ERIC Number: ED351193
Record Type: RIE
Publication Date: 1992-Jan
Reference Count: N/A
Students' Tendency To Assume Resemblances between a Function and Its Derivative.
Nemirovsky, Ricardo; Rubin, Andee
This study was designed to determine students' abilities and difficulties in articulating the relationship between function and derivative. High-school students were presented 15 problems during two 75-minute interviews in which they were asked to construct functions experimentally in three different contexts: motion, fluids, and number-change. In each of the environments the students utilized tools, ranging from computer software to manipulative materials, that enabled them to generate functions. Analysis of the interviews indicated that students had the tendency to assume resemblances between the behavior or appearance of the function and its derivative in all three contexts. Three types of cues that activated resemblances in the predicted functions were identified: syntactic, semantic, and linguistic. Approaches that students used to move from the derivative to the function and vice-versa are described. A case study of one 17-minute episode of a student working with an airflow device describes the evolution of one such approach. The report concluded that the construction of such an approach was complex and that tools to explore the mathematical ideas helped frame the interviewer/student discourse through which the approach was developed. (MDH)
Descriptors: Air Flow, Calculus, Cognitive Development, Cognitive Processes, Cognitive Style, College Mathematics, Computer Assisted Instruction, Concept Formation, Discovery Learning, Discovery Processes, Functions (Mathematics), Interviews, Learning Processes, Mathematics Education, Motion, Qualitative Research, Secondary Education
TERC Communications, 2067 Massachusetts Avenue, Cambridge, MA 02140 ($5).
Publication Type: Reports - Research
Education Level: N/A
Sponsor: National Science Foundation, Washington, DC.
Authoring Institution: TERC Communications, Cambridge, MA.
Identifiers: Connections (Mathematics); Differentiation
Note: An earlier version of this paper was presented at the Annual Meeting of the American Educational Research Association (Chicago, IL, April, 1991).