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)

Reviews research using diagrams, number sentences, and algorithms to help students learn to add and subtract; poses questions on the relationship of instruction to children's knowledge construction; and proposes a research agenda in this area. (86 references) (MKR)

Differences in students' (aged 12-14) construction and analysis of mathematical algorithms may be explained by the differences between predicative and functional cognitive structures. Analyzes the central role of internal and external representations and the characteristics of each. Discusses prototypical research design and development of a…

Examines the issue of how calculators and computers can best be used in mathematics education. Contends that practicing a procedure is noncognitive and does not produce learning. Suggests utilizing customized computerized tools in schools for getting answers to algorithmic problems instantly, thus allowing teachers to explain and students to…