The use of reasoning in the resolution of geometric problems

The cognitive processes of 15-year-old students, when they solve geometrical problems involving the construction of isosceles triangles, and the different forms of rea- soning which they use, are investigated in this paper. First we explore the large variety of reasoning processes which appear, categorize them in three approaches (visual, heuristic and theoretical) and look at the language which is used by each one. Then we focus on the weaknesses of students’ reasoning and examine their reasons. The analysis of the data intends to support teachers to recognize and understand the relationship between students’ reasoning (nature of justification) and their geometrical thought.