Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)

Hypothesizing that subtraction of (negative) integers requires formal operations, the author describes a study of children's understanding of related concepts. The study involves the use of apparatus embodying properties of the number line. (SD)

Two enrichment articles are presented; one dealing with finding partial fractions and reducing to polynomials; the other, with finding the heaviest object from eleven others of equal weight where all twelve are identical in appearance. (JG)

Research on college students' ability to estimate means and variances for sets of data showed that they were more able to estimate means, and that various characteristics of the data (e.g. magnitude of numbers) influenced the accuracy of estimates. (SD)

Activities involving estimation of the number of objects in a configuration can motivate students to consider parametric models. (SD)

Examination of models for representing integers demonstrates that formal operational thought is required for establishing the operations on integers. Advocated is the use of many models for introducing negative numbers but, apart from addition, it is recommended that operations on integers be delayed until the formal operations stage. (JP)

A summary with examples of the use of the environment in the teaching of mathematics in British elementary schools. (MM)