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)

Results from a British study on Strategies and Errors in Secondary Mathematics are considered. Students' views of algebra and their difficulties are summarized, with some suggestions for teachers. (MNS)

Analysis of errors children make is modeled both with and without computers. Patterns of thinking are traced for a fifth grader, with the discussion focused on getting clues for remedial instruction by analyzing the dialog. (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)

An overall schema of interpretation for programming instructors is given, so that the misconceptions students develop in programming can be determined more readily. Types of language-independent and -dependent bugs, how they can be identified, and how to help students overcome them are addressed. (MNS)

The technique individuals use to narrow the possible responses in "solicits" (demands, requests, or questions requiring a response) in and outside the classroom often helps to avoid miscommunication and can be a useful tool for classroom teachers. A narrowing exercise was completed by 35 classes of native English and English as a second language…