Understanding the Problem by Modeling the Subject Area (with the Goal of Creating a Task Generator)
Abstract
This article presents a theoretical analysis of the problem of comprehending educational material in mathematics on the example of a problem that was proposed by NN Pangina as a “touchstone” for studying the interaction of a teacher and a student in organizing the latter’s independent work (from ed.: Pangina’s article is published in this issue of the journal).
The article discusses a methodological approach based on changing the pedagogical goal in relation to the task. Instead of starting with a search for a solution to the problem with specific data and focusing the student’s attention on “building a route” from the conditions of the problem to what needs to be found, it is proposed to build models that allow generating new problems similar to the one given.
This formulation of the problem changes the psychological attitude of the student, relieves him of responsibility for the success of solving a specific problem. At the same time, prompted pushed by the teacher, the student builds various simulation models that can be easily programmed and turned into problem generators, thereby forming a mathematical model of the problem area in which the problem was set.
The proposed approach is based on the activity approach proposed in the works of AN Leontiev in the 70s of the last century [1], the idea of bringing out difficult-to-understand intellectual actions outside in order to use the mechanism of internalization [1, 2] and the works of Simour Papert related to the use of computer artifacts as intermediaries for comprehending new mathematical ideas [3, 4].
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