Student Comprehension of The Concept of a Geometrical Figure: The Case of Straight Lines and Parallel Line

patrick Tchonang youkap(1*),

(1) University of Yaounde 1
(*) Corresponding Author

Abstract


The objective of this paper is to identify some student’s conceptions of the straight line and two parallel lines. This will allow us to evaluate the distance that exists between their conceptions and the theory of these concepts. In doing so, we analyzed the students’ answers to a questionnaire: the questionnaire concerned the explication of the straight line and two parallel lines. The results indicate that the students have difficulties to produce an acceptable definition of a straight line and two parallel lines. They have difficulties to find appropriate terms to express their comprehension of these concepts. The definitions they produce are ambiguous and seem to be related to the drawings they have encountered in the classroom. Their answers indicate that their comprehension on the straight line and two parallel lines seem to be in conflict with the theory of these concepts.


Keywords


Concept image; concept definition; straight line; parallel lines

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References


Coppé, S., Dorier, J.-L., & Moreau, V. (2005). Différents types de dessins dans les activités d’argumentation en classe de 5ème. Petit X, (68), 8–37.

De Villiers, M. (1998). To teach definitions in geometry or teach to define? Proceedings of the Twentysecond International Conference for the Psychology of Mathematics Education, 2(July), 248–255.

Durand-Guerrier, V., Hausberger, T., & Spitalas, C. (2015). Définitions et exemples : prérequis pour l’apprentissage de l’algèbre moderne. In Annales de Didactiques et de Sciences Cognitives (Vol. 20, pp. 101–148).

Freudenthal, H. (2012). Mathematics as an educational task. Springer Science & Business Media.

Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior.

https://doi.org/10.1016/j.jmathb.2011.08.003

Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3–20.

https://doi.org/10.1080/14794800008520167

Gobert, S. (2007). Conditions nécessaires à l’usage des dessins en géométrie déductive. Petit X, 47, 34–59.

Gutiérrez, A., & Jaime, A. (1999). Preservice primary teachers’ understanding of the concept of altitude of a triangle. Journal of Mathematics Teacher Education, 2, 253–275.

Njomgang, J., & Tchonang, P. (2018). La ligne droite, un objet d’étude au début du secondaire : une analyse institutionnelle des manuels. Revue de Mathématiques Pour l’école, 230, 23–29.

Ouvrier-Buffet, C. (2003). Construction de définitions / construction de concept : vers une situation fondamentale pour la construction de définitions en mathématiques. Université Joseph-Fourier - Grenoble I.

Robert, A. (2003). Un point de vue sur les spécificités du travail géométrique des élèves à partir de la quatrième : l’organisation des connaissances en niveaux de conceptualisation. Petit X, 63, 7–29.

Tall, D., & Vinner, S. (1981). Concept Images and Concept Definitions in Mathematics With Particular Reference to Limits and Continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/bf00305619

Vergnaud, G. (2009). The theory of conceptual fields. Human Development. https://doi.org/10.1159/000202727

Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293–305. https://doi.org/10.1080/0020739830140305

Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. Advanced Mathematical Thinking, 65–81.

Walter, A. (2001). Quelle géométrie pour l’enseignement en collège ? Petit X, 54, 31–49.

Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education. https://doi.org/10.2307/27646367




DOI: https://doi.org/10.31327/jme.v6i2.1408

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