The article is devoted to the development and substantiation of the information-semiotic model of mathematical education as an effective tool that improves the quality of the educational process.
Digital changes and the decline in the importance of simple knowledge actualize the need for models, developing a culture of thinking and students’ metacognitive skills. Modern standards shift the focus to practice and learning outcomes, while maintaining the important role of working out concepts and connections within the academic subject.
The research methodology is based on an integrative approach, combining the principles of semiotics and cognitive psychology. The materials include textbooks, monitoring studies on the level of mathematical education of Russian schoolchildren, and international statistics on trends in mathematical education. The empirical basis of the study is presented by the results of the diagnosis of educational achievements of 75 high school students participating in the experimental application of the model.
Metacognitiveness, which is understood as awareness and regulation of one’s own cognitive processes, is becoming a key factor in learning success. The use of the information-semiotic model increases students’ proficiency in cognitive methods, increases the proportion of successful solutions to problems of increased complexity, and qualitatively changes the perception of mathematical knowledge. The results showed that the model promotes the steady acquisition of mathematical knowledge and builds strong critical thinking skills.
The proposed model has proven its effectiveness by providing a systematic perception of mathematical knowledge, stimulating cognitive flexibility and serving as a tool for metacognitive development. The data indicate significant improvements in learning outcomes and the development of students’ metacognitive abilities. The model demonstrates good adaptability to various levels of mathematical training, opening up prospects for further improvement of educational practices.
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