Described is a case in which a young student stumbles upon the "integer" technique for subtraction which differs from the techniques of decomposition and equal addition. (MN)

A process for helping students in the elementary grades develop their own algorithms for subtraction with carrying is described. Pupils choose their own times and ways to move from manipulative materials to written notation. (MP)

The aim of this article is to identify the natural relationships that exist between using computer programming in BASIC, and some particular mathematical concepts. Specific examples are given for use by the mathematics teacher who has the necessary facilities available. (MN)

An example of a lesson involving calculators that focused on calculator use is given. An examination of the traditional algorithm by the students led to student-directed investigations. (MP)

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)

A one-to-one teaching session with a student is described and analyzed in an attempt to communicate how student attempts at discovery in mathematics can be thwarted by teachers who do not allow room for creativity. (MP)

More mental computation and organized and enjoyable activities to practice such skills are advocated. Suggestions for brief sessions involving challenging questions and quick recall of number facts are presented. The author presents and comments on several sample lessons designed for a wide range of student abilities. (MP)