Abstract
In an article that appeared in the Arithmetic Teacher, Madell (1985) described findings from a private school in New York City in which children were not taught any algorithms until the end of the third grade. Without algorithms, the children devised their own ways of solving computation problems. Madell's observation of the children's thinking led him to conclude that “children not only can but should create their own computational algorithms” (p. 20) and that “children can and should do their own thinking” (p. 22). The purpose of the present article is to reiterate Madell's call for reform, with supporting evidence from a public school near Birmingham, Alabama.
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