The development of probabilistic thinking at school requires enhancing combinatorial and proportional reasoning. For this reason, 190 sixth-grade elementary school students (11–12-year-old), without previous instruction in the topic, solve a task consisting of five questions that address both types of reasoning. This study explores the problem-solving strategies used by schoolchildren. The results obtained indicate that, in general, the students do not show strategies in the answers to the combinatorial questions. In addition, it is observed that they have difficulties in understanding the proposed statements and arguing the issues that explicitly require a justification.

The aim of this work is to explore the impact of the use of five lenses for the professional development of mathematics teachers in a Practicum environment of a master’s degree in Teaching in Secondary Schools in Spain, based on based on the video-related model and facilitated by a tutor. This qualitative ethnographic study is part of an action research and focuses on two cases of future secondary mathematics teachers who share a university tutor. The results indicate that the application of the lenses in the video-related model produces signs of changes in professional development, both in terms of the notable events noticed by the teachers and in their narrative, and, in addition, promotes self-regulation of training. It should be noted that, throughout this process, the intervention of the university tutor or facilitator is essential. It is concluded that this model can be replicated in other STEM teacher training specializations.