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ERIC Number: EJ1317467
Record Type: Journal
Publication Date: 2021
Pages: 27
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1098-6065
EISSN: N/A
Available Date: N/A
Figurative and Operative Partitioning Activity: Students' Meanings for Amounts of Change in Covarying Quantities
Mathematical Thinking and Learning: An International Journal, v23 n4 p291-317 2021
Researchers have emphasized the importance of characterizing students' abilities to coordinate changes in covarying quantities. In this paper, we characterize three undergraduate students' coordination of covarying quantities' amounts of change during a teaching experiment. We adopt Piagetian notions of figurative and operative thought to describe the extent their meanings for covariational relationships are constrained to or supported by their partitioning activity -- the mental and physical actions associated with constructing accruals in quantities' magnitudes. Our analysis suggests that students' construction of amounts of change is constrained by figurative "partitioning activity" that requires carrying out or emulating particular actions on perceptually available material. In contrast, operative partitioning activity supports the students' transformation and (anticipated) regeneration of partitioning activity in order to conceive equivalent covariational relationships among various situations and representational systems. We conclude by discussing how documenting these distinctive meanings contributes to extant literature on covariational reasoning and, more broadly, the theorization of mathematical concept construction.
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL); National Science Foundation (NSF), Division of Undergraduate Education (DUE)
Authoring Institution: N/A
Grant or Contract Numbers: DRL1350324; DUE1920538
Author Affiliations: N/A