Mathematics teachers' specialized knowledge regarding fraction division in the context of problem formulation

The aim of this paper is to present the specialized knowledge revealed by mathematics teachers through a training task related to the formulation of fraction division problems. It is a qualitative investigation, and the methodology is an instrumental case study, whose analysis was based on the teachers' productions and plenary discussions during the training. The results show that the teachers have knowledge of: the sense of sharing; solving problems using the invert-multiply algorithm; and continuous representation in rectangular form. However, the teachers have difficulties with the sense of measurement of division; continuous and discrete representation; and problem formulation, especially when the divisor and dividend are fractions. It can be seen that problem formulation contributes to learning fraction division, as it helps to understand mathematical concepts and solve problems.