Students’ approaches while solving a non-typical geometrical problem

In the paper we present the results of two teaching episodes, which took place in two middle school classes with 13- and 14-year-old students. The students in both classes were asked to solve the same geometrical problem;then a discussion followed, in which they had to justify their solutions. In both cases the students had no prior experience in solving non-typical mathematical problems. Additionally, the students were asked to justify theiranswers, which is not a common characteristic of a ‘typical’ mathematics classroom at that level. The problem was chosen from a wider study, in which twenty classes from twenty different schools were analysed. One of theaims of the present study was to analyse the skills that require a deeper understanding of mathematical concepts and properties. Particularly, we aimed to investigate students’ different solution methods and justifications duringproblem solving. The results show considerable differences among the two classes, not only concerning the depth of investigating (which was expected due to the different age groups), but also concerning the relationship betweenachievement (as assessed by the mathematics teacher) and success in solving the problem. These results demonstrate the need for re-directing mathematics education from a pure algorithmic to a deeper thinking approach.