Kaput - three strands of algebra

BOOK REVIEW: Mathematics Educators Respond to Kaput’s "Algebra Problem": A Review of Algebra in the Early Grades
by Dan Chazan and Ann R. Edwards
JRME March 2010, Volume 41, Issue 2, Pages 203 - 204 [pdf]

In chapter 1, Kaput offers an overarching characterization of algebra and algebraic reasoning that unifies the diverse perspectives represented in this volume. His analysis presents two core aspects of algebra— algebra as the systematic symbolizing of generalizations and algebra as syntactic action in conventional symbol systems.

These core aspects are embodied in three strands of algebra:

1. algebra as the study of structures and systems abstracted/generalized from arithmetic and quantitative reasoning;
2. algebra as the study of functions (the generalization of variability); and
3. algebra as a modeling tool.

Picking up on these threads, chapter 2 (Kaput, Blanton, & Moreno) and chapter 5 (E. Smith) further explicate algebra as embodied in the linked processes of generalization and symbolization—Kaput, et al. examining symbolization in the context of equation solving and Smith focusing on the role of argumentation in the establishment of generality.

Chapter 4 (J. Smith & Thompson) takes a contrasting view, arguing that the development of algebraic reasoning can effectively be based in reasoning about relationships between physical quantities.