Problem-Solving Approaches to Algebra: Two Aspects

Abstract

Problem solving by forming and solving equations is a historic route into algebra. Now it is along with generalizing and working with functions and formulas, one of the main modes of algebraic activitiy that need to be learned. But the exploration of generic problems and their extensions that provides a mathematically authentic and motivating mode of activity through which all of algebra can be learned. The chapter reviews the nature of algebra and outlines such and approach, giving examples of typical tasks and of student work.