Methodical Aspects of Pupils’ Teaching to Solve Mathematical Task

Abstract

Mathematical tasks are the most efficient and often irreplaceable means of assimilation by pupils the concepts, methods of a school course of mathematics and mathematical theories in general. Such tasks play a huge role in development of thinking, mathematical education of pupils and skills how to use math for specific purposes.

The article considers the procedural component of a technique of math teaching. Based on the analysis of scientific and methodical literature, comparison, generalization, studying of pedagogical experience, various approaches to the concept of "task" are considered. The author gives a definition of the above-mentioned concept, offers classification and function of the tasks in math teaching by their perfecting according to the contemporary requirements. In addition, the model of the process of the solution of the task presented by four stages is offered: the analysis of a condition, making the plan of the decision, realization the plan of the decision and examining the found solution.

The result of a research considers the fact that these stages are filled with the content, which, on the one hand, is a self-contained object in a technique of math teaching, on the other hand, it is obviously necessary and a sufficient condition for the realization of stages of the task solution.

The received results can be applied to further theoretical researches as a starting point because the material of article covers structurally all types of activity peculiar to the solution of a mathematical task. The material of article will be useful for the students of "pedagogical education" in the format of a specific lecture where the positions of various authors according to math teaching receive uniform interpretation.

The presented results will be interesting to the expert teachers as they present the structural model for development of a specific method for pupils’ teaching how to solve a concrete type of mathematical tasks. Within the frame of intermediate and final conclusions the author repeatedly emphasizes the positive role of task solving in achievement not only subject mathematical, but also systemic and activity results of teaching.

Keywords: mathematical task, standard and non-standard tasks, solution of a task, stages of the solution of a task, math teaching, teaching how to solve a task.