Teachers’ conceptions of tangent line |
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Authors: | Rosa Elvira Páez Murillo Laurent Vivier |
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Institution: | 1. Universidad Autónoma de la Ciudad de México (UACM), Calzada Ermita Iztapalapa 4163, Col. Lomas de Zaragoza, Del. Iztapalapa, C.P. 09620, Mexico;2. Laboratoire de Didactique André Revuz, Université Paris Diderot, Case 7018, 75205 Paris Cedex 13, France |
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Abstract: | In order to study the conceptions, and their evolutions, of the tangent line to a curve an updating workshop which took place in México was designed for upper secondary school teachers. This workshop was planned using the methodology of cooperative learning, scientific debate and auto reflection (ACODESA) and the conception-knowing-concept model (cK¢) developed mainly by Balacheff. In order to initiate the conceptions reorganization, an initial activity was made in the graphic frame; it seems optimal to start the debates without leading participants to failure. The mathematical core of the workshop was formed by an algebraic method to find tangents to algebraic curves which is close to Descartes’ method. The ACODESA methodology allowed some intense debates mainly concerning the local character of a tangent, generating the teachers’ cognitive unbalance which is a starting point for the refinement or transformation of their conceptions. On the other hand, the cK¢ model allows to understand the conceptions of participants and to analyze the evolution of their knowings. |
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Keywords: | Tangent line Algebraic curve ACODESA methodology Conceptions Knowing |
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