DEVELOPMENT OF A CRITERIA-BASED EVALUATION SYSTEM BASED ON THE E.O. OMAROV MATHEMATICAL MODEL FOR THE STUDY OF THE LAWS OF PHONETICS OF THE KAZAKH LANGUAGE

Abstract

This paper presents, for the first time, a criteria-based assessment system for teaching mathematics in grades 5–6, algebra in grade 7, and geometry in grades 7–11 of secondary school. The proposed system is developed on the basis of the apparatus of formal grammars and a mathematical model in the form of an automaton introduced by E.O. Omarov in 1927. This model, ahead of its time, generalizes principles conceptually close to the Turing machine and was originally designed to study the phonetic laws of the Kazakh language. The E.O. Omarov automaton makes it possible to formalize language as a strictly ordered sequence of chains composed of ordered sets (groups of elements), which forms the basis for constructing the input alphabet of the assessment system. The input alphabet is represented by elements of the updated mathematics curriculum, including educational programs, subject content, textbooks, and teaching materials developed by the scientific school of A.Ye. Abylkassymova. The automaton model consists of four main components: the input alphabet, the set of states (memory), the output alphabet, and the mapping between them. The combination of the input alphabet and the set of states allows for the formalization of the structure and content of the educational process and its representation as a strictly ordered system of formative and summative assessment procedures (by sections, quarters, and academic year). Assessment results are generated using various methods, the key one being the descriptor-based approach, which ensures that outcomes are represented in the form of the output alphabet. The proposed system is universal in nature and can be adapted to other subjects, such as physics or biology, by modifying the parameters of the input alphabet. Thus, the developed criteria-based assessment system based on the E.O. Omarov automaton represents a theoretically grounded and practically applicable model in the field of pedagogical sciences, with strong potential for further development through the use of modern computer technologies.