Mathematical concepts are not isolated entities. They form hierarchical systems, with higher or lower levels of generality.
The study undertaken for improving the system for designing teaching activities in school education combines the strategies of fundamental, historical and comparative research, which implies:
- highlighting the theoretical and methodological bases needed to reconstruct the discipline didactics in the curricular spirit;
- identifying the optimal correlations between general and applied pedagogy that may be operationalized at the level of a designing model, needed in the context of teaching-learning-evaluating the discipline;
- analysing the applied methodologies/ didactics (of Mathematics) from a historical (synchronic-diachronic) perspective and exploiting them at the level of the new structure of the models of constructing mathematical concepts of discipline didactics mathematics;
- presenting the basics of applied didactics in terms of objectives, curricular contents, training methodology, evaluation of training, the teaching-learning-evaluation actions of a discipline; designing the teaching activities at the level of some disciplines;
- presenting the epistemological and psychological basics of science didactics, complementary to applied didactics, concerning the models of constructing mathematical concepts.
What is the relation between image and concept in the process of building mathematical concepts by performing reasonings that are subject to other verifications, research, abstractions, desubstantializations with a virtual perfection, existing only at the hypothetical, mental level? Also, in this context, the generalizations performed as notions, concepts, formulas, theorems, rules will be applied to other abstractions.
If we elaborate and present the models on building mathematical concepts, then the students who wish to take on a teaching career will show efficiency in conducting their teaching practice lessons.