Abstract
The article presents an analysis of a number of projects in which the authors of the article participated. All projects are related to computer support for the productive activities of students in the process of studying mathematics. All analyzed systems can be considered as systems that make human cognitive mechanisms interact with machine “computational intelligence”. Based on the analysis of projects, various ways of coordinating the user’s mental activity with the pseudo-intellectual behavior of systems, which provide an intelligent dialogue in the process of solving mathematical problems, are identified. It is shown that the support of productive activity of students, including research and constructive activity, requires non-standard computer systems, and that the separation of intellectual operations between a learning system and a person supports the productive components of the learning process and initiates the development of new pedagogical approaches.
The study was carried out with the financial support of the Russian Foundation for Basic Research within the framework of the scientific project No. 19-29-14141: study of the relationship between conceptual mathematical concepts, their digital representations and meanings as the basis for the transformation of school mathematics education.
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Akimushkin, V.A., Pozdniakov, S.N., Chukhnov, A.S.: Constructive problems in the structure of the Olympiad in discrete mathematics and theoretical informatics. Olympiads Inform. 11, 3–18 (2017)
Bogdanov, M., Pozdnyakov, S., Pukhov, A.: Multiplicity of the knowledge representation forms as a base of using a computer for the studying of the discrete mathematics. PEDAGOGIKA 96, 136–142 (2009)
Bogdanov, M.S.: Avtomatizaciya proverki resheniya zadachi po formal’nomu opisaniyu ee usloviya/zh. Komp’yuternye instrumenty v obrazovanii 4, 51–57 (2006)
Chukhnov, A.S.: Constructive tasks as a tool of invasive and non-invasive assessment of knowledge. Comput. Tools Educ. 3, 96–104 (2019). https://doi.org/10.32603/2071-2340-2019-3-96-10
Chukhnov, A., Maytarattanakhon, A., Posov, I., Pozdniakov, S.: Constructive graph tasks in distant contests. Inform. Educ. 19(3), 343–359 (2020). https://doi.org/10.15388/infedu.2020.16
Konkurs, E.S.B.: “Konstruiruj, Issleduj, Optimiziruj’’ i ego vliyanie na razvitie tvorcheskih sposobnostej shkol’nikov. Komp’yuternye instrumenty v shkole 2, 18–31 (2020)
Ivanov, S.G.: Rabota na urokah matematiki so sredoj Verifier. Komp’yuternye instrumenty v obrazovanii 1, 58–66 (1998)
Kynigos, S., Lagrange, J.-B.: Cross-analysis as a tool to forge connections amongst theoretical frames in using digital technologies in mathematical learning. Educ. Stud. Math. 85, 321–327 (2014). https://doi.org/10.1007/s10649-013-9521-3
Laborde, C.: Relationships between the spatial and theoretical in geometry: the role of computer dynamic representations in problem solving. In: Tinsley, D., Johnson, D.C. (eds.) Information and Communications Technologies in School Mathematics. ITIFIP, pp. 183–194. Springer, Boston, MA (1998). https://doi.org/10.1007/978-0-387-35287-9_22
Maier, V.R.: Programmirovanie kak instrument poznaniya v kurse geometrii. Informatika i obrazovanie 5, 15–18 (1997)
Mancerov, D.I.: Sreda Verifier-KD: verifikaciya reshenij zadach po matematike. ZH. “Komp’yuternye instrumenty v obrazovanii” 4, 36–41 (2006)
Mancerov, D.I.: Sistema verifikacii dlya parametricheskih klassov zadach po matematike. ZH. Nauchno-tekhnicheskie vedomosti SPbGPU. Informatika, telekommunikacii, upravlenie, 5(65), 183–189 (2008)
Maytarattanakon, A., Posov, I.A.: Automation of distance contests based on research problems in mathematics and informatics. Comput. Tools Educ. 6, 45–51 (2014). (in Russian)
Marvin, M.: A framework for representing knowledge. In: Winston, P.H. (ed.) The Psychology of Computer Vision. McGraw-Hill, New York (1975)
Minsky, M.: The Society of Mind. Simon and Schuster, New York (1987)
Papert, S.: An exploration in the space of mathematics educations. Int. J. Comput. Math. Learn. 1(1), 95–123 (1996). https://doi.org/10.1007/BF00191473
Perchenok, O.V., Pozdnyakov, S.N., Posov, I.A.: Avtomatizaciya proverki resheniya geometricheskih zadach po opisaniyu ih uslovij na predmetno-orientirovannom yazyke. Komp’yuternye instrumenty v obrazovanii. - SPb. 1, 37–44 (2012)
Posov, I.A.: Razbor zadach “Zadacha otshel’nikov” i “Matematicheskoe skalolazanie” konkursa KIO-2009. Komp’yuternye instrumenty v shkole. - SPb. 4, 20–27 (2009)
Pozdniakov, S.N., Posov, I.A., Puhkov, A.V., Tsvetova, I.V.: Science popularization by organizing training activities within the electronic game laboratories. Int. J. Digital Literacy Digital Competence 3(1), 17–31 (2012)
Vavilov, N.A.: Komp’yuter kak novaya real’nost’ matematiki. Komp’yuternye instrumenty v obrazovanii 3, 1–45 (2020)
Wing, J.M.: Computational thinking. Commun. ACM 49, 33–35 (2006)
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Pozdniakov, S., Posov, I., Anton, C. (2021). Interaction of Human Cognitive Mechanisms and “Computational Intelligence” in Systems that Support Teaching Mathematics. In: Cristea, A.I., Troussas, C. (eds) Intelligent Tutoring Systems. ITS 2021. Lecture Notes in Computer Science(), vol 12677. Springer, Cham. https://doi.org/10.1007/978-3-030-80421-3_28
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