But Why Does It Work

Author: Susan Jo Russell
Publisher: Heinemann Educational Books
ISBN: 032508114X
Size: 18.51 MB
Format: PDF, ePub, Mobi
View: 76

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

Author: Andreas J. Stylianides
Publisher: Oxford University Press
ISBN: 9780198723066
Size: 10.69 MB
Format: PDF, ePub, Mobi
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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

Author: Sophia Cohen
Publisher: Routledge
ISBN: 9781135632267
Size: 12.55 MB
Format: PDF, ePub, Docs
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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

Author: Bharath Sriraman
Publisher: IAP
ISBN: 9781681236346
Size: 11.55 MB
Format: PDF, ePub
View: 21

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)

The Emergence Of Mathematical Meaning

Author: Paul Cobb
Publisher: Routledge
ISBN: 9781136486104
Size: 14.24 MB
Format: PDF, ePub, Mobi
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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.

Elementary Mathematics Is Anything But Elementary Content And Methods From A Developmental Perspective

Author: Damon Bahr
Publisher: Cengage Learning
ISBN: 9780618928170
Size: 18.32 MB
Format: PDF, ePub, Mobi
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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.

More Best Practices For Elementary Classrooms

Author: Randi Stone
Publisher: Corwin Press
ISBN: 9781452237770
Size: 14.41 MB
Format: PDF, Kindle
View: 87

In this sequel to Randi Stone's Best Classroom Practices, award-winning elementary teachers showcase their best strategies for classroom management, instruction, involving parents, and making inclusion work.