The symbolic world of mathematics
https://doi.org/10.17583/redimat.2017.2391
Downloads
Abstract
In understanding upper secondary school students’ interpretations of information in symbolic representations of a distance-time-relation, little attention has been paid to the analysis of the condition of the conceptual development related to utterances. Understanding this better can help improve the teaching of attribute and information in symbolic representations of different phenomena. Two theoretical perspectives have been used to conduct the analysis: Tall and Vinner's theoretical perspectives on learning and Gray’s & Talls’s theory of three mathematical worlds. The findings provide evidence that a detailed analyse of student’s utterances show difference in quality related to student’s interpretations of a distance-time relation. The qualities were related to student’s concept images of functions and derivatives.
Downloads
References
Breidenbach, D., Hawks, J., Nichols, D., & Dubinsky, E. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(4), 247–285.
Google Scholar CrossrefElby, A. (2000).What students' learning of representations tells us about constructivism. Journal of Mathematical Behavior, Volume 19, issue 4 (4th quarter, 2000), p. 481-502.
Google Scholar CrossrefFriel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: critical factors influencing comprehension and instructional implications: Journal for Research in Mathematics Education, 32, 124- 158.
Google Scholar CrossrefGray, E. & Tall, D. (1994). Duality, ambiguity, and flexibility: A proceptual view of simple arithmetic. Journal for Research in Mathematics Education, 25, 116 - 140.
Google Scholar CrossrefHähkiöniemi, Markus (2006): The Role of Representations in Learning The Derivative. Dissertation from University of Jyväskylä, Department of Mathematics and Statistics.
Google Scholar CrossrefLeinhardt, G., Zaslavsky, O., & Stein, M. M. (1990). Functions, graphs, and graphing: Tasks, Learning and Teaching. Review of Educational Research, 60(1), pp. 1-64. American Educational Research Association.
Google Scholar CrossrefLinell, P. 1994. Transcription of talk and conversation. Theory and practise. Reports from Theme K: 99-0831950-7 1994: 9. Linkoping University: Sweden
Google Scholar CrossrefSfard, A. (1992). Operational origins of mathematical objects and the quandary of reification—the case of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 59–84). Washington DC: MAA.
Google Scholar CrossrefTall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.
Google Scholar CrossrefTall, D. (2004).Thinking Through Three Worlds of Mathematics. Proceedings of the 28th Conference of PME, Bergen, Norway, 4, s. 281-288.
Google Scholar CrossrefTrigueros, M., & Martínez-Planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73(1), 3-19.
Google Scholar CrossrefDownloads
Published
Almetric
Dimensions
Issue
Section
License
Copyright (c) 2017 Thomas Lingefjärd, Djamshid Farahani
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal the right of first publication but allow anyone to share: (unload, , reprint, distribute and/or copy) and adapt (remix, transform reuse, modify,) for any proposition, even commercial, always quoting the original source.