But Why Does It Work

But Why Does It Work Author Susan Jo Russell
ISBN-10 032508114X
Release 2017
Pages 176
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If you ask students, "Why does that work?" do they know what you're asking and do you know what to listen for in their responses? Do you have images of what mathematical argument looks like in the elementary grades and how to help students learn to engage in this important practice? Do you have so much content to cover that finding time for this kind of work is difficult? But Why Does It Work? offers a simple, efficient teaching model focused on mathematical argument for developing the ability of students to justify their thinking and engage with the reasoning of others. Designed for individuals as well as study groups, this book includes access to classroom-ready instructional sequences, each built on a model supporting students in: noticing relationships across sets of problems, equations, or expressions articulating a claim about what they notice investigating their claim through representations such as manipulatives, diagrams, or story contexts using their representations to demonstrate why a claim must be true or not extending their thinking from one operation to another. Establishing a classroom culture where students gain confidence in their own mathematical voice and learn to value the contributions of their peers is a critical part of this work. The authors tell us, "If the idea underlying a student's reasoning is not made explicit, the opportunity for all students to engage in such thinking is lost." As students become a true community of mathematicians, they heighten each other's understanding by investigating questions, conjectures, and examples together. Enhanced with extensive video showing the instructional sequences in action-along with guiding focus questions and math investigations-But Why Does It Work? is a flexible approach that will help students confidently articulate and defend their reasoning, and share their deep thinking with others.

Proving in the Elementary Mathematics Classroom

Proving in the Elementary Mathematics Classroom Author Andreas J. Stylianides
ISBN-10 9780198723066
Release 2016-07-14
Pages 208
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Although proving is core to mathematics as a sense-making activity, it currently has a marginal place in elementary classrooms internationally. Blending research with practical perspectives, this book addresses what it would take to elevate the place of proving at elementary school. The book uses classroom episodes from two countries to examine different kinds of proving tasks and the proving activity they can generate in the elementary classroom. It examines further the role of teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that arise for teachers as they implement each kind of proving task. In addition to its contribution to research knowledge, the book has important implications for teaching, curricular resources, and teacher education.

Teachers Professional Development and the Elementary Mathematics Classroom

Teachers  Professional Development and the Elementary Mathematics Classroom Author Sophia Cohen
ISBN-10 9781135632267
Release 2004-07-13
Pages 208
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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 Mathematics Enthusiast Issue

The Mathematics Enthusiast Issue Author Bharath Sriraman
ISBN-10 9781681236346
Release 2016-11-01
Pages 134
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The Mathematics Enthusiast (TME) is an eclectic internationally circulated peer reviewed journal which focuses on mathematics content, mathematics education research, innovation, interdisciplinary issues and pedagogy. The journal exists as an independent entity. It is published on a printondemand basis by Information Age Publishing and the electronic version is hosted by the Department of Mathematical Sciences University of Montana. The journal is not affiliated to nor subsidized by any professional organizations but supports PMENA [Psychology of Mathematics Education North America] through special issues on various research topics. Indexing Information: Australian Education Index; EBSCO Products (Academic Search Complete); EDNA; Directory of Open Access Journals (DOAJ); PsycINFO (the APA Index); MathDI/MathEDUC (FiZ Karlsruhe); Journals in Higher Education (JIHE); SCOPUS; Ulrich's Periodicals Directory; Emerging Sources Citation Index (Thompson Reuters)

Best Practices for Elementary Classrooms

Best Practices for Elementary Classrooms Author Randi Stone
ISBN-10 9781632209597
Release 2015-07-28
Pages 264
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There is no better way to learn the craft of teaching than by watching an expert teacher at work. In this sequel to Randi Stone's Best Classroom Practices, nationally recognized, award-winning elementary teachers showcase selected practices from their classroom repertoire to share with their colleagues. Learn what it takes to build a productive, engaged community of learners from some of the nation's best teachers in their own words. This inspirational, one-stop guide covers everything from classroom management to teaching reading, writing, math, science, social studies, music, art, technology, and physical education. You will find: - Detailed, successful teaching strategies with lists of relevant standards and materials needed - Innovative activities, projects, lesson plans, and units of study for every content area - Classroom strategies across the curriculum, including ideas for involving parents and ways to make inclusion work Best Practices for Elementary Classrooms provides a wide array of excellent lessons to choose from, road-tested by your award-winning colleagues.

Elementary Mathematics Is Anything but Elementary Content and Methods From A Developmental Perspective

Elementary Mathematics Is Anything but Elementary  Content and Methods From A Developmental Perspective Author Damon Bahr
ISBN-10 9780618928170
Release 2008-12-19
Pages 544
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Inspiring, empowering, and preparing preservice teachers for today’’s classroom, ELEMENTARY MATHEMATICS IS ANYTHING BUT ELEMENTARY: CONTENT AND METHODS FROM A DEVELOPMENTAL PERSPECTIVE is a comprehensive program that delivers both a content and a methods text. Serving as a professional development guide for both pre-service and in-service teachers, this text’’s integrated coverage helps dissolve the line between content and methods—and consequently bolsters teachers’’ confidence in their delivery of math instruction. A strong emphasis on the National Council of Teachers of Mathematics five core standards provides key information common to most state curricula relative to NCTM standards for pre-K through sixth grade. In addition, text content is based on thorough elementary mathematical scope and sequences that have been shown to be an effective means for guiding the delivery of curriculum and instruction. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Second International Handbook of Mathematics Education

Second International Handbook of Mathematics Education Author Alan Bishop
ISBN-10 9789401002738
Release 2012-02-02
Pages 982
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ALAN 1. BISHOP The first International Handbook on Mathematics Education was published by Kluwer Academic Publishers in 1996. However, most of the writing for that handbook was done in 1995 and generally reflected the main research and development foci prior to 1994. There were four sections, 36 chapters, and some 150 people contributed to the final volume either as author, reviewer, editor, or critical friend. The task was a monumental one, attempting to cover the major research and practice developments in the international field of mathematics education as it appeared to the contributors in 1995. Inevitably there were certain omissions, some developments were only starting to emerge, and some literatures were only sketchy and speculative. However that Handbook has had to be reprinted three times, so it clearly fulfilled a need and I personally hope that it lived up to what I wrote in its Introduction: The Handbook thus attempts not merely to present a description of the international 'state-of-the-field', but also to offer synthetic and reflective overviews on the different directions being taken by the field, on the gaps existing in our present knowledge, on the current problems being faced, and on the future possibilities for development. (Bishop et aI. , 1996) Since that time there has been even more activity in our field, and now seems a good time to take stock again, to reflect on what has happened since 1995, and to create a second Handbook with the same overall goals.

Second International Handbook of Mathematics Education

Second International Handbook of Mathematics Education Author Alan Bishop
ISBN-10 1402010087
Release 2003-06-30
Pages 986
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TheSecond International Handbook of Mathematics Educationis an essential resource for students, researchers, teacher educators and curriculum policy makers in the field of mathematics education. It is a follow-up to the firstHandbook, which laid down the base-line in many areas of the field of mathematics education. The firstHandbookwas published in 1996, covering research done prior to 1994. ThisSecond Handbook: *covers the changes and developments that have occurred in the field since 1994; *has a section focusing on public policy and mathematics education; *is an essential reference to all those who shape educational policy.

The Emergence of Mathematical Meaning

The Emergence of Mathematical Meaning Author Paul Cobb
ISBN-10 9781136486104
Release 2012-12-06
Pages 320
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This book grew out of a five-year collaboration between groups of American and German mathematics educators. The central issue addressed accounting for the messiness and complexity of mathematics learning and teaching as it occurs in classroom situations. The individual chapters are based on the view that psychological and sociological perspectives each tell half of a good story. To unify these concepts requires a combined approach that takes individual students' mathematical activity seriously while simultaneously seeing their activity as necessarily socially situated. Throughout their collaboration, the chapter authors shared a single set of video recordings and transcripts made in an American elementary classroom where instruction was generally compatible with recent reform recommendations. As a consequence, the book is much more than a compendium of loosely related papers. The combined approach taken by the authors draws on interactionism and ethnomethodology. Thus, it constitutes an alternative to Vygotskian and Soviet activity theory approaches. The specific topics discussed in individual chapters include small group collaboration and learning, the teacher's practice and growth, and language, discourse, and argumentation in the mathematics classroom. This collaborative effort is valuable to educators and psychologists interested in situated cognition and the relation between sociocultural processes and individual psychological processes.

Mathematics for Elementary School Teachers A Process Approach

Mathematics for Elementary School Teachers  A Process Approach Author Mark A. Freitag
ISBN-10 9781285528762
Release 2013-01-01
Pages 1104
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Freitag's MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS: A PROCESS APPROACH was developed using the five Content Standards from the NCTM Principles and Standards for School Mathematics, and the Common Core State Standards for Mathematics. Traditionally, books for pre-service elementary teachers have focused on problem solving. However, problem solving is not the only process through which mathematics is learned. It is also learned through mathematical reasoning, communication, representation, and connections. Recent trends in mathematics education now advocate implementing all five processes as a vital part of learning and doing mathematics. Consequently, you need to have concrete experiences with these processes that you will be required to teach. The goal of this book is to treat each of the processes equitably by using an approach in which the five processes serve as the central pedagogical theme. Most of the examples, exercises, and activities are designed to either model the processes or to directly engage you in working with them. As a result, you will not only come to understand the different processes, but also appreciate them as an integral to learning and doing mathematics. If this broader view can be instilled, you are more likely to give your students a more well-rounded and holistic view of mathematics once you enter the classroom. The content of the book is directly related to the mathematics that is taught in grades K - 8. The purpose is not to reteach elementary mathematics. Rather, the intent is to look at the content from a theoretical or generalized point of view, so that you can better understand the concepts and processes behind the mathematics you will teach. In short, the book focuses on the why behind the mathematics in addition to the how. Available with InfoTrac Student Collections http://gocengage.com/infotrac. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Why Do We Educate

Why Do We Educate Author David L. Coulter
ISBN-10 9781444307221
Release 2009-03-23
Pages 200
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This book reflects the editors; concerns that too many public discussions of education are dominated by too few ideas, and is intended to serve as a kind of handbook for those who wish to enter the conversation about education A work of impressive scholarship accessible to the general reader A unique collection of essays written by internationally recognized and emerging thinkers from the field of education and related disciplines Contributors, among others, include Anthony Appiah (Princeton); Seyla Benhabib (Yale); Eamonn Callan (Stanford); Joseph Dunne (St. Patrick’s College, Ireland); Kieran Egan (Simon Fraser); Ursula Franklin (Toronto); Nel Noddings (Stanford); Martha Nussbaum (Chicago) and Diane Ravitch (New York)

The Learning to write Process in Elementary Classrooms

The Learning to write Process in Elementary Classrooms Author Suzanne Bratcher
ISBN-10 9781136606465
Release 2012-07-26
Pages 248
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This text models for teachers how to help children learn and write by establishing comfort with writing, building confidence, and developing competence. Several themes run through the learning-to-write-process presented in this text: * Writing is communication; * Writing is a powerful tool for learning; * How children feel about their writing and themselves as writers affects how they learn to write; * Teachers are coworkers with students; children from many backgrounds can learn to write together. The text sythesizes what we know about how children learn, how we write, and what we write into a process of teaching children to write. It is intended to serve as a starting place for developing theories of how to best teach writing.

Beyond Classical Pedagogy

Beyond Classical Pedagogy Author Terry Wood
ISBN-10 9781135658717
Release 2014-04-04
Pages 328
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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.

Algebra K theory Groups and Education

Algebra  K theory  Groups  and Education Author Hyman Bass
ISBN-10 9780821810873
Release 1999
Pages 238
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This volume includes expositions of key developments over the past four decades in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. Many of the articles are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass. Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field.

The Construction of New Mathematical Knowledge in Classroom Interaction

The Construction of New Mathematical Knowledge in Classroom Interaction Author Heinz Steinbring
ISBN-10 9780387242538
Release 2006-03-30
Pages 236
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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.

Second Handbook of Research on Mathematics Teaching and Learning

Second Handbook of Research on Mathematics Teaching and Learning Author Frank K. Lester
ISBN-10 9781607527091
Release 2007-02-01
Pages 725
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The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.

Teachers Engaged in Research

Teachers Engaged in Research Author Stephanie Z. Smith
ISBN-10 9781607527244
Release 2006-03-01
Pages 261
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This volume was written primarily for teachers who have developed (or who are being encouraged to develop) an awareness of and commitment to teaching mathematics for understanding. The research findings presented in these chapters suggest instructional implications worthy of these teachers’ consideration. Often, the authors in this volume describe instructional practices or raise issues that have the potential to broaden views of teaching and learning mathematics. These chapters provide interesting problems and tasks used in the authors’ work that readers can use in their own classrooms.