{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:34:25Z","timestamp":1760150065995,"version":"build-2065373602"},"reference-count":13,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,2]],"date-time":"2023-10-02T00:00:00Z","timestamp":1696204800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The computational capabilities of computer tools expand the student\u2019s search capabilities. Conducting computational experiments in the classroom is no longer an organizational problem. This raises the \u201cblack box\u201d problem, when the student perceives the computational module as a magician\u2019s box and loses conceptual control over the computational process. This article analyses the use of various computer tools, both existing and specially created for \u201ckey\u201d computational experiments, that aim at revealing the essential aspects of the introduced concepts using specific examples. This article deals with a number of topics of algebra and calculus that are transitional from school to university, and it shows how computational experiments in the form of a \u201ctransparent\u201d box can be used.<\/jats:p>","DOI":"10.3390\/computation11100194","type":"journal-article","created":{"date-parts":[[2023,10,2]],"date-time":"2023-10-02T11:56:49Z","timestamp":1696247809000},"page":"194","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Computational \u201cAccompaniment\u201d of the Introduction of New Mathematical Concepts"],"prefix":"10.3390","volume":"11","author":[{"given":"Andrey","family":"Lavrenov","sequence":"first","affiliation":[{"name":"Department of Algorithmic Mathematics, Saint Petersburg Electrotechnical University \u201cLETI\u201d, ul. Professora Popova 5, 197022 St. Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0552-7245","authenticated-orcid":false,"given":"Elena","family":"Tolkacheva","sequence":"additional","affiliation":[{"name":"Department of Algorithmic Mathematics, Saint Petersburg Electrotechnical University \u201cLETI\u201d, ul. Professora Popova 5, 197022 St. Petersburg, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1899-9145","authenticated-orcid":false,"given":"Sergei","family":"Pozdniakov","sequence":"additional","affiliation":[{"name":"Department of Algorithmic Mathematics, Saint Petersburg Electrotechnical University \u201cLETI\u201d, ul. Professora Popova 5, 197022 St. Petersburg, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,2]]},"reference":[{"key":"ref_1","unstructured":"Leontev, A.N. (1978). Activity, Consciousness, and Personality, Prentice-Hall."},{"key":"ref_2","unstructured":"Shapiro, S.I. (1973). From Algorithms to Judgments (Experiments on Teaching the Elements of Mathematical Thinking), Soviet Radio."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Holton, D., Artigue, M., Kirchgr\u00e4ber, U., Hillel, J., Niss, M., and Schoenfeld, A. (2001). The Teaching and Learning of Mathematics at University Level, Springer. New ICMI Study Series.","DOI":"10.1007\/0-306-47231-7"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/S0732-3123(99)00029-2","article-title":"What Is the Object of the Encapsulation of a Process?","volume":"18","author":"Tall","year":"1999","journal-title":"J. Math. Behav."},{"key":"ref_5","unstructured":"Cook, J.D. (2023, August 03). Psychological Encapsulation. Available online: https:\/\/www.johndcook.com\/blog\/2011\/03\/02\/psychological-encapsulation\/."},{"key":"ref_6","unstructured":"Khinchin, A.Y. (1963). On Formalism in School Teaching of Mathematics, Publishing House of the Academy of Pedagogical Sciences of the RSFSR. (In Russian)."},{"key":"ref_7","unstructured":"Pankratiev, E.V. (2016). Introduction to Computer Algebra, (In Russian)."},{"key":"ref_8","first-page":"51","article-title":"Automation of checking the solution of the problem according to the formal description of its conditions","volume":"4","author":"Bogdanov","year":"2006","journal-title":"Comput. Tools Educ."},{"key":"ref_9","unstructured":"Erdniev, P.M. (1986). Enlargement of Didactic Units in Teaching Mathematics: A Book for Teachers, Computer Prosveschenie. (In Russian)."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Vygotsky, L.S. (1962). Thought and Language, MIT Press.","DOI":"10.1037\/11193-000"},{"key":"ref_11","unstructured":"Papert, S. (1980). Division of HarperCollins 10 E, 53rd, ed., Basic Books, Inc."},{"key":"ref_12","first-page":"106","article-title":"Domain specific language approach to technology-enhanced learning","volume":"3","author":"Pozdniakov","year":"2014","journal-title":"Res. J. Math. Technol."},{"key":"ref_13","unstructured":"Posov, I.A. (2007). Busy Beaver, Computer Tools in Education."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/10\/194\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:04:11Z","timestamp":1760130251000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/11\/10\/194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,2]]},"references-count":13,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["computation11100194"],"URL":"https:\/\/doi.org\/10.3390\/computation11100194","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2023,10,2]]}}}