Study of the relationship between ideal and real knowledge in the learning process (based on teaching mathematics)

the article highlights the importance of quality of learning outcomes in teaching Natural Sciences, more specifically, Mathematics. The material reveals the discrepancy between a high level of abstraction in Natural Sciences and Mathematics and insufficient level of abstract thinking of primary and secondary school students. Based on the analysis of literary resources as well as teaching practice, the author suggests an idea how to overcome the above-mentioned conflict through interconnection between ideal and real forms of knowledge in learning. Practical and sensual experiences underlie the development of abstract thinking which contributes to the improvement of visual, kinetic, and metaphoric thinking. The author puts forward the following scheme of idea realization: thing – action − word; and image − action – thing. Fraction addition was used as a valid illustration of effectiveness of the method.