Three Perspectives in Research on Functions: Multi-Representational, Quantitative, and Phenomenological
American Educational Research Association Annual Meeting,
Much research on student understanding of functions has been characterized by a "multi-representational" perspective that investigates students' efforts to make connections among conventionally accepted mathematical representations such as graphs, tables, and equations. In contrast, a "quantitative" perspective explores students' efforts to identify the quantities and relationships between quantities in a function, and a "phenomenological" perspective considers the social and experiential aspects inherent in students' learning experiences. Two research studies have demonstrated ways to incorporate the three research perspectives. One studied how seventh graders develop their understandings of linear functions as they interact with software in the social setting of a traditional classroom. The other study investigated how quantitative reasoning affects the nature of students' generalizations about linear functions and rates of change. Design features of each experiment that explores the three research perspectives are outlined. (Contains 5 figures and 36 references.) (SLD)
Lobato, J. & Bowers, J. (2000). Three Perspectives in Research on Functions: Multi-Representational, Quantitative, and Phenomenological. Presented at American Educational Research Association Annual Meeting 2000.