In this paper, we aim to show that studies on the new epistemology of mathematics and other sciences are crucial, not only from a theoretical perspective but also in terms of practical aspects, which are particularly significant in the context of teaching and the development of new competences among teachers. The first aspect addressed here is the age of AI and its potential impact, not just on scientists but on society as a whole. The second aspect focuses on mental imagery, which can be influenced by various factors and, in turn, shape scientific thinking. The third aspect, briefly mentioned, is the issue of the social responsibility of science. Our research approach is grounded in actor-network theory as well as the extended mind thesis.
The main problem analysed here is the relationship between the diversity of mental representations and critical concept kinds in the context of solving mathematical problems (e.g., constructing new structures). Our key conclusion is that this diversity in mental representations can be linked to the presence of critical concept kinds, thereby aiding in the effective construction of new concepts and problem-solving. The need for this diversity in representations can – and should – be cultivated and introduced at the educational level.
