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Teaching of Mathematics
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2010, vol. 13, br. 2, str. 63-92
Local rate of change: A Socratic experience in van Hiele's model framework
(naslov ne postoji na srpskom)
aDepartment of Applied Mathematics, University of Seville, Seville, Spain
bDepartment of Applied Mathematics, Polytechnical University of Valencia, Valencia, Spain

e-adresamanavarro@us.es
Ključne reči: model; change; rate of change; visualization; approximation; local rate of change
Sažetak
(ne postoji na srpskom)
Our aim is to provide an educative experience concerning the study of rate of change, to be implemented prior to its formal treatment in the classroom. By means of a Socratic dialog and the manipulation of a computer generated visualization tool, we shall provoke answers to questions such as How much?, How steep? and How fast? by identifying all key ingredients necessary to provide a sound concept image of the concept of derivative of a function at a point. Our study is framed in van Hiele's educational model methodology. This first of two articles deals with the interview and the list of descriptors which allow the detection of the levels of reasoning the model postulates. In a forthcoming article we shall concern ourselves with the analysis of all students responses, cognitive obstacles encountered and tutorial actions needed to overcome them.
Reference
Llorens, J.L., Prez, C.P. (1997) An extension of van Hiele's model to the study of local approximation. Int. J. Math. Education Sci. Tech, 28, 713-726
Navarro, A., Carreras, P.P. (2006) Constructing a concept image of convergence of sequences. u: Hitt F., Harel G., Selden A. [ur.] The Van Hiele framework: Research in collegiate mathematics education VI, CBMS issues in mathematics education, 13, AMS/MAA, 61-98
Tall, D.O., Vinner, S. (1981) Concept image and concept definition mathematics with particular reference to limits and continuity. Education Studies in Mathematics, 12, 2, 159-169
van Hiele, P.M. (1986) Structure and insight: A theory of mathematics education. New York: Academic Press, Inc
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
objavljen u SCIndeksu: 02.03.2011.

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