Countering the ideology of certainty through reflective knowledge in mathematical modeling

Abstract

This article intends to reveal the overlap between certainty in mathematics and the development of a critical view. For this, we use the ideology of certainty concept, which can be understood as a tendency to consider mathematics always right, being the final statement of arguments and applicable in all circumstances, without exception. Additionally, to describe the students’ critical posture, we used reflective knowledge. This qualitative analysis was based on the improvement of the steps suggested by Ole Skovsmose for the development of reflective knowledge. The mathematical modeling activities had topics of interest to the students and were carried out in groups. We found that reflective knowledge tends to improve after the production of a first model and that the development of this knowledge is directly associated with the destabilization of the ideology of certainty. On the other hand, many students found it difficult to delve deeper into reflective knowledge and, consequently, have a greater distance from the ideology of certainty. Thus, we realize that it is necessary that assistance be given to students so that they can improve reflective knowledge and counter the ideology of certainty.