Divisão entre frações: resolução e discussão de tarefas e de caso de ensino em um curso de Licenciatura em Matemática

This article aims to present the analysis of a classroom activity containing three situations - two tasks and one teaching case - applied during a research with mathematics student-teachers at a private university in Sao Paulo. The goal was to identify the professional knowledge of the future teachers about the meanings of fraction division.  Based on knowledge levels as proposed by Ball, Thames and Phelps, and on mathematics division models as well as on the meanings of division by Pinto and Monteiro, the analyzed task focused on division models as established by Pinto and Monteiro as "division as measurement" and "partition". The research was developed according to the Design Experiment concepts. Data analysis used qualitative methodology. Results showed that participants correctly represent both fraction through partition in assigned figures and the expression of the problem-situation presented. However, they lack knowledge to deal with issues that required the identification of reference units. It was also observed the (re)signifying of required knowledge for the teaching of fraction division on teachers' reflections carried out during the experiment.