Mathematical modelling: a methodology favourable to the manifestation of critical mathematics consciousness

Abstract

This study aims to characterise and understand the manifestation of critical mathematics consciousness (CMC) in the modelling process and the relationships that are established between mathematical modelling as a teaching methodology and the development of critical consciousness. Based on a contextualised topic of interest, the students produced mathematical models, and an improved analytical framework based on education for critical mathematical consciousness was used to analyse the interpretations and validations produced. In addition, a questionnaire was applied to ascertain consciousness at an individual level. The results show that the application of the analytical framework generated insights into the development of critical mathematics consciousness. Furthermore, it was noted that the use of questions seems to help in the development of mathematical modelling by deepening discussions and benefiting the development of CMC. This suggestion contributes to the evolution of CMC, through the reflection on social issues in the production of a model. It appears that mathematical modelling is favourable to the manifestation of CMC.

KEYWORDS:

• Critical consciousness
• mathematical modelling
• critical mathematics education
• social justice pedagogy
• differential equations

Disclosure statement

No potential conflict of interest was reported by the author.

Data availability statement

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

Notes

1 In order to obtain a deeper understanding of the world, allowing social and political contradictions to be exposed, Paulo Freire (1974, 2021), when developing the concept of critical consciousness, elaborated a gradation of critical consciousness and included naive critical consciousness.