Different methods of subtracting are described; the equal additions and the decomposition methods are discussed in detail. (DT)

The author advocates the classroom consideration of new algorithms as a means of leading students to make original hypotheses. He discusses a multiplication algorithm based on the differences between squares. (SD)

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)

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

Upper elementary school students created their own algorithms for finding products of whole numbers. The algorithms were similar to familiar ones for finding products involving 9 and 11. (SD)

Children are asked to describe the subtraction process or to describe a context in which subtraction may be used. (JLH)

These three brief articles concern problems students encounter in solving simple linear equations, children's conceptions of number, and the distinction between adding objects and adding numbers as illustrated by students' problems with Euler's formula. (SD)

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)

The observations of a fifth-grade student concerning number patterns are recorded and discussed. (SD)

A method is described for working multiplication problems by counting on fingers. (DT)

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)