Cognitive analysis of probability comparison tasks by preservice primary school teachers

To promote mathematical learning, teachers must be able to analyze, interpret and assess students' mathematical activity, making decisions about their understanding of, and difficulties in, solving mathematical tasks. This cognitive analysis skill enables teachers to understand mathematical learning processes and to establish different ways of institutionalizing the mathematical knowledge involved. [Objective] This work is intended to present the results of an assessment of preservice Primary Education teachers' knowledge and abilities to interpret students' responses to probability comparison tasks, identify incorrect strategies and recognize proportional reasoning in mathematical activity. Furthermore, the strategies proposed by preservice teachers to help students overcome the difficulties that led them to obtain inadequate solutions are analyzed. [Methodology] Descriptive and qualitative research was carried out with the collaboration of 116 preservice Primary Education teachers from the University of Almeria (Spain). The investigation was carried out once the process of training in the mathematical contents of Statistics and Probability had been completed. [Results] One of the most important results obtained is a didactic-mathematical knowledge of the type of proportional and probabilistic reasoning that impedes preservice teachers in their interpretation and decision-making about student responses. [Conclusions] These results highlight the need to implement educational solutions to adequately resolve these common situations in schools.