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…

Coordinates anthropological and cognitive perspectives on one child's learning of the standard addition algorithm in second and third grade. Analysis showed that the student abandoned his self-generated computational algorithms in favor of less understood conventional procedures. (25 references) (Author/MKR)

A 14-year-old Brazilian boy in the fourth grade was given 170 problems orally, each asking for the sum of 2 2-digit numbers. Responses indicated he had invented his own algorithm for addition, similar to the school one, based largely on his experiences with money. (Contains 13 references.) (JAF)

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…