The symbolic world of mathematics

Authors

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

Download data is not yet available.

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 Crossref

Elby, 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 Crossref

Friel, 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 Crossref

Gray, 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 Crossref

Hähkiöniemi, Markus (2006): The Role of Representations in Learning The Derivative. Dissertation from University of Jyväskylä, Department of Mathematics and Statistics.

Google Scholar Crossref

Leinhardt, 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 Crossref

Linell, P. 1994. Transcription of talk and conversation. Theory and practise. Reports from Theme K: 99-0831950-7 1994: 9. Linkoping University: Sweden

Google Scholar Crossref

Sfard, 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 Crossref

Tall, 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 Crossref

Tall, D. (2004).Thinking Through Three Worlds of Mathematics. Proceedings of the 28th Conference of PME, Bergen, Norway, 4, s. 281-288.

Google Scholar Crossref

Trigueros, M., & Martínez-Planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73(1), 3-19.

Google Scholar Crossref

Downloads

Published

2017-06-24

Almetric

Dimensions

Issue

Section

Articles