Over the years, like a pendulum. the emphasis in mathematics education has swung from a focus on concepts and understanding (e.g., the new-math movement) on the one hand to skill with facts and algorithms (e.g., the back-to-basic movement) on the other. Currently. children can adequately perform algorithms, but they may do so with little understanding of the underlying concepts (Resnick 1982, 136–55). In part, the difficulty lies in students having lo t sight of the role of symbols in mathematical thinking. The development of approache. that help children integrate the insight of symbolic understanding with the power of algorithmic technique should be of value. Accordingly, the intent of this article is to suggest how children can be guided to see and personally feel the power and simplicity that thinking with and about mathematical symbols can bring to their algorithmic competence. Although, for the sake of concretene and pecificity, attention hall be confined to computation, stress shall be placed on an approach that the reader may find generalize to other areas.
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Daiyo Sawada (1985) studied this question.