Comparative Analysis of the Formation of Mathematical Concepts among Students through the Prism of APOS Theory: Urban vs. Rural

<p>The materials presented in the article are devoted to studying the influence of regional characteristics, which define the context of the social component of secondary education (in urban and rural areas), on the formation of mathematical concepts among students. The authors aim to demonstrate the degree of formation of mathematical concepts among students depending on the regional aspect. The study presented in this article involved 96 first-year students from the Institute of Construction at Kazan State University of Architecture and Engineering. The research emphasizes that it is grounded in the APOS theory (Action-Process-Object-Schema), which allows for a step-by-step tracking of the understanding process, identifying typical errors and classifying them. According to its principles, a questionnaire was prepared to analyze the process of understanding mathematical concepts among students. The empirical foundation was formed by the data from a written survey conducted among students, with quantitative indicators analyzed at each stage of APOS, considering geographical diversity. Errors were classified as conceptual and procedural, allowing for the recognition of differences in students' competence levels according to the stages of the APOS theory. The work demonstrates the effectiveness of applying the APOS theory to a comparative analysis of the mathematical skills of urban and rural students. The research revealed no statistically significant differences in procedural errors between urban and rural students. The study established that at the Schema stage, statistically significant differences in the mastery of mathematical concepts exist between students from different groups. The article concludes that a step-by-step analysis of students' cognitive development is crucial for identifying their potential and contributes to developing effective teaching methods.</p>