Visualization of geometrical problems and its influence on | 17740
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Visualization of geometrical problems and its influence on the strategy adopted by the learner and the facilitator in secondary school in Lebanon


Naim El Rouadi and Noha Al Husni

This study aims at creating an interactive instructional strategy that varies in application according to the type of Geometrical problems solved in the Secondary Grade levels in Lebanon. When solving real life problems, this involves visualization and implementation of the correct mathematical language in addition to analysis to reach informal deduction on Pierre Van Hiele Scale .On Alain Kuzniak Scale, solving real life problems includes the natural geometry or intuition/experience and the natural axiomatic geometry or hypothetical deductive laws. The basis of learning theories behind such strategy are two: The Zone of Proximal Development in Socio-Constructivism as per Lev Vygotsky and the Scaffolding in the Cognitive Theory as per Jerome Bruner without forgetting Rene Descartes’ contribution in suggesting that the main key to solve a problem is by breaking it into smaller ones (Problem reduction or decomposition).Our strategy drives the learner to narrate his solution as a story line. In this paper, a real life problem started for Grade 10level with facilitators’ intentions to solve it as a Geometry practice or application; it turned out through narrative problem solving to admit three other different solutions implementing Analytical Geometry, Trigonometry, and Elementary Algebra despite the fact that each of the solutions can be discussed following the didactic contract in different Grade levels to conform with the sequence requirements of K-12 curriculum in Lebanon. In the reflection phase of narrative analysis, the contributors synthesized the importance of geometry to visualize the situation through a geometric drawing ahead of looking for different solutions to the problem. Facilitators also emphasized the importance of narrative problem solving on facilitators’ level and on learners’ level.

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