Connecting Arithmetic to Algebra
Connecting Arithmetic to Algebra

Author: Susan Jo Russell

Publisher: Heinemann Educational Books

Published: 2011

Total Pages: 0

ISBN-13: 9780325041919

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"To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics." -Susan Jo Russell, Deborah Schifter, and Virginia Bastable Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles. Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course. For information on the PD course offered through Mount Holyoke College, download the flyer.

Algebra, Arithmetic, and Geometry
Algebra, Arithmetic, and Geometry

Author: Yuri Tschinkel

Publisher: Springer Science & Business Media

Published: 2010-04-11

Total Pages: 700

ISBN-13: 0817647473

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EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

Bridging the Gap Between Arithmetic & Algebra
Bridging the Gap Between Arithmetic & Algebra

Author: Bradley S. Witzel

Publisher:

Published: 2016

Total Pages: 196

ISBN-13: 9780865865099

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Although two federal panels have concluded that all students can learn mathematics and most succeed through Algebra 2, the abstractness of algebra and missing precursor understandings may be overwhelming to many students ... and their teachers. Bridging the Gap Between Arithmetic & Algebra responds to this need for instruction and interventions that go beyond typical math lesson plans. Providing a review of evidence-based practices, this book is an essential reference for mathematics teaches and special education teachers when teaching mathematics to students who struggle with the critical concepts and skills necessary for success in algebra.

Algebra, Arithmetic, and Geometry
Algebra, Arithmetic, and Geometry

Author: Yuri Tschinkel

Publisher: Springer Science & Business Media

Published: 2010-08-05

Total Pages: 723

ISBN-13: 0817647457

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EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

Integrated Arithmetic and Basic Algebra
Integrated Arithmetic and Basic Algebra

Author: Bill E. Jordan

Publisher: Addison-Wesley Longman

Published: 2008

Total Pages: 0

ISBN-13: 9780321442550

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Integrated Arithmetic and Basic Algebra, Fourth Edition, integrates arithmetic and algebra to allow students to see the big picture of math. Rather than separating these two subjects, this text helps students recognize algebra as a natural extension of arithmetic. As a result, students see how concepts are interrelated and are better prepared for future courses.

Thinking Mathematically
Thinking Mathematically

Author: Thomas P. Carpenter

Publisher: Heinemann Educational Books

Published: 2003

Total Pages: 166

ISBN-13:

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In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic

Arithmetic Algebraic Geometry
Arithmetic Algebraic Geometry

Author: Brian David Conrad

Publisher: American Mathematical Soc.

Published:

Total Pages: 588

ISBN-13: 9780821886915

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The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

Bringing Out the Algebraic Character of Arithmetic
Bringing Out the Algebraic Character of Arithmetic

Author: Analúcia D. Schliemann

Publisher: Routledge

Published: 2006-08-29

Total Pages: 104

ISBN-13: 1136799613

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Bringing Out the Algebraic Character of Arithmetic contributes to a growing body of research relevant to efforts to make algebra an integral part of early mathematics instruction, an area of studies that has come to be known as Early Algebra. It provides both a rationale for promoting algebraic reasoning in the elementary school curriculum and empirical data to support it. The authors regard Early Algebra not as accelerated instruction but as an approach to existing topics in the early mathematics curriculum that highlights their algebraic character. Each chapter shows young learners engaged in mathematics tasks where there has been a shift away from computations on specific amounts toward thinking about relations and functional dependencies. The authors show how young learners attempt to work with mathematical generalizations before they have learned formal algebraic notation. The book, suitable as a text in undergraduate or graduate mathematics education courses, includes downloadable resources with additional text and video footage on how students reason about addition and subtraction as functions; on how students understand multiplication when it is presented as a function; and on how children use notations in algebraic problems involving fractions. These three videopapers (written text with embedded video footage) present relevant discussions that help identify students' mathematical reasoning. The printed text in the book includes transcriptions of the video episodes in the CD-ROM. Bringing Out the Algebraic Character of Arithmetic is aimed at researchers, practitioners, curriculum developers, policy makers and graduate students across the mathematics education community who wish to understand how young learners deal with algebra before they have learned about algebraic notation.

The Development of Arabic Mathematics: Between Arithmetic and Algebra
The Development of Arabic Mathematics: Between Arithmetic and Algebra

Author: R. Rashed

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 392

ISBN-13: 9401732744

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An understanding of developments in Arabic mathematics between the IXth and XVth century is vital to a full appreciation of the history of classical mathematics. This book draws together more than ten studies to highlight one of the major developments in Arabic mathematical thinking, provoked by the double fecondation between arithmetic and the algebra of al-Khwarizmi, which led to the foundation of diverse chapters of mathematics: polynomial algebra, combinatorial analysis, algebraic geometry, algebraic theory of numbers, diophantine analysis and numerical calculus. Thanks to epistemological analysis, and the discovery of hitherto unknown material, the author has brought these chapters into the light, proposes another periodization for classical mathematics, and questions current ideology in writing its history. Since the publication of the French version of these studies and of this book, its main results have been admitted by historians of Arabic mathematics, and integrated into their recent publications. This book is already a vital reference for anyone seeking to understand history of Arabic mathematics, and its contribution to Latin as well as to later mathematics. The English translation will be of particular value to historians and philosophers of mathematics and of science.