Presents results of a project with second and third graders to establish concepts of equality that led to the realization that teachers often help students too much and may push them algorithmically beyond their ability without the development of proper referents. (Author/MKR)

Limitations in children's understanding of the symbols of arithmetic may inhibit choice of appropriate solution procedures. The teacher's role involves negotiation of new meanings for words and symbols to match extensions to solution procedures. (MKR)

This response to Usiskin's editorial comment on calculator use in the May 1983 issue considers why arithmetic is taught. The belief that mathematics improves thinking and the humanist position that it is part of our cultural heritage are noted. The role of mathematics in the curriculum should be reconsidered. (MNS)

The author presents and elaborates on a division algorithm devised by his 9-year-old son. (MK)

Based on Piaget's theory that children acquire number concepts by constructing them from within, the authors conclude that teaching algorithms harms mathematics learning. A better approach is allowing them to construct their own logico-mathematical knowledge and invent their own efficient procedures. (JOW)

An education major enrolled in a mathematics education course ponders confusing definitions of "multiplication" functions in dictionaries and in a handout on Euclid. This student teacher wants to teach elementary students what multiplication really is, not just impart an algorithmic skill. (MLH)

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date. Alternative algorithms, such as mental algorithms, calculators, and nonstandard written methods, are discussed. (MP)

Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)

Changes in the elementary and junior high school mathematics curriculum that have occurred in the last 20 years and that may occur in the future are discussed. (MK)

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)

This study investigated the relationship between the level of conservation of displaced volume and the degree to which sixth graders learn the volume algorithm of a cuboid, i.e., volume = length x width x height (v = l x w x h). The problem is a consequence of an apparent discrepancy between the present school programs and the theory of Piaget…