Connecting Arithmetic to Algebra

Connecting Arithmetic to Algebra
Author: Susan Jo Russell
Publisher: Heinemann Educational Books
Total Pages: 0
Release: 2011
Genre: Education
ISBN: 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 and Algebraic Thinking in School Mathematics

Algebra and Algebraic Thinking in School Mathematics
Author: Carole E. Greenes
Publisher:
Total Pages: 352
Release: 2008
Genre: Education
ISBN:

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Examines the status of algebra in our schools and the changes that the curriculum has undergone over the past several years. Includes successful classroom practises for developing algebraic reasoning abilities and improving overall understanding.

Thinking Mathematically

Thinking Mathematically
Author: Thomas P. Carpenter
Publisher: Heinemann Educational Books
Total Pages: 166
Release: 2003
Genre: Education
ISBN:

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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

Algebra For Parents: A Book For Grown-ups About Middle School Mathematics

Algebra For Parents: A Book For Grown-ups About Middle School Mathematics
Author: Ron Aharoni
Publisher: World Scientific
Total Pages: 237
Release: 2021-01-22
Genre: Mathematics
ISBN: 9811209243

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The book goes through middle school mathematics and techniques and methods of its teaching. It is meant to aid parents who wish to be involved in the mathematical education of their children, as well as teachers who wish to learn principles of mathematics and of its teaching.

Regular Algebra and Finite Machines

Regular Algebra and Finite Machines
Author: John Horton Conway
Publisher: Courier Corporation
Total Pages: 162
Release: 2012-09-16
Genre: Mathematics
ISBN: 0486310582

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A world-famous mathematician explores Moore's theory of experiments, Kleene's theory of regular events and expressions, differential calculus of events, the factor matrix, theory of operators, much more. Solutions. 1971 edition.

Algebra Connections

Algebra Connections
Author: Ira J. Papick
Publisher: Prentice Hall
Total Pages: 0
Release: 2007
Genre: Algebra
ISBN: 9780131449282

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Uses an introduction to basic concepts of number theory and modern algebra to provide an understanding of mathematical ideas to be taught in the classroom.

Moonshine beyond the Monster

Moonshine beyond the Monster
Author: Terry Gannon
Publisher: Cambridge University Press
Total Pages: 493
Release: 2023-07-31
Genre: Science
ISBN: 1009401580

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But why Does it Work?

But why Does it Work?
Author: Susan Jo Russell
Publisher: Heinemann Educational Books
Total Pages: 0
Release: 2017
Genre: Education
ISBN: 9780325081144

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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.

Advanced Math for Young Students

Advanced Math for Young Students
Author: Philip Keller
Publisher: Createspace Independent Publishing Platform
Total Pages: 0
Release: 2014-10-22
Genre: Algebra
ISBN: 9781502817334

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Written for middle school and high school students. Emphasizing functions, graphs and equations, it demonstrates how the language of algebra is used, drawing examples from physics, chemistry and economics. This is not a traditional "Algebra 1" book. It is designed to be used before (or during) your first algebra class, though it also introduces some concepts from Algebra 2 and Pre-calculus

Discovering Group Theory

Discovering Group Theory
Author: Tony Barnard
Publisher: CRC Press
Total Pages: 286
Release: 2016-12-19
Genre: Mathematics
ISBN: 1315405768

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Discovering Group Theory: A Transition to Advanced Mathematics presents the usual material that is found in a first course on groups and then does a bit more. The book is intended for students who find the kind of reasoning in abstract mathematics courses unfamiliar and need extra support in this transition to advanced mathematics. The book gives a number of examples of groups and subgroups, including permutation groups, dihedral groups, and groups of integer residue classes. The book goes on to study cosets and finishes with the first isomorphism theorem. Very little is assumed as background knowledge on the part of the reader. Some facility in algebraic manipulation is required, and a working knowledge of some of the properties of integers, such as knowing how to factorize integers into prime factors. The book aims to help students with the transition from concrete to abstract mathematical thinking.