The Rectangular Doorway to Algebra

Abstract: W.W. Sawyer in his “Vision in Elementary Mathematics” provides key insights for demystifying a child’s first introduction to Algebra. Introducing ‘x’, through the simple game “Think of a number”, teaching multiplication via area of rectangles, and building on this to understand the multiplication of algebraic expressions and polynomials are the essence of Sawyer’s approach. In addition “Vision” provides gems of pedagogical wisdom, such as “not introducing negative numbers in algebra initially”, which facilitate understanding of important and useful aspects of algebraic multiplication. Sawyer’s rectangular doorway to Algebra is put together with the two-step learning process of Universal Active Mathematics- first learning by doing, by constructing physical shapes and sizes, and then translating this understanding into the language of pencil and paper, to build a concept construction sequence for introductory algebra. Place value multiplication and multiplication of polynomials in one variable are seen to be isomorphic so that algebra at many levels is not a new subject. The new aspects of algebra arise in the solution of equations

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