The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date. Alternative algorithms, such as mental algorithms, calculators, and nonstandard written methods, are discussed. (MP)

Three different methods of teaching fraction computation were compared using community college student scores on measures of fraction computation, fraction understanding, and attitude towards mathematics. One method used conventional algorithms; the second, a control for the effect of using a calculator, used conventional algorithms and…

Argues that the type of calculator that is used in mathematics instruction is very important. Suggests that four-function calculators fail to give correct values of mathematical expressions far more often than do scientific calculators. (PK)