The authors present a coherent picture of the process of problem inversion as an effective tool for developing flexibility of thinking in school students when teaching mathematics. The process of problem inversion is represented as a model in a graphic and symbolical form. Semantic differences between the terms "inverse problem" and "inverted problem" are shown. Some indicators characterizing the process of inversion and inverted problems are introduced. The procedure of problem inversion is described, some methodological features of its main stages are identified. An algorithmic instruction for mathematical problem inversion by school students is proposed.
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