The informal subtraction strategies that children develop are discussed in detail, with the role of the counting-down strategy described. Problems and remedies for difficulties caused by counting backward and the double count are also presented. (MNS)

Dialogue from an interview with a child about division basic facts is presented. The facts are considered by groups, and specific errors are noted. Finally, remediation ideas are given. (MNS)

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)