Аннотация:The present study provides analysis of mathematical concepts as components of personal knowledge. To describe the process of development of school mathematical concepts, we conducted an empirical comparison of representational system of concepts by students with different level of math background. The study revealed that intermediate level students often represent concepts by images of plots transformation or by memorizing the process of calculation, while the most frequent forms of representation for advanced students are verbal, static visual and algebraic representations. These results indicate that development of math concept arises from adequate mathematical activity and then ability to consciously express the meaning of concept emerges.