On the Mastery of Elementary Geometric Concepts

We publish here the report by N.F. Talyzina to a Conference on Psychology in 1955 and released two years later in the proceedings of that conference (N.F. Talyzina [1957]. In B.G. Anan′yeva et al. [Eds.], Materialy soveshchaniia po psikhologii. July 1–6, 1955. Moscow: Publishing House of the Academy of Pedagogical Sciences of the RSFSR.) This report is of particular interest, since it describes some of the first formative experiments based on the theory of planned stage-by-stage formation of mental actions; the text does not yet discuss the formation of actions, but only the application of the attributes of concepts to solving problems. The text presents the results of a study of the formation of elementary geometric concepts according to the theory of planned stage-by-stage formation of mental actions and concepts. Twenty-two subjects from grades 6–9 formed geometric concepts such as “line,” “angle,” “angle bisector,” “perpendicular,” “adjacent angles,” and “supplementary angles.” These attributes were formed in the process of their application to solving different types of problems. Observational and then formative (training) experiments were performed individually. The article contains excerpts from the subjects’ protocols as they solved the problems. It was shown that stage-by-stage development (identifying attributes from a definition, saying them aloud, and then applying them to solving problems) leads to mastery not only of the geometric concepts themselves, but also of the method of action with definitions in general, allowing students to transfer the method they have learned to concepts from another field of knowledge.