Epistemic and cognitive configurations of preservice teachers when solving a missing value problem

Proportionality is an important integrative thread that connects many of the mathematics topics studied in grade 6-8 (NCTM, 2000). A great deal of research literature on proportional reasoning is located on strategies, errors and difficulties expressed by pupils. Nonetheless, many pre-service teachers show shortcomings in their pedagogical content knowledge to teach it (Ben-Chaim, Keret, & Ilany, 2007). In this short oral we will report the first results of a descriptive study about ratio and proportion knowledge of 60 pre-service teachers, as it is put into action while solving a missing value problem.

The identification of objects and meanings put into effect when educator and students solve a missing value problem was done using the epistemic and cognitive analysis. These analyses have allowed identifying epistemic and cognitive configurations. Using the former, the trainer was able to get an idea of the complexity of mathematical meanings underlying the solutions. Thus the trainer was able to foresee the possible strategies, errors and difficulties that could be manifested by students. This identification, according to Hill, Ball and Schilling (2008), encourage the development of trainer mathematical knowledge for teaching. The teaching model implemented made use of epistemic and cognitive configurations, that in turn, have allowed identifying some relevant issues that could be useful for the educator in his work with pre-service teachers; just to mention a few: (a) the numeric and the algebraic: manifested in the resolution of the problem by using the rule of three, (b) the verbal-symbolic modelling: that transforms the problem statement into a symbolic representation of the rule of three, (c) the symbolic-symbolic modelling: that transforms a symbolic expression (rule of three).