
MAIN PAGE
> Back to contents
Modern Education
Reference:
Volkova E.S., Gisin V.B. —
On the assessment of formation of the system of main concepts of mathematical analysis
// Modern Education.
– 2020. – № 2.
– P. 12  27.
DOI: 10.25136/24098736.2020.2.32942 URL: https://en.nbpublish.com/library_read_article.php?id=32942
On the assessment of formation of the system of main concepts of mathematical analysis
Volkova Elena Sergeevna
PhD in Physics and Mathematics
Docent, the department of Data Analysis, Decisionmaking and Financial Technologies, Financial University under the Government of the Russian Federation
125993 (GSP3), Russia, g. Moscow, ul. Leningradskii Prosp., 49

evolkova@fa.ru



Gisin Vladimir Borisovich
PhD in Physics and Mathematics
Professor, the department of Information Security, Financial University under the Government of the Russian Federation
125993 (GSP3), Russia, g. Moscow, ul. Lenigradskii Prospekt, 49

vgisin@yandex.ru



DOI: 10.25136/24098736.2020.2.32942
Review date:
19052020
Publish date:
26052020
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.
Keywords:
derivative, function, limit, inventory, basuc concepts, CCI test, item response theory, Rush model, calculus, parameter estimation
This article written in Russian. You can find full text of article in Russian
here
.
References
1.

Maslak A. A., Moiseev S. I., Osipov S. A. Sravnitel'nyi analiz otsenok parametrov modeli Rasha, poluchennykh metodami maksimal'nogo pravdopodobiya i naimen'shikh kvadratov // Problemy upravleniya. 2015. № 5. S. 5766.

2.

Brennan R. L. Generalizability theory and classical test theory // Applied Measurement in Education. 2010. V. 24. № 1. P. 121.

3.

Cronbach L. J., Shavelson R. J. My current thoughts on coefficient alpha and successor procedures // Educational and psychological measurement. – 2004. V. 64. № 3. P. 391418.

4.

DiBello L. V., Roussos L. A., Stout W. Review of cognitively diagnostic assessment and a summary of psychometric models (Ch. 31A)/ Rao C. R., Rao C. R., Govindaraju V. (ed.). Handbook of statistics. – Amsterdam: Elsevier, 2006. V. 26. P. 9791030.

5.

Epstein J. The Calculus Concept Inventory — Measurement of the Effect of Teaching Methodology in Mathematics // Notices of the AMS. 2013. V. 60. № 8. P. 10181026.

6.

Fan X. Item response theory and classical test theory: An empirical comparison of their item/person statistics // Educational and psychological measurement. 1998. V. 58. № 3. P. 357381.

7.

Gleason J., White D., Thomas M., Bagley S., Rice L. The calculus concept inventory: a psychometric analysis and framework for a new instrument / Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education.Pittsburgh, Pennsylvania: SIGMAA, 2015. P. 135149.

8.

Gleason J., Bagley S., Thomas M., Rice L., White D. The calculus concept inventory: a psychometric analysis and implications for use // International Journal of Mathematical Education in Science and Technology. 2019. V. 50. № 6. P. 825838.

9.

Hake R. R. Interactiveengagement versus traditional methods: A sixthousandstudent survey of mechanics test data for introductory physics courses // American journal of Physics. 1998. V. 66. № 1. P. 6474.

10.

Hestenes D., Wells M., Swackhamer G. Force concept inventory // The physics teacher. 1992. V. 30. № 3. P. 141158.

11.

Hiebert J., Lefevre P. Conceptual and procedural knowledge in mathematics: An introductory analysis // Conceptual and procedural knowledge: The case of mathematics. 1986. V. 2. P. 127.

12.

Pellegrino J. W., DiBello L. V., James K., Jorion N., Schroeder L. Concept inventories as aids for instruction: A validity framework with examples of application / Proceedings of Research in Engineering Education Symposium.Madrid, Spain: Polytechnic University of Madrid, 2011. P.16.

13.

Pellegrino J. W., DiBello L. V., Brophy S. P. The science and design of assessment in engineering education / Johri A., Olds B. M. (ed.). Cambridge handbook of engineering education research. – Cambridge University Press, 2014. P. 571598.

14.

Steyer R., Smelser N. J., Jena D. Classical (psychometric) test theory / Smelser N. J. et al. (ed.). International encyclopedia of the social and behavioral sciences. – Amsterdam: Elsevier, 2001. P. 19551962.

15.

Suen H. K. Principles of test theories. – N.Y., London: Routledge, 2012. 236 P.

16.

Thomas M., Lozano G. Analyzing Calculus Concept Inventory gains in introductory calculus / Proceedings of the Sixteenth Annual Conference on Research in Undergraduate Mathematics Education.Denver, CO: SIGMAA, 2013. V.2. P. 637646.

Link to this article
You can simply select and copy link from below text field.

