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…

This study characterizes how a cohort of 33 middle and secondary mathematics preservice teachers' inferential reasoning changed while enrolled in a statistics course designed for future teachers. Changes in inferential reasoning from pre- to post-assessments are analyzed and further elucidated by midcourse clinical interviews conducted with a…

In this paper we report on a research aimed to identify and characterize secondary school students' reasoning and proof abilities when working with 3-dimensional geometric solids. We analyze students' answers to two problems asking them to prove certain properties of prisms. As results of this analysis, we get, on the one side, a characterization…

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…