Reports research designed to explore the possibility that conceptually different forms of common-fraction understanding can be identified. Such forms may be associated with differences in fraction problem solving-performance. Contains 50 references. (DDR)

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…

Interviews with 72 mixed ability students, aged 7 to 12, about arithmetic problem-solving strategies, indicated that the preference between procedural and deductive strategies becomes a divergent reality across ability levels. Among the conclusions is that more able children tend to be doing a qualitatively different sort of mathematics than their…

Investigated the upper limits of (n=22) seventh-grade students' informal processes in solving first degree equations in one unknown prior to instruction. Results indicated the existence of a cognitive gap between arithmetic and algebra characterized as the students' inability to operate spontaneously with or on the unknown. (37 references)…

Presents a developmental framework for the study of culture and cognition in which cultural practice is a key organizing construct. Argues that systematic analysis of either cultural change or cognitive development requires that they be understood relative to one another in a single integrative treatment. (Author/SD)