Author : Carole E. Greenes
Publisher :
Page : 352 pages
File Size : 30,77 MB
Release : 2008
Category : Education
ISBN :
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.
Author : Carole E. Greenes
Publisher :
Page : pages
File Size : 48,61 MB
Release : 1998
Category : Algebra
ISBN : 9780762205547
The puzzles and problems cover six areas of algebra: presentation, proportional reasoning, balance, variable, function, and inductive reasoning.
Author : Maria L. Blanton
Publisher :
Page : 102 pages
File Size : 30,91 MB
Release : 2011
Category : Algebra
ISBN : 9780873536684
Like algebra at any level, early algebra is a way to explore, analyse, represent and generalise mathematical ideas and relationships. This book shows that children can and do engage in generalising about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential understandings for developing algebraic thinking in grades 3-5. The big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships and functional thinking to generalise relationships between covarying quantities. The book examines challenges in teaching, learning and assessment and is interspersed with questions for teachers’ reflection.
Author : Paul Gray
Publisher :
Page : pages
File Size : 17,66 MB
Release : 2016-09-01
Category :
ISBN : 9780988679696
Algebraic Reasoning is a textbook designed to provide high school students with a conceptual understanding of algebraic functions and to prepare them for Algebra 2..
Author : Maryann Wickett
Publisher : Math Solutions
Page : 331 pages
File Size : 18,85 MB
Release : 2002
Category : Education
ISBN : 0941355489
Lessons for K-8 teachers on making algebra an integral part of their mathematics instruction.
Author : Thomas P. Carpenter
Publisher : Heinemann Educational Books
Page : 166 pages
File Size : 36,82 MB
Release : 2003
Category : Education
ISBN :
In this book the authors reveal how children's developing knowledge of the powerful unifying ideas of mathematics can deepen their understanding of arithmetic
Author : Jinfa Cai
Publisher : Springer Science & Business Media
Page : 631 pages
File Size : 28,34 MB
Release : 2011-02-24
Category : Education
ISBN : 3642177352
In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.
Author : Carolyn Kieran
Publisher : Springer
Page : 443 pages
File Size : 30,20 MB
Release : 2017-12-04
Category : Education
ISBN : 3319683519
This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.
Author : Center for Science, Mathematics, and Engineering Education
Publisher : National Academies Press
Page : 206 pages
File Size : 49,88 MB
Release : 1998-10-07
Category : Education
ISBN : 0309522455
With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.
Author : Susan Jo Russell
Publisher : Heinemann Educational Books
Page : 0 pages
File Size : 16,53 MB
Release : 2011
Category : Education
ISBN : 9780325041919
"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.
