Raising aspects, formulating assumptions and mathematizing in mathematical modeling

Abstract

This paper presents a mathematical modeling activity entitled "the issue of the water bill" conducted with an undergraduate class of future Geography teachers at the Instituto Federal de Minas Gerais – Campus Ouro Preto. The activity had as objective the guidance of the students toward the development of a comprehension of the significance of aspect, assumption and mathematization as related to mathematical modeling, understood as elements not always explicit for students in the construction of models, although commonly implicit in the activity. The analysis shows that student modelers tended to state assumptions in mathematical language and to conceptualize and realize modeling procedures based on arithmetic thinking. Thus, when considering modeling in which students make explicit their judgments on aspects to consider, formulate assumptions and mathematize, interference by the teacher may be important for them to assign meanings to these three actions, as well as to use algebra to generalize arithmetic elaborations.