Resumen

Background: anticipating students’ answers involves reasoning with knowledge from scientific domains supporting the practice of teaching mathematics and it is an evidence of preservice teachers’ reasoning curricular. A key aspect in the geometrical thinking development is to understand the relationship between definition and classification of geometric objects. Thus, the way in which preservice teachers relate the definition and classification can provide information about their curricular reasoning. Objective: the aim of this study is to characterise how preservice teacher anticipate students’ answers to hierarchical classification tasks of quadrilaterals and prisms. Design: the data collection instrument was a hierarchical classification task with four versions in which preservice teacher had to define geometric objects take into account some inclusion conditions. Setting and participants: twenty-eight preservice teacher from a university of Spain participated in this study. Data collection and analysis: the data was collected in two moments, firstly preservice teachers answered to the task with 2d figures and then to the 3d shapes. We carried out an inductive analysis through two phases take into account the specialization of definitions and transitivity of inclusion relationships. Results: we identified three profiles of the preservice teachers' curricular reasoning considering how they define the geometrical object considering the inclusion relations. Furthermore, some variability between the quadrilaterals and prisms was displayed considering curricular reasoning. Conclusions: the results under light the relationship between geometry knowledge and preservice teachers’ curricular reasoning.