Diagnostics of the ability to understand mathematical texts by school graduates

Abstract

The ability to understand the text plays a leading role among the basic educational competencies of students. In this paper the technology for diagnosing the ability to understand mathematical texts by school graduates is presented. The discussed technology is built in accordance with the requirements of ontological diagnostics, which makes the diagnostic result unambiguously interpreted, that is, the tools used in this diagnosis meet the validity requirement. Ontological diagnostics is based on the method of “dialectical deduction” (Hegel’s method), which assumes the choice of an initial predicate for its sequential morphologization with a specific content. In the work, the concept of ontological diagnostics is being clarified as a methodological basis for constructing a conceptual and technological scheme for diagnosing the ability to understand mathematical texts. The construction of a system of postulates that provide the formation of a conceptual and technological scheme of the considered diagnostics is discussed. On the basis of this study, a list of abilities was obtained that provide an adequate understanding of mathematical texts by respondents. As a result, the proposed diagnostics makes it possible to reveal the presence or absence of the certain abilities to understand mathematical texts from this list: the ability to choose a basic predicate corresponding to the proposed subject of thought, i. e. ego; the ability to construct complex predicates by the addition and refinement method based on the selected basic predicates; ability to construct the content of the predicate; the ability to read the content of the predicate and the ability to compare the content of the predicate with ego for their identity. A brief description of the conceptual-technological scheme of the regarded diagnostics is given, and a specific example of the constructed technology application is considered for diagnosing the ability to understand mathematical texts by school graduates.