Conference Program

Mathematical knowledge is often associated with a certain dogmatic nature, detached from the world of human meanings and everyday contexts. This can result in a situation where a teacher presents mathematical theory in isolation from the individual needs and cognitive processes of individual students or groups (Zhou 2022).

The philosophy of mathematical practice perspective adopted in our research (Löwe and Müller 2010; Giardino 2018; Carter 2019; Van Kerkhove 2009) does not confer on mathematics the status of exceptional knowledge. Mathematics can be perceived not only as an abstract discipline, but also as a profoundly social phenomenon, as a construct born of interpersonal interactions, a language and tool embedded in social practices. One of the important aspects of this approach is research on the epistemology of visual thinking in cognition, reasoning, and even mathematical proof.

In (Tytko et al. 2023) mathematical practice is described from a psychological and social perspective. There is introduced the notion of Critical Concept Kinds. This notion is strongly related to the presence of visual representations in cognitive processes.

In this presentation, we will focus on a deeper analysis of the proposal of fostering Critical Concept Kinds in math and mathematical education (based on Critical Math Kinds defined by Mangraviti 2024, and Critical Gender Kinds defined by Dembroff 2019).

Df.: „a critical concept kind is a way of working with a concept which destabilizes mainstream ways of working with the “same” concept. Critical individual mental practices are those practices that generate critical concept kinds” (Tytko et al. 2023).

This proposal highlights the gap between the idealistic understanding of mathematical language and the process of creating, applying and learning mathematics, with particular emphasis on the processes and conditions that influence these processes. Especially multimodal aspects. Since the mental mechanisms and relationships observed in mathematical and math education practices can also be observed in other types of human practices, because of their psycho-experiental background, mathematics can also be a tool – especially in the educational context – for analyzing and shaping society.

It is fit to the need in the education model, for changing an absolutist epistemology to one based on critical thinking skills and team/project collaboration (Anna Nitecka-Walerych, 2021). There are two advantages to this:

1. More effective problem-solving at a technical level, based on practice, knowledge, and skills.

2. Contribution to a more inclusive (less harmful) society – complementing Bettcher’s (2014) proposal regarding the existence of multiple worlds of meaning, in which certain concepts have different meanings. Bettcher’s proposal primarily concerns practices that ultimately lead to a change in the meaning of concepts. Our proposal begins by fostering awareness and the need for critical thinking about mathematical concepts, aiming to foster the ability to reconsider dominant concept kinds in the social space, which may be harmful.