Presents research on students' use and understanding of algorithms in Poland. Concludes that there are detrimental side effects that stem from the teaching and learning of standard written algorithms. (ASK)

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)

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)

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 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)