Download or read book Reconceptualizing the Relationship Between Teaching Mathematics and Learning to Teach Mathematics written by Natasha Makeba Murray and published by . This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematics for Equity written by Na’ilah Suad Nasir and published by Teachers College Press. This book was released on 2014-12-04 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, nationally renowned scholars join classroom teachers to share equity-oriented approaches that have been successful with urban high school mathematics students. Compiling for the first time major research findings and practitioner experiences from Railside High School, the volume describes the evolution of a fundamentally different conception of learners and teaching. The chapters bring together research and reflection on teacher collaboration and professional community, student outcomes and mathematics classroom culture, reform curricula and pedagogy, and ongoing teacher development. Mathematics for Equity will be invaluable reading for teachers, schools, and districts interested in maintaining a focus on equity and improving student learning while making sense of the new demands of the Common Core State Standards. Book Features: Core principles of an equity-centered mathematics program. Examples of how to focus and organize the collaborative work of a math department to develop a shared pedagogy. Student experiences with an equity pedagogy that focuses on building perseverance, flexibility in thinking, and deep conceptual understanding. Connections between reconceptualizing learners and teaching, and achieving deep mathematics learning and equitable outcomes. Contributors include: Jo Boaler, Ilana Seidel Horn, Judith Warren Little, and Rachel Lotan. “Mathematics for Equity provides a kaleidoscopic view, in the voices of teachers, researchers, and students themselves, of one of the nation’s most ambitious and successful attempts at teaching mathematics for equity. It shows what it takes to create a climate that supports students and teachers in engaging in meaningful mathematical activity—and, alas, how vulnerable such environments are to the wrong kinds of ‘accountability.’ Read it and learn.” —Alan H. Schoenfeld, University of California at Berkeley “Want to fix what's wrong with mathematics instruction in your school? Read this book with your colleagues and do what it inspires you to do. Written by the brave teachers and former students who did it, as well as researchers.” —Phil Daro, writing team, Common Core Standards, Strategic Education Research Partnership
Download or read book Reconceptualizing Mathematics written by Judith Sowder and published by W. H. Freeman. This book was released on 2009-12-25 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is today a greater awareness that elementary mathematics is rich in important ideas and that its instruction requires far more than simply knowing the “math facts” and a handful of algorithms. Mathematics courses for teachers must reflect the intellectual depth and challenge of the elementary school curriculum. The Conference Board of Mathematical Sciences (CBMS) recommends that the preparation of mathematics teachers include courses that develop a “deep understanding of the mathematics they teach,” that are designed to “develop careful reasoning and ‘common sense’ in analyzing conceptual relationships, . . . that develop the habits of mind of a mathematical thinker and that demonstrate flexible, interactive styles of teaching” (CBMS, 2000, pp. 7-8). Judy Sowder, Larry Sowder, and Susan Nickerson recognize and accept the challenge of presenting mathematics to teachers in a manner that addresses these recommendations. In doing so they provide instruction that will lead teachers of mathematics to reconceptualize the mathematics they often think they already know, thus allowing them to develop a deeper understanding of the mathematics they will teach. The authors believe that teachers must know mathematics differently than most people do. Teachers need to know the mathematics they teach in a way that allows them to hold conversations about mathematical ideas and mathematical thinking with their students. A persistent pursuit of explanation is a hallmark of a classroom in which learning is taking place. A common axiom is that teachers teach the way they were taught. Prospective teachers are unlikely to demonstrate flexible, interactive styles of teaching unless they have experienced mathematics taught this way. Instructors of the Reconceptualizing Mathematics courses, however, may not have experienced such instruction themselves. Thus the authors provide many forms of instructional assistance to help instructors better understand the mathematics their prospective teachers need to know, to begin to model teaching strategies that these prospective teachers will be expected to use in their own classrooms, and to assist them in many ways throughout the course.
Download or read book Multiple Perspectives on Mathematics Teaching and Learning written by Jo Boaler and published by Bloomsbury Publishing USA. This book was released on 2000-07-30 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Perspectives on Mathematics Teaching and Learning offers a collection of chapters that take a new look at mathematics education. Leading authors, such as Deborah Ball, Paul Cobb, Jim Greeno, Stephen Lerman, and Michael Apple, draw from a range of perspectives in their analyses of mathematics teaching and learning. They address such practical problems as: the design of teaching and research that acknowledges the social nature of learning, maximizing the impact of teacher education programs, increasing the learning opportunities of students working in groups, and ameliorating the impact of male domination in mixed classrooms. These practical insights are combined with important advances in theory. Several of the authors address the nature of learning and teaching, including the ways in which theories and practices of mathematics education recognize learning as simultaneously social and individual. The issues addressed include teaching practices, equity, language, assessment, group work and the broader political context of mathematics reform. The contributors variously employ sociological, anthropological, psychological, sociocultural, political, and mathematical perspectives to produce powerful analyses of mathematics teaching and learning.
Download or read book Mathematical Relationships in Education written by Laura Black and published by Routledge. This book was released on 2011-01-13 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: While demand for the mathematically literate citizen increases, many learners continue to reject mathematics and experience it as excluding and exclusive, even when they succeed at it. In exploring this phenomenon, this volume examines the ways in which learners form particular relationships with mathematics in the context of formal schooling.
Download or read book Reconceptualizing Mathematics Education written by Melinda Ann Smith and published by . This book was released on 2004 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Learning to Improve written by Anthony S. Bryk and published by Harvard Education Press. This book was released on 2015-03-01 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a field, education has largely failed to learn from experience. Time after time, promising education reforms fall short of their goals and are abandoned as other promising ideas take their place. In Learning to Improve, the authors argue for a new approach. Rather than “implementing fast and learning slow,” they believe educators should adopt a more rigorous approach to improvement that allows the field to “learn fast to implement well.” Using ideas borrowed from improvement science, the authors show how a process of disciplined inquiry can be combined with the use of networks to identify, adapt, and successfully scale up promising interventions in education. Organized around six core principles, the book shows how “networked improvement communities” can bring together researchers and practitioners to accelerate learning in key areas of education. Examples include efforts to address the high rates of failure among students in community college remedial math courses and strategies for improving feedback to novice teachers. Learning to Improve offers a new paradigm for research and development in education that promises to be a powerful driver of improvement for the nation’s schools and colleges.
Download or read book Learning Through Teaching Mathematics written by Roza Leikin and published by Springer Science & Business Media. This book was released on 2010-04-10 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Loose leaf Version for Reconceptualizing Mathematics written by Judith Sowder and published by Macmillan Higher Education. This book was released on 2023-03-03 with total page 4164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn by doing with active resources, discussions, and support in Reconceptualizing Mathematics and Achieve! Student-centered lessons model the teaching that will eventually be expected of you as you gain valuable hands-on experience with technology, problem solving, and quantitative reasoning.
Download or read book The Construction of New Mathematical Knowledge in Classroom Interaction written by Heinz Steinbring and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is generally considered as the only science where knowledge is uni form, universal, and free from contradictions. „Mathematics is a social product - a 'net of norms', as Wittgenstein writes. In contrast to other institutions - traffic rules, legal systems or table manners -, which are often internally contradictory and are hardly ever unrestrictedly accepted, mathematics is distinguished by coherence and consensus. Although mathematics is presumably the discipline, which is the most differentiated internally, the corpus of mathematical knowledge constitutes a coher ent whole. The consistency of mathematics cannot be proved, yet, so far, no contra dictions were found that would question the uniformity of mathematics" (Heintz, 2000, p. 11). The coherence of mathematical knowledge is closely related to the kind of pro fessional communication that research mathematicians hold about mathematical knowledge. In an extensive study, Bettina Heintz (Heintz 2000) proposed that the historical development of formal mathematical proof was, in fact, a means of estab lishing a communicable „code of conduct" which helped mathematicians make themselves understood in relation to the truth of mathematical statements in a co ordinated and unequivocal way.
Download or read book Teaching Mathematics written by Brent Davis and published by Routledge. This book was released on 2013-02-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an approach to the teaching of mathematics that departs radically from conventional prescription-oriented and management-based methods. It brings together recent developments in such diverse fields as continental and pragmatist philosophy, enactivist thought, critical discourses, cognitive theory, evolution, ecology, and mathematics, and challenges the assumptions that permeate much of mathematics teaching. The discussion focuses on the language used to frame the role of the teacher and is developed around the commonsense distinctions drawn between thought and action, subject and object, individual and collective, fact and fiction, teacher and student, and classroom tasks and real life. The discussion also addresses the question of how mathematics teaching can be reformed to better suit current academic and social climates. Making use of the theoretical framework of enactivism, the book explores the subject through an account of a middle school teacher's appreciation and understanding of her role. Teaching mathematics, as both the report of this teacher's experience and the discussion make clear, demands an embracing of ambiguity, uncertainty, complexity, and moral responsibility. Courses for Adoption Education: Mathematics for Elementary Teachers, Methods for Teaching Elementary Schools, Methods for Teaching Secondary Schools, Curriculum Studies, Critical Pedagogy Special Features *Elucidates the importance and relationship between theory and practice. Employs reflective teaching techniques to focus students on their own learning, knowledge, and understanding of mathematics.Details a collaborative venture that traces the development of new thinking and insights about math teaching and learning. *A fine blending of theory with practice.
Download or read book Mathematics as the Science of Patterns written by Patrick M. Jenlink and published by IAP. This book was released on 2022-02-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Democracy and Mathematics Education written by Kurt Stemhagen and published by Routledge. This book was released on 2021-05-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Democracy and Mathematics Education, Kurt Stemhagen and Catherine Henney develop a way of thinking about the nature and purposes of math that is inclusive, participatory, and thoroughly human. They use these ideas to create a school mathematics experience that can enhance students’ math abilities and democratic potential. They locate mathematics’ origins in human activity and highlight the rich but often overlooked links between mathematical activity and democratic, social practices. Democratic mathematics education foregrounds student inquiry and brings to light the moral dimensions of a discipline that has both remarkable utility and inevitable limitations. For math educators, the book’s humanities approach helps to see the subject anew. For philosophers, it provides an important real world context for wrestling with perennial and timely questions, engaging democratic and evolutionary theory to transform school math. This alternative approach to mathematics and mathematics education provides a guide for how to use math to make democracy a larger part of school and wider social life. 2021 Winner of the AESA Critics’ Choice Book Award.
Download or read book The Language of Mathematics written by Patrick M. Jenlink and published by Rowman & Littlefield. This book was released on 2020-02-04 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Amongst Mathematicians written by Elena Nardi and published by Springer Science & Business Media. This book was released on 2008 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique perspective on ways in which mathematicians: perceive their students' learning; teach; reflect on their teaching practice. Elena Nardi achieves this by employing two fictional, yet entirely data-grounded, characters to create a conversation on these important issues. The construction of these characters is based on large bodies of data including intense focused group interviews with mathematicians and extensive analyses of students' written work, collected and analyzed over a substantial period.
Download or read book Developing Mathematical Thinking written by Jonathan D. Katz and published by Rowman & Littlefield. This book was released on 2014-07-07 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.
Download or read book Embracing Mathematics written by Peter Appelbaum and published by Routledge. This book was released on 2008-06-30 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This alternative textbook for courses on teaching mathematics asks teachers and prospective teachers to reflect on their relationships with mathematics and how these relationships influence their teaching and the experiences of their students. Applicable to all levels of schooling, the book covers basic topics such as planning and assessment, classroom management, and organization of classroom experiences; it also introduces some novel approaches to teaching mathematics, such as psychoanalytic perspectives and post-modern conceptions of curriculum. Traditional methods-of-teaching issues are recast in a new discourse, provoking new ideas for making mathematics education meaningful to teachers as well as their students. Co-authored by a professor and coordinator of mathematics education programs, with illustrative contributions from practicing elementary, middle, and high school mathematics teachers, this book is a unique collaboration across all pre-college grades, making it ideal for teacher discussion groups at any level. Embracing Mathematics: integrates pedagogy and content exploration in ways that are unique in mathematics education features textboxes with reflection questions and suggested explorations that can be easily utilized as homework for a course or as discussion opportunities for teacher reading groups offers examples of teachers’ action research projects that grew out of their interactions with the main chapters in the book is not narrowly limited to mathematics education but incorporates curriculum studies – an invaluable asset that allows instructors to find more ways to engage students in self-reflexive acts of teaching Embracing Mathematics is intended as a method text for undergraduate and master’s-level mathematics education courses and more specialized graduate courses on mathematics education, and as a resource for teacher discussion groups.
