Pre-service mathematics teachers’ discourse: Differences between defining in task situations involving prototypical and non-prototypical solids

The literature has highlighted the significant role of definitions and defining in mathematics learning and teaching. Furthermore, non-prototypical figures are particularly important when teaching geometry, but teachers and pre-service teachers still have problems defining them. For these reasons, we investigated whether there were differences in the way that pre-service mathematics teachers constructed and selected definitions for prototypical and non-prototypical solids. In particular, the commognitive framework was employed to investigate the differences in the discourse of 33 pre-service secondary-school teachers when constructing and selecting definitions in task situations that involved prototypical and non-prototypical solids. Moreover, we studied if some commognitive conflicts appeared in task situations involving non-prototypical solids but not in similar task situations involving prototypical solids. The findings show some differences between the pre-service teachers’ discourses in both types of task situations. Additionally, some commognitive conflicts appeared only in task situations with non-prototypical solids. Lastly, we classified those commognitive conflicts.