تحليل دور أمثلة المتعلمين التلقائية في البرهان الرياضي باستخدام نموذج تولمن : دراسة حالة لطالبات المرحلة الثانوية

الملخص EN

The present research aimed to analyze the role that examples may play in enhancing the ability of high school students to develop mathematical proofs.

As well as identifying the obstacles that might hinder high school students from benefiting from examples in the mathematical proof.

The current research used case study design.

The research sample consisted of twelve female high school students.

The students were divided into six cooperating pairs, and each pair was given one activity sheet to solve it together.

The interactions between students and their written solutions were analyzed using the Toulmin argument model.

Data collection tools were semi-structured task-based interviews, field notes, and student worksheets.

The results clarified five main roles that examples played in helping students to understand and develop the mathematical proof.

These roles are: understanding a mathematical phrase, assessing validity of a mathematical phrase, justification based on observing mathematical structures, generalizing understanding, and refuting conjecture.

The results also revealed some obstacles that hindered some students from benefiting from examples in understanding and developing the proof.

These constraints are: the use of various confirmed examples, the use of experimental examples in a random manner, lack of awareness of the role of counterexamples, and jumping to algebraic solutions.

In light of the findings, the research recommends that students at all levels of classes receive an explicit instruction on how to think strategically about examples and analyze them during proofing activity.