On the assessment of formation of the system of main concepts of mathematical analysis

Abstract

The object of this research is the results of experimental use of the test for inventory of the concepts of mathematical analysis (Calculus Concept Inventory, CCI), which is aimed at assessment of the key concepts of mathematical analysis, such as function, limit and derivative. The test was conducted in the period from 2016 to 2020 and involved Bachelor’s degree students of Financial University under the Government of the Russian Federation on the discipline “Applied Mathematics and Informatics”. “Mathematical Analysis” is one of the key disciplines in formation of mathematical competencies of students majoring “Applied Mathematics and Informatics”. Test was developed by the leading experts from the United States in the area of mathematics and teaching mathematics in the universities, and was implemented in Russian practice for the first time. For quality assessment of the test was applied Cronbach's alpha coefficient, and the results were evaluated based on the Item Response Theory. Although in universities of the United States the implementation of this test showed relatively low effectiveness, for the students of Financial University the coefficient values were significantly higher and allow making an unequivocal conclusion on the informativeness of results. The article also applies the values of discriminant coefficient. Their fluctuation allows using the test not only for assessing the achievement in learning mathematical analysis of students in groups, but also individual results. The results demonstrate that the traditional approach in teaching the principles of mathematical analysis that is widely recognized in the Russian universities is ineffective, which underlines the need to rearrange the content and methods of teaching mathematical analysis in a university.