Technology of implementing the competence-based approach within the school course of mathematics

Introduction. The article describes in detail the stages of the author's technology of implementing the competence-based approach in the educational process, which is demonstrated by the example of teaching the topic of irrationality in the school course of Mathematics. Methodology. The author relies on the methodology and technology of implementing the competence-based approach in the process of teaching and learning mathematics at secondary schools; uses materials and methods of teaching the topic of irrationality. Results. The author introduces two models based on the established technology: the model of basic competence development, and the model of the enhancing teachers’ competence concerning the topic of irrationality. The author introduces a more appropriate definition of the term equality of mathematical objects (equations, inequalities, systems and sets), which contributes to more effective teaching the school course of Mathematics, in particular the topic of irrationality. The article contains a brief outline of the technology of implementing the competence-based approach in education. The author emphasizes that 1) the key concepts of the competence-based approach are very complicated; 2) the concepts of the competence-based approach are often confused; 3) it is difficult to understand the essence of any technology by means of brief schemas. Therefore, the author offers this article, which considers implementing the above-mentioned technology in the process of teaching and learning the topic of the irrationality (also known as "The rational Function of variable degree and its applications"). Choosing this topic is explained by the following reasons: this topic causes great difficulties for teachers (not only Russian), students of pedagogical universities and, as a consequence, high school students; tasks based on this topic are included into the national state examinations; there is a small number of textbooks aimed at mastering the topic of irrationality. Conclusion. Implementation of the proposed technology in teaching Mathematics will contribute to improving the quality of mathematical education and personal development of students.