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| 1 | The article presents an attempt to identify the aspects of development of mathematical abilities of schoolchildren in the process of formation of concepts representing the design in the form of three-dimensional model projected in (substantive, functional and conditional) planes. The model is based on the identified logical characteristics (volume, content, classification), types and stages of formation of the levels of formation of a concept, identified criteria adequate to the four levels of schoolchildern’s MA (discrete, fragmented, structured and holistic). For the first time developed a criterion for assessing the development of schoolchildren’s MА in the formation of concepts, according to which the four levels are marked. In general, the article shows the process of schoolchildren’s MА in the form of multifunctional dynamic and hierarchical model of the formation of concepts embodied at the output of the internal educational product and the student by correcting ascertaining certain result of a higher order. Keywords: development of mathematical abilities of students, notion, preconcepts, criterion, ways and stages of formation, levels, model | 932 | ||||