Abstract:

The MDM method (mathematical and didactic modeling) is a contraction of the concept of “problem-based learning” (Problem-Based Learning-PBL) in the study of mathematics and computer science and disciplines where mathematics has its own field of application.

The purpose of creating a “mathematical model” is to solve a given problem or task (from various fields of science and technology), which was originally reformulated into mathematical language. When implementing MDM, the part related to “didactic modeling” is a set of technologies and activities aimed at modifying the students' individual experience. This experience includes multidisciplinary knowledge, as well as knowledge of each of the contacting disciplines. However, in addition to the accumulation of new knowledge, the modification of individual experience includes changes in the psycho-physiological settings of students and teachers.

The purpose of the didactic component of MDM is to evaluate and use the regularities that underlie the modification of the student’s individual experience. One of these regularities at the psyche level is the modeling of mental adjustment (MMA), which is related with the task fulfillment of creating a mathematical model and the context surrounding this problem. The formation and structure of the MMA primarily depend on newly emerging interdisciplinary connections. Our approach is close to A.N. Meltzoff and others, designated as “New science of learning”.

We consider the following elements to be significant components of the MMA (as a semantic construction): the purpose of doing, the motive of doing, “context”, “mismatch”, “perception of one’s thinking”.

A large role in the content of the MMA context is made by the historical themes related to the problem of research. We distinguish the logical (mathematical), biological (ideas about the functioning of the human brain), and the social (for example, career growth) components of the MMA context.

We also highlight the important stage of accumulation of experience, which neurophysiologists called "mismatch." It arises due to the fact that the ways of coordinating the metabolic “needs” of neurons that were previously formed within the framework of the existing structure of experience are ineffective under the conditions of a persistent change in the microenvironment of neurons. It is revealed that the artificial "mismatch" of MMA (controlled by the teacher) is a useful link in the learning process.

Students (future teachers of mathematics), in addition to designing a mathematical information model of the proposed phenomenon or process using computer programs, are given the task of developing a methodology for teaching the design of this model to their future students at school. Therefore, they analyze the whole process of developing the MDM project from all sides.

The result of the study is that the implementation of a multidisciplinary approach allows you to model mental adjustment, which, being an integral part of the MDM methodology is an effective means of learning and developing students' cognitive interest in the learning process.

Keywords:

Mathematics, methodology, mathematical and didactic modeling, systemic psychophysiology.