ORGANIZATION OF REFLEXIVE SEARCH OF SOLUTIONS TO MATHEMATICAL PROBLEMS ON THE BASIS
OF ACTIVITY AND PROCEDURAL APPROACH 

Rodionov Mikhail Alekseevich, Doctor of pedagogical sciences, professor, head of sub-department of theory
and methods of mathematics and informatics teaching, Penza State University, (40 Krasnaya street, Penza, Russia), do7tor@mail.ru
Guseva Elena Valer'evna, Postgraduate student, Penza State University (40 Krasnaya street, Penza, Russia), e.guseva2010@yandex.ru

372.851

Background. Methods of working with mathematical problem take a critical position in the mathematics training methodology. The analysis of pedagogical practice of well-known educators shows that their recommendations do not provide the needed extent (the logical chain of actions, which fits to one or another search aim, is not determined; possible ways to solve the problem are only marked, but these steps don’t fully fit each other). Thus, the goal of this study is to work out the methodology to work with the mathematical problem. In the framework of the activity and procedural approach this methodology should make the search process logical and continuous.
Materials and methods. The analysis of the activity approach options in learning search work shows the necessity to study its procedural part, which is not entirely characterized in psychological and pedagogical research works. When solving mathematical problems it is important to find out the so called «study-and-search view» of the activity approach in a form of the activityprocedural approach. Such work can be organized in a form of logical chain of search actions.
Results. It is described in details that under the activity approach for the methodology for a mathematical problem it is necessary to use procedural search work on the basis of specially organized chain of search actions. This idea preconditioned the necessity of introduction of a category of the activity and procedural approach. The example of its usage is given in the article.
Conclusions. In the framework of the activity and procedural approach the methodology for mathematical problems is a specially organized process of research activity and search actions, which follow it on the surface. It provides the logical and continuous search process due to its reflexive and motivated tone as opposed to other traditional tactics.

reflection of the search process, activity and procedural approach, teaching to search ways to solve mathematical problems, orientation and search activity.

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