a forum for discussing key questions regarding theories on teaching: Which theories of teaching do we have? What are their attributes? What do they contain? How are they generated? How context-sensitive and content-specific do they need to be? Is it possible or even desirable to develop a comprehensive theory of teaching? The book identifies areas of convergence and divergence among the answers to these questions by prominent international scholars in research on teaching. Initiating exchanges among the authors, it then evaluates whether consensus can be reached on the areas of divergence. The book concludes by discussing lessons learned from this endeavor and outlines steps that need to be taken for advancing future work on theorizing teaching. As such, the book is aimed at readers interested in an overview of the theorizing of teaching and key open questions that, if addressed, help to move the field forward.
Mathematics Beyond The Classroom
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Author : Rose Marie Walker M Ed
language : en
Publisher: Independently Published
Release Date : 2019-07-18
Mathematics Beyond The Classroom written by Rose Marie Walker M Ed and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with categories.
Mathematics Beyond the Classroom gives you the power to transform your child's Mathematical experiences. It provides quick and easy ways to do various calculations and ensures that students understand difficult concepts by providing the reasoning behind several formulas. In addition, we have eliminated some of the pain associated with learning the timetable.. Mathematics Beyond the Classroom is user-friendly and the explanations provided will help students to successfully prepare for any internal or external examinations. Get ready to have highly motivated children who, as they engage in these calculations, will develop an appreciation for the subject. Consequently, the information provided can be used to teach or reinforce topics. This Mathematics book is appropriate and fun for students at any level but it is ideal for Mathematics program that focus on Critical Thinking and getting children to think "out of the box.
The Learning And Teaching Of Geometry In Secondary Schools
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Author : Pat Herbst
language : en
Publisher: Taylor & Francis
Release Date : 2017-03-16
The Learning And Teaching Of Geometry In Secondary Schools written by Pat Herbst and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-16 with Education categories.
IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction. Areas covered include: teaching and learning secondary geometry through history; the representations of geometric figures; students’ cognition in geometry; teacher knowledge, practice and, beliefs; teaching strategies, instructional improvement, and classroom interventions; research designs and problems for secondary geometry. Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.