A theoretical model describing young students' (Grades 1-3) functional-thinking modes was formulated and validated empirically (n = 345), hypothesizing that young students' functional-thinking modes consist of recursive patterning, covariational thinking, correspondence-particular, and correspondence-general factors. Data analysis suggested that…

This study considers tertiary calculus students' and instructors' conceptualizations of slope. Qualitative techniques were employed to classify responses to 5 items using conceptualizations of slope identified across various research settings. Students' responses suggest that they rely on procedurally based conceptualizations of…

The pamphlet examines the kinds of play that are useful in developing the basis for later abstract thinking--specifically the development of mathematical concepts. The mathematical concepts included are numbers, conservation, one-to-one correspondence, counting and sequencing, ordering, sorting and classification, sorting and sets, and equivalence…

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)

Discusses the use of writing to enhance learning in mathematics from a conceptual development perspective. Shuell's phases of learning are described as a general model for conceptual development and subsequently matched with Britton's categories for transactional-informative writing. Sample mathematics assignments for each writing category are…