Technology for organizing mathematical problem solving using the concept of stage-by-stage development of mental actions and criteria-based assessment when training future mathematics teachers

Mathematical knowledge, due to the specific nature of its acquisition through problem solving, plays a special role in the development of various forms of thinking. When solving mathematical problems through the interiorisation of heuristic techniques, a cultural form of creative thinking is formed. The acquisition of analytical heuristics can be influenced by specific methods of organizing the learning process. This paper describes a tool for organizing the teaching of mathematical problem solving as a process aimed at developing guidelines – heuristics – according to the third type of orientation of P.Ya. Galperin’s theory of the stage-by-stage development of mental actions. The paper presents the results of a formative experiment on the acquisition of the proposed framework (the scheme for organizing mental activity, hereinafter referred to as the OMA) by future mathematics teachers while studying the integral calculus of one variable functions. Using the Mann–Whitney U-test, statistically significant differences in the levels of development of the Problem Setting Analysis heuristic were obtained in the control and experimental groups. Due to the small number of groups, a qualitative analysis of the experimental results was conducted. The feasibility of using the OMA framework to implement a strategy of complete acquisition and formative assessment is demonstrated. As it is hypothesized, the systematic use of the OMA framework in teaching to solve problems implements a third-type orientation teaching method and is appropriate for training maths teachers.