Images and Definitions for the Concept of Function
Abstract
Images held by 271 college students and 36 junior high school teachers for the concept of a mathematical function were compared to the definitions they gave for the concept. A questionaire was designed to exhibit the cognitive schemes for the function concept that become active in identification and construction problems and to make possible the comparison of these schemes with the definition. Many of the definitions and even more of the images were primitive among all but the mathematics majors and the teachers. Discrepancies between image and definition were frequent for all subjects who gave the Dirichlet-Bourbaki definition.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Cites
Tall, D., & Vinner, S. (1981) · Educational Studies in Mathematics · doi:10.1007/bf00305619 · Cited by 1,880 · see citing works
Self-citationConcept definition, concept image and the notion of function
Vinner, S. (1983) · International Journal of Mathematical Education in Science and Technology · doi:10.1080/0020739830140305 · Cited by 428 · see citing works
Self-citationIntelligence, Learning and Action
Lunzer, E. A., & Skemp, R. R. (1980) · British Journal of Educational Studies · doi:10.2307/3120297 · Cited by 214 · see citing works
Mathematical Thinking: The Struggle for Meaning
Burton, L. (1984) · Journal for Research in Mathematics Education · doi:10.5951/jresematheduc.15.1.0035 · Cited by 124 · see citing works
Intuitive Functional Concepts: A Baseline Study on Intuitions
Dreyfus, T., & Eisenberg, T. A. (1982) · Journal for Research in Mathematics Education · doi:10.5951/jresematheduc.13.5.0360 · Cited by 105 · see citing works
Self-citationHistorical and pedagogical aspects of the definition of function†
Malik, M. A. (1980) · International Journal of Mathematical Education in Science and Technology · doi:10.1080/0020739800110404 · Cited by 50 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Sfard, A. (1991) · Educational Studies in Mathematics · doi:10.1007/bf00302715 · Cited by 1,852 · see citing works
Functions, Graphs, and Graphing: Tasks, Learning, and Teaching
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990) · Review of Educational Research · doi:10.3102/00346543060001001 · Cited by 1,012 · see citing works
Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study
Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002) · Journal for Research in Mathematics Education · doi:10.2307/4149958 · Cited by 599 · see citing works
Generalizations of third and fifth graders within a functional approach to early algebra
Pinto, E., & Cañadas, M. C. (2021) · Mathematics Education Research Journal · doi:10.1007/s13394-019-00300-2 · Cited by 42 · see citing works
“We adopt the concept of function as “a correspondence between two nonempty sets that assigns to every element in the first set (the domain) exactly one element in the second set (codomain)” (Vinner and Dreyfus 1989, p. 357).”
Method
- Authors
- Vinner, S., & Dreyfus, T.
- Affiliations
- Hebrew University of Jerusalem (IL)
- ORCID
- Dreyfus, Tommy
- Venue
- Journal for Research in Mathematics Education
- Published
- 1989-07
- Volume
- 20
- Issue
- 4
- Pages
- 356
- ISSN
- 0021-8251 (ISSN-L)
- OpenAlex
- W2079553224
- Cited by
- 506
- References
- 6
- Citations by year
- 2026: 11 · 2025: 13 · 2024: 9 · 2023: 12 · 2022: 27 · 2021: 17 · 2020: 29 · 2019: 32 · 2018: 23 · 2017: 22 · 2016: 17 · 2015: 32 · 2014: 22 · 2013: 27 · 2012: 21
- FWCI
- 27.66
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal for Research in Mathematics Education (publishedVersion)
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Physical Sciences › Mathematics › Theoretical Computer Science › History and Theory of Mathematics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Keywords
- concept of function, cognitive schemas, university students, junior high school teachers, mathematics education
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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