American International Journal of Social Science

Demonstration in Euclidean Geometry
Dr. Naim Rouadi, Noha Husni

Abstract
Drawing out a model or a generalization in mathematic classes for cycle 3 – Grades 7,8 and 9 – is one of the major difficulties the learners face. However, exposing the learners to excessive practice and training on strategies and demonstrations through analysis and intermediate hints can lead to appreciable improvement in the learners’ abilities to solve mathematical problems which come to closure by carrying out a generalization. The aforementioned hypothesis was justified through conducting two examples on particular segments in a triangle in Grades 7, 8, and 9. Two theories support the approach of this action research. The theory of the Dutch researcher - Pierre Marie Van Hiele - who divided the Geometry learning into 5 sequential or linear steps: visualization, analysis, informal deduction, deduction, and rigor. On the other hand, the theory of the French researcher - Alain Kuzniak - who presented the Geometry learning as a back and forth navigation between three levels of Geometry specifying in each level the role of intuition, experience, deduction, kinds of spaces, status of drawing, and the privilege aspect.

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