Open AccessJournal Article
Descriptions and Conflicts in Dynamic Geometry
TL;DR: It is argued that this student’s different background allowed her to experience a conflict, which has given her means to expand her conceptualization, and the narrowing effect of mere formulae application is compared with the typical response given by teachers to the same problem during in-service courses.
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Abstract: We expand the theoretical perspective based on the notions of description and conflict, which was previously used to the learning of functions and calculus, to the learning of deductive geometry supported by Dynamic Geometry (DG) environments. Based on prior studies on functions and on the potential role of a DG software, we analyze a case study in which the student’s reaction to a problem strongly differ from the pattern observed during in-service courses for teachers. We argue that this student’s different background allowed her to experience a conflict, which has given her means to expand her conceptualization. Finally, we contrast this behavior with the narrowing effect of mere formulae application, which has been observed in the typical response given by teachers to the same problem during in-service courses.
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Citations
Student's Learning Progression through Instrumental Decoding of Mathematical Ideas
Stavroula Patsiomitou
- 01 Jan 2014
TL;DR: Excerpts are presented from dynamic hypothetical learning paths (DHLP) s and students' learning progression that develop the students' geometrical thinking through the development of their ability to solve real-world problems.
Análisis de las estrategias empleadas en el uso de programas dinámicos de geometría y tipos de actividades para la enseñanza de la geometría
A Ronny Gamboa,L Yuri Morales +1 more
- 01 Jan 2010
TL;DR: In this article, una serie de actividades realizadas con el uso of un programa dinamico de geometria tipo exploratorioconstructivo and constructivo-deductivo, with the fin of explorar ciertas propiedades geometricas and, consecuentemente, valorar las fortalezas of las mismas.
2
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Concept Image and Concept Definition in Mathematics with particular reference to Limits and Continuity
TL;DR: The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept and may have aspects which are quite different from the formal concept definition as discussed by the authors.
The Role of Definitions in the Teaching and Learning of Mathematics
Shlomo Vinner
- 01 Jan 2002
TL;DR: It is claimed that the presentation and the organization of mathematics in many text books and classrooms are partly based on the following assumptions: mathematics is a deductive theory, and primary notions, axioms and proofs are defined.
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“Knowing” vs “seeing”. problems of the plane representation of space geometry figures
TL;DR: There is a loss of information when moving from a geometrical object to its drawing, but pupils often have the illusion that they can, thanks to a drawing sufficiently sophisticated and close to the object, make a representation of it in which there is no ambiguity at all.
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