Constructing algebraic problems in special conditions Learning

Abstract

The article explores the theoretical and methodological approaches to designing the content of algebraic problems as a didactic tool aimed at developing mathematical thinking, fostering logical and operational skills, and maintaining the cognitive activity of learners under conditions of limited resources and a non-standard educational environment. The purpose of the article is to determine the theoretical and methodological foundations for designing algebraic problems in special learning conditions, particularly in distance, blended, and crisis-based formats, as well as to analyze the specifics of adapting educational content with regard to learners’ individual educational needs and ensuring the effective acquisition of algebraic competencies. The study employed the following methods: theoretical analysis of scientific literature (content analysis and systematization), the comparative method, and methods of modeling and forecasting. The results of the study identify the key methodological and psychological-pedagogical principles for designing algebraic problems for learners with diverse educational needs in distance, blended, and crisis learning environments. It has been established that the formation of algebraic competencies requires adaptation of task complexity levels, differentiation of solution strategies, and the use of digital resources. The application of step-by-step problem design contributes to increased motivation and the development of critical thinking and analytical skills. The findings confirm the necessity of a systematic approach to the design of educational tasks, taking into account learners’ individual characteristics and the specifics of the educational environment. The conclusions emphasize that designing algebraic problems in specific learning conditions constitutes a component of adaptive pedagogy and a factor in the individualization of the educational process. Its relevance increases in distance, blended, and crisis learning contexts, which necessitate the updating of methodological approaches. The effectiveness of forming algebraic competencies depends on considering learners’ cognitive and motivational-psychological characteristics, task features, the integration of traditional and digital tools, and the differentiation of tasks by complexity level to sustain motivation and prevent overload.