Diagnostic teaching is described and discussed. Different types of errors are explained and examples of errors and their possible diagnoses are given. (MK)

A study to determine if "random" or "careless" errors in multiplication made by individual students take on discernible patterns is described. Implications for teaching are discussed. (MK)

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)

Diagnostic evaluation is a major way to help students overcome errors. How such evaluation can be done is discussed, with comments on what should be checked and recorded by the teacher. (MNS)

Four basic types of student errors in computation are noted and described. These are: (1) mechanical, (2) careless, (3) conceptual, and (4) procedural. It is felt many teachers deal with all errors as if they were of the unhabituated procedural type, with not enough attention given to other possibilities. (MP)

Instructional strategies that will develop the concept of a fraction are presented. Fractions as counting numbers, measures, and subdivisions are included, with a combination of regions and number lines suggested as a teaching aid. (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)