The paper presents findings of a small scale study of a few items related to problem solving with squares and roots, for different teacher groups (pre-service and in-service mathematics teachers: elementary and junior high school). The research participants were asked to explain what would be the units digit of a natural number to be squared in…

The self-weighted mean ("WS')--in which each value is weighted by itself--is presented in several contexts and illustrated. It is incorporated in a set of more familiar means. Intuitions concerning "WS" are explored.

The paper discusses the interaction between intuitive biases of probabilistic thinking and mathematical knowledge. It would appear that students may answer numerical problems correctly but falter on simple descriptive solutions. Students appear to relinquish formal knowledge for simpler heuristics when attempting to describe the outcome of an…

Abstracts of 12 mathematics education research reports and critical comments (by the abstractors) about the reports are provided in this issue of Investigations in Mathematics Education. The reports are: "More Precisely Defining and Measuring the Order-Irrelevance Principle" (Arthur Baroody); "Children's Relative Number Judgments:…