Developing Algebraic Thinking in the Context of Arithmetic
By Susan Jo Russell, Deborah Schifter, and Virginia Bastable
A chapter from Early Algebraization: A Global Dialogue from Multiple Perspectives edited by Jinfa Cai and Eric Knuth
From our work with elementary and middle grade teachers, the authors of this chapter have identified four mathematical activities that underlie both arithmetic and algebra and, therefore, provide a bridge between the two. These are:
- understanding the behavior of the operations,
- generalizing and justifying,
- extending the number system, and
- using notation with meaning.
These themes emerge from content at the heart of the elementary mathematics program and can be highlighted and pursued by teachers who learn to recognize the opportunities that arise in their classrooms. Focusing on these aspects of arithmetic addresses two major goals: (1) It enables students to grow from arithmetic towards algebra, and (2) it strengthens their understanding of arithmetic operations and contributes to computational fluency.
This chapter is based on research on early algebra carried out in the context of several projects that focused on developing curriculum for students and professional development materials for teachers. In collaboration with teachers in grades K-8, we have been investigating how students articulate, represent, and justify general claims about the operations. In this chapter, we describe classroom episodes that illustrate how teachers can recognize the implicit generalizations that arise in the course of students’ study of arithmetic and make them explicit objects of study for their students.
Contact Info: Deborah Schifter (1-800-225-4276 x2564)
Published by: Springer Publishing Company Order Info
Learn more about this title on the publisher’s website: http://www.springer.com/education+%26+language/mathematics+education/book/978-3-642-17734-7
Price: $129.00
ISBN: 9783642177347
(623 pp.) Print