<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">infojournal</journal-id><journal-title-group><journal-title xml:lang="ru">Информатика и образование</journal-title><trans-title-group xml:lang="en"><trans-title>Informatics and education</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">0234-0453</issn><issn pub-type="epub">2658-7769</issn><publisher><publisher-name>Publishing House Education and Informatics</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.32517/0234-0453-2024-39-3-53-65</article-id><article-id custom-type="elpub" pub-id-type="custom">infojournal-1095</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ПЕДАГОГИЧЕСКИЙ ОПЫТ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PEDAGOGICAL EXPERIENCE</subject></subj-group></article-categories><title-group><article-title>Формирование индивидуальной образовательной траектории студента вуза на основе модифицированного муравьиного алгоритма</article-title><trans-title-group xml:lang="en"><trans-title>Formation of individual educational trajectory of university student based on modified ant colony optimization algorithm</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8185-3010</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Захарченков</surname><given-names>К. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Zakharchenkov</surname><given-names>K. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Константин Васильевич Захарченков, канд. тех. наук, доцент</p><p>электротехнический факультет; кафедра «Программное обеспечение информационных технологий»</p><p>Могилев</p></bio><bio xml:lang="en"><p>Konstantin V. Zakharchenkov, Candidate of Sciences (Engineering), Associate Professor</p><p>Faculty of Electrical Engineering; Department of “Information Technologies Software”</p><p>Mogilev</p></bio><email xlink:type="simple">zaharchenkovkv@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4402-6259</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мрочек</surname><given-names>Т. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Mrochek</surname><given-names>T. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Татьяна Владимировна Мрочек, канд. тех. наук, доцент</p><p>электротехнический факультет; кафедра «Программное обеспечение информационных техно­логий»</p><p>Могилев</p></bio><bio xml:lang="en"><p>Tatiana V. Mrochek, Candidate of Sciences (Engineering), Associate Professor</p><p>Faculty of Electrical Engineering; Department of “Information Technologies Software”</p><p>Mogilev</p></bio><email xlink:type="simple">mrovlad@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4767-6003</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кутузов</surname><given-names>В. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Kutuzov</surname><given-names>V. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Виктор Владимирович Кутузов, канд. тех. наук, доцент, зав. кафедрой</p><p>электротехнический факультет; кафедра «Программное обеспечение информационных технологий»</p><p>Могилев</p></bio><bio xml:lang="en"><p>Victor V. Kutuzov, Candidate of Sciences (Engineering), Docent, Head of the Department</p><p>Faculty of Electrical Engineering; Department of “Information TechnologiesSoftware”</p><p>Mogilev</p></bio><email xlink:type="simple">kutuzov.bru@yandex.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Белорусско-Российский университет<country>Беларусь</country></aff><aff xml:lang="en">Belarusian-Russian University<country>Belarus</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>25</day><month>08</month><year>2024</year></pub-date><volume>39</volume><issue>3</issue><fpage>53</fpage><lpage>65</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Захарченков К.В., Мрочек Т.В., Кутузов В.В., 2024</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="ru">Захарченков К.В., Мрочек Т.В., Кутузов В.В.</copyright-holder><copyright-holder xml:lang="en">Zakharchenkov K.V., Mrochek T.V., Kutuzov V.V.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://info.infojournal.ru/jour/article/view/1095">https://info.infojournal.ru/jour/article/view/1095</self-uri><abstract><p>   Индивидуальная образовательная траектория позволяет предоставить каждому обучающемуся последовательность учебных материалов в соответствии с его темпом, стилем обучения и имеющимися пробелами в познаниях. В условиях цифровизации образования появляется возможность использовать современные способы повышения качества обучения для создания индиви­дуальной образовательной траектории. В статье представлена модель адаптации учебного контента, которая содержит алгоритм построения индивидуальной образовательной траектории, основанный на модифицированном муравьином алгоритме (алгоритме муравьиной колонии) и обеспечивающий персонализированный подбор последовательности учебных материалов. Модель адаптации учебного контента рассматривается на примере изучения языка SQL в рамках курса «Базы данных». Предложенная модификация алгоритма муравьиной колонии позволяет повысить эффективность формирования компетенций при прохождении учебных дисциплин, имеющих значительную продолжительность и состоящих из слабо связанных между собой модулей, за счет отнесения каждого студента к наиболее подходящей подгруппе в соответствии с выбранной профессиональной ролью и организации полноценного повторения на протяжении изучения всей дисциплины. В качестве спецификаторов групп обучающихся предложено использовать желаемый квалификационный уровень освоения языка SQL (базовый или профессиональный) или направление подготовки (специальность). Повторение основ решения задач в процессе изучения дисциплины предложено выполнять на основе определяемых алгоритмом муравьиной колонии значений «феромона», формула для расчета которых обеспечивает высокую вероятность перенаправления студента на решение задач из списка на повторение при превышении допустимого количества взятых подсказок или попыток решения.</p></abstract><trans-abstract xml:lang="en"><p>   Individual educational trajectory allows to provide each learner with a sequence of learning materials in accordance with their pace, learning style and existing gaps in knowledge. Under the conditions of education digitalization, there is an opportunity to use modern ways to improve learning quality to create an individual educational trajectory. The article presents a model of learning content adaptation which contains an algorithm for building an individual educational trajectory based on a modified ant colony optimization algorithm that provides a personalized selection of a sequence of educational materials. The model of learning content adaptation is illustrated on the example of learning SQL within the framework of the course “Databases”. The proposed modification of the ant colony optimization algorithm allows to increase in the efficiency of competence formation in the course of academic disciplines which have a significant duration and consist of loosely related modules by assigning each student to the most appropriate subgroup in accordance with the chosen professional role and organizing full­fledged repetition throughout the discipline. It is proposed to use the desired qualification level of mastering the SQL (basic or professional) or the direction of training (specialty) as specifiers of student groups. The repetition of the basics of problem solving in the process of studying the discipline is proposed to be performed based on pheromone values determined by the ant colony optimization algorithm. The calculating formula for these values provides a high probability of redirecting the student to the solution of problems from the list for repetition when exceeding the permissible number of taken hints or attempts to solve.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>алгоритмы роевого интеллекта</kwd><kwd>муравьиный алгоритм</kwd><kwd>алгоритм муравьиной колонии</kwd><kwd>профессиональ­ная подготовка по SQL</kwd><kwd>компетенции</kwd><kwd>индивидуальная образовательная траектория</kwd><kwd>учет забывания</kwd><kwd>модель обучающегося</kwd><kwd>модель адаптации учебного контента</kwd></kwd-group><kwd-group xml:lang="en"><kwd>swarm intelligence algorithms</kwd><kwd>ant colony optimization algorithm</kwd><kwd>ACO algorithm</kwd><kwd>professional SQL training</kwd><kwd>competencies</kwd><kwd>individual educational trajectory</kwd><kwd>accounting for forgetting</kwd><kwd>learner model</kwd><kwd>training content adaptation model</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Machado M. D. O. C., Bravo N. F. S., Martins A. F., Ber­nardino H. S., Barrere E., De Souza J. F. Metaheuristic-­based adaptive curriculum sequencing approaches : A systematic review and mapping of the literature. Artificial Intelligence Re­view. 2020;54:711–754. DOI: 10.1007/s10462-020-09864-z.</mixed-citation><mixed-citation xml:lang="en">Machado M. D. O. C., Bravo N. F. S., Martins A. F., Ber­nardino H. S., Barrere E., De Souza J. F. Metaheuristic-­based adaptive curriculum sequencing approaches : A systematic review and mapping of the literature. Artificial Intelligence Re­view. 2020;54:711–754. DOI: 10.1007/s10462-020-09864-z.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Шершнева В. А., Вайнштейн Ю. В., Кочеткова Т. О. Адаптивная система обучения в электронной среде. Программные системы: теория и приложения. 2018;9(4):159–177. EDN: DNBANN. DOI: 10.25209/2079-3316-2018-9-4-159-177.</mixed-citation><mixed-citation xml:lang="en">Shershneva V. A., Vainshtein Yu. V., Kochetkova T. O. Adaptive system of web­based teaching. Program Systems: Theory and Applications. 2018;9(4):159–177. (In Russian.) EDN: DNBANN. DOI: 10.25209/2079-3316-2018-9-4-159-177.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Медведева С. Н. Проектирование информационных технологий обучения в профессиональной математической подготовке в инженерном образовании. Казань: Редакционно­-издательский центр «Школа»; 2014. 261 с. EDN: WLJFDT.</mixed-citation><mixed-citation xml:lang="en">Medvedeva S. N. Designing information technology of training in vocational mathematical training in engineering education. Kazan, Editorial and publishing center “Shkola”; 2014. 261 p. (In Russian.) EDN: WLJFDT.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Титовская Н. В., Титовский С. Н. Методика обу­чения будущих IT-­специалистов проектированию и разработке баз данных на основе интерактивного подхода. Вестник Красноярского государственного педагогического университета им. В. П. Астафьева (Вестник КГПУ). 2019;(4(50)):75–87. EDN: CQHLFY. DOI: 10.25146/1995-0861-2019-50-4-164.</mixed-citation><mixed-citation xml:lang="en">Titovskaya N. V., Titovsky S. N. Technique of teaching design and development of databases to future information technology experts. Bulletin of Krasnoyarsk State Pedagogical University Named After V. P. Astafyev (Bulletin KSPU). 2019;(4(50)):75–87. (In Russian.) EDN: CQHLFY. DOI: 10.25146/1995-0861-2019-50-4-164.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Rastegarmoghadam M., Ziarati K. Improved modeling of intelligent tutoring systems using ant colony optimization. Educational Information Technologies. 2016;22:1067–1087. DOI: 10.1007/s10639-016-9472-2.</mixed-citation><mixed-citation xml:lang="en">Rastegarmoghadam M., Ziarati K. Improved modeling of intelligent tutoring systems using ant colony optimization. Educational Information Technologies. 2016;22:1067–1087. DOI: 10.1007/s10639-016-9472-2.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Menai M., Alhunitah H., Al­Salman H. Swarm intelligence to solve the curriculum sequencing problem. Computer Applications in Engineering Education. 2018;26(5):1393–1404. DOI: 10.1002/cae.22046.</mixed-citation><mixed-citation xml:lang="en">Menai M., Alhunitah H., Al­Salman H. Swarm intelligence to solve the curriculum sequencing problem. Computer Applications in Engineering Education. 2018;26(5):1393–1404. DOI: 10.1002/cae.22046.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Bobryakov A. V., Borisov V. V., Yanukovich S. P., Zakharchenkov K. V. A method for managing engineers training processes using swarm intelligence algorithms. Proc. 5sup&gt;th&lt;/sup&gt; Int. Conf. on Information Technologies in Engineering Education (Inforino 2020). New Jersey, USA, Institute of Electrical and Electronics Engineers Inc.; 2020:1–5. EDN: FSUSCL. DOI: 10.1109/Inforino48376.2020.9111788.</mixed-citation><mixed-citation xml:lang="en">Bobryakov A. V., Borisov V. V., Yanukovich S. P., Zakharchenkov K. V. A method for managing engineers training processes using swarm intelligence algorithms. Proc. 5sup&gt;th&lt;/sup&gt; Int. Conf. on Information Technologies in Engineering Education (Inforino 2020). New Jersey, USA, Institute of Electrical and Electronics Engineers Inc.; 2020:1–5. EDN: FSUSCL. DOI: 10.1109/Inforino48376.2020.9111788.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Dharshini A. P., Chandrakumarmangalam S., Arthi G. Ant colony optimization for competency based learning objects sequencing in e­learning. Applied Mathematics and Computation. 2015;263:332–341. DOI: 10.1016/j.amc.2015.04.067.</mixed-citation><mixed-citation xml:lang="en">Dharshini A. P., Chandrakumarmangalam S., Arthi G. Ant colony optimization for competency based learning objects sequencing in e­learning. Applied Mathematics and Computation. 2015;263:332–341. DOI: 10.1016/j.amc.2015.04.067.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Светлов А. В. Особенности методики преподавания курса «Базы данных» для направления подготовки бакалавриата «Прикладная информатика». Вестник Волгоградского государственного университета. Серия 6: Университетское образование. 2012;(13):74–79. EDN: PVUJSB.</mixed-citation><mixed-citation xml:lang="en">Svetlov A. V. Essentials of the teaching the database for undergraduate students in applied informatics. Vestnik Volgogradskogo Gosudarstvennogo Universiteta. Seriya 6: Universitetskoe Obrazovanie. 2012;(13):74–79. (In Russian.) EDN: PVUJSB.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Литвак Е. Г. Методика преподавания проектирования баз данных на основе четырехкомпонентной модели педагогического дизайна. Информатика и образование. 2022;37(4):46–53. EDN: QHQUNG. DOI: 10.32517/0234-0453-2022-37-4-46-53.</mixed-citation><mixed-citation xml:lang="en">Litvak E. G. A methodology for teaching database design based on a four­component instructional design model. Informatics and Education. 2022;37(4):46–53. (In Russian.) EDN: QHQUNG. DOI: 10.32517/0234-0453-2022-37-4-46-53.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Смирнов М. В., Поленок В. М. Опыт разработки веб-­приложения для моделирования реляционных баз данных с функцией прямого инжиниринга для обучения студентов технических специальностей. Информатика и образование. 2021;36(9):55–62. EDN: XMMSOH. DOI: 10.32517/0234-0453-2021-36-9-55-62.</mixed-citation><mixed-citation xml:lang="en">Smirnov M. V., Polenok V. M. Experience in developing a web application for relational databases modeling with a for ward engineering function for training students of technical specialties. Informatics and Education. 2021;36(9):55–62. (In Russian.) EDN: XMMSOH. DOI: 10.32517/0234-0453-2021-36-9-55-62.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Dorigo M., Gambardella L. M. Ant colonies for the travelling salesman problem. Biosystems. 1997;43(2):73–81. DOI: 10.1109/4235.585892.</mixed-citation><mixed-citation xml:lang="en">Dorigo M., Gambardella L. M. Ant colonies for the travelling salesman problem. Biosystems. 1997;43(2):73–81. DOI: 10.1109/4235.585892.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Sivakumar D., Praveena R. Determining optimized learning path for an e­learning system using ant colony optimization algorithm. International Journal of Computer Science &amp; Engineering Technology. 2015;6(2):61–66. Available at: https://ijcset.com/docs/IJCSET15-06-02-059.pdf</mixed-citation><mixed-citation xml:lang="en">Sivakumar D., Praveena R. Determining optimized learning path for an e­learning system using ant colony optimization algorithm. International Journal of Computer Science &amp; Engineering Technology. 2015;6(2):61–66. Available at: https://ijcset.com/docs/IJCSET15-06-02-059.pdf</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Дюличева Ю. Ю. Алгоритмы роевого интеллекта и их применение для анализа образовательных данных. Открытое образование. 2019;23(5):33–43. EDN: RGICOG. DOI: 10.21686/1818-4243-2019-5-33-43.</mixed-citation><mixed-citation xml:lang="en">Dyulicheva Y. Yu. The swarm intelligence algorithms and their application for the educational data analysis. Open Education. 2019;23(5):33–43. (In Russian.) EDN: RGICOG. DOI: 10.21686/1818-4243-2019-5-33-43.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Wong L.­H., Looi C.­K. Adaptable learning pathway generation with ant colony optimization. Educational Technology &amp; Society. 2009;12(3):309–326. Available at: https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=10eea4e23902bf19754c95493d43f9bb246103de</mixed-citation><mixed-citation xml:lang="en">Wong L.­H., Looi C.­K. Adaptable learning pathway generation with ant colony optimization. Educational Technology &amp; Society. 2009;12(3):309–326. Available at: https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=10eea4e23902bf19754c95493d43f9bb246103de</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Allach S., Ahmed M. B., Ghadi A., Essaaidi M. Modeling of e­learning based on ant colony algorithm. International Journal of Networks and Systems. 2012;1(1):37–42. Avail­able at: https://www.researchgate.net/publication/253645653_Modeling_of_e-learning_based_on_Ant_Colony_algorithm</mixed-citation><mixed-citation xml:lang="en">Allach S., Ahmed M. B., Ghadi A., Essaaidi M. Modeling of e­learning based on ant colony algorithm. International Journal of Networks and Systems. 2012;1(1):37–42. Avail­able at: https://www.researchgate.net/publication/253645653_Modeling_of_e-learning_based_on_Ant_Colony_algorithm</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Benabdellah N. C., Gharbi M., Bellafkih M. Ant colony algorithm and new pheromone to adapt units sequence to learners’ profiles. Proc. 9sup&gt;th&lt;/sup&gt; Int. Conf. on Intelligent Systems: Theories and Applications (SITA­14). New Jersey, USA, Institute of Electrical and Electronics Engineers Inc.; 2014:1–8. DOI: 10.1109/SITA.2014.6847300.</mixed-citation><mixed-citation xml:lang="en">Benabdellah N. C., Gharbi M., Bellafkih M. Ant colony algorithm and new pheromone to adapt units sequence to learners’ profiles. Proc. 9sup&gt;th&lt;/sup&gt; Int. Conf. on Intelligent Systems: Theories and Applications (SITA­14). New Jersey, USA, Institute of Electrical and Electronics Engineers Inc.; 2014:1–8. DOI: 10.1109/SITA.2014.6847300.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Kamsa I., Elouahbi R., El Khoukhi F. The combination between the individual factors and the collective experience for ultimate optimization learning path using ant colony algorithm. International Journal on Advanced Science, Engineering and Information Technology. 2018;8(4):1198–1208. DOI: 10.18517/IJASEIT.8.4.2787.</mixed-citation><mixed-citation xml:lang="en">Kamsa I., Elouahbi R., El Khoukhi F. The combination between the individual factors and the collective experience for ultimate optimization learning path using ant colony algorithm. International Journal on Advanced Science, Engineering and Information Technology. 2018;8(4):1198–1208. DOI: 10.18517/IJASEIT.8.4.2787.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Bobryakov A. V., Borisov V. V., Prokopenko S. A., Misnik A. E. Approaches to the implementation of information analytical processes in complex technical­organizational systems. Proc. 5sup&gt;th&lt;/sup&gt; Int. Conf. on Information Technologies in Engineering Education (Inforino 2020). 2020:9111833. EDN: RBGRWS. DOI: 10.1109/Inforino48376.2020.9111833.</mixed-citation><mixed-citation xml:lang="en">Bobryakov A. V., Borisov V. V., Prokopenko S. A., Misnik A. E. Approaches to the implementation of information analytical processes in complex technical­organizational systems. Proc. 5sup&gt;th&lt;/sup&gt; Int. Conf. on Information Technologies in Engineering Education (Inforino 2020). 2020:9111833. EDN: RBGRWS. DOI: 10.1109/Inforino48376.2020.9111833.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Борисов В. В., Мисник А. Е., Прокопенко С. А., Кутузов В. В., Захарченков К. В. Моделирование образовательных процессов на основе нейронечетких темпоральных сетей Петри. Прикладная информатика. 2021;16(4):35–47. EDN: AWVDXP. DOI: 10.37791/2687-0649-2021-16-4-35-47.</mixed-citation><mixed-citation xml:lang="en">Borisov V. V., Misnik A. Е., Prakapenka S. А., Kutuzov V. V., Zakharchenkov K. V. Modeling of educational processes based on neuro­fuzzy temporal Petrinets. Journal of Applied Informatics. 2021;16(4):35–47. (In Russian.) EDN: AWVDXP. DOI: 10.37791/2687-0649-2021-16-4-35-47.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Карпенко А. П. Современные алгоритмы поисковой оптимизации. Алгоритмы, вдохновленные природой. М.: Издательство МГТУ им. Н. Э. Баумана; 2021. 448 с. EDN: NCAEFY.</mixed-citation><mixed-citation xml:lang="en">Karpenko A. P. Modern search engine optimization algorithms. Algorithms inspired by nature. Moscow, Publishing House of Bauman Moscow State Technical University; 2021. 448 p. (In Russian.) EDN: NCAEFY.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Liu Q., Huang J., Wu L., Hu J., Hu M. Study on learner model in adaptive learning system based on ant colony algorithm. Proc. 8sup&gt;th&lt;/sup&gt; Int. Conf. on Hybrid Learning: Innovation in Educational Practices (ICHL 2015). Springer Cham; 2015;9167:267–280. DOI: 10.1007/978-3-319-20621-9_22.</mixed-citation><mixed-citation xml:lang="en">Liu Q., Huang J., Wu L., Hu J., Hu M. Study on learner model in adaptive learning system based on ant colony algorithm. Proc. 8sup&gt;th&lt;/sup&gt; Int. Conf. on Hybrid Learning: Innovation in Educational Practices (ICHL 2015). Springer Cham; 2015;9167:267–280. DOI: 10.1007/978-3-319-20621-9_22.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Ebbinghaus H. Memory: A contribution to experimental psychology. New York, USA, Teachers college, Columbia University; 1913. 142 p. Available at: https://archive.org/stream/memorycontributi00ebbiuoft</mixed-citation><mixed-citation xml:lang="en">Ebbinghaus H. Memory: A contribution to experimental psychology. New York, USA, Teachers college, Columbia University; 1913. 142 p. Available at: https://archive.org/stream/memorycontributi00ebbiuoft</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Черемошкина Л. В., Осинина Т. Н. О забывании учебного материала. Экспериментальная психология. 2011;4(3):97–125. EDN: OJQAWD.</mixed-citation><mixed-citation xml:lang="en">Cheremoshkina L. V., Osinina T. N. Forgetting of educational material. Experimental Psychology (Russia). 2011;4(3):97–125. (In Russian.) EDN: OJQAWD.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Блинов В. И., Сергеев И. С., Родичев Н. Ф. Микрообучение — из бизнеса в образование: перспективное направление развития дидактики. Образование и наука. 2022;24(9):43–68. EDN: ISEUGU. DOI: 10.17853/1994-5639-2022-9-43-68.</mixed-citation><mixed-citation xml:lang="en">Blinov V. V., Sergeev I. S., Rodichev N. F. The microlearning — from business to education: A promising direc­tion for the development of didactics. Education and Science Journal. 2022;24(9):43–68. (In Russian.) EDN: ISEUGU. DOI: 10.17853/1994-5639-2022-9-43-68.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Михайлов И. Э., Балакшин П. В. Метод модификации последовательности интервального повторения, основанный на активности пользователя в сети Интернет. Научно-­технический вестник информационных тех­нологий, механики и оптики. 2019;19(4):689–696. EDN: UFRROB. DOI: 10.17586/2226-1494-2019-19-4-689-696.</mixed-citation><mixed-citation xml:lang="en">Mikhailov I. E., Balakshin P. V. Modi⁄cation method of spaced repetition sequence based on user’s online activity. Scientific and Technical Journal of Information Technologies, Mechanics and Optics. 2019;19(4):689–696. (In Russian.) EDN: UFRROB. DOI: 10.17586/2226-1494-2019-19-4-689-696.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Маклаков А. Г. Общая психология. Санкт-Петербург: Питер; 2012. 583 с.</mixed-citation><mixed-citation xml:lang="en">Maklakov A. G. General psychology. Saint Petersburg, Piter; 2012. 583 p. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Токтарова В. И. Адаптивная система математиче­ской подготовки студентов вуза: учет стилевых типологий обучающихся. Вестник Челябинского государственного педагогического университета. 2017;(6):108–116. EDN: ZHZYML.</mixed-citation><mixed-citation xml:lang="en">Toktarova V. I. Adaptive system of mathematical training of the university students: Accounting of style typologies. Vestnik Chelyabinskogo Gosudarstvennogo Pedagogicheskogo Universiteta. 2017;(6):108–116. (In Russian.) EDN: ZHZYML.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Валуева Е. А., Лаптева Е. М. Феномен подсказки при решении задач: взгляд со стороны психологии творчества. Часть 2. Эффекты подсказки в решении сложных когнитивных задач. Психология. Журнал Высшей школы экономики. 2012;9(3):140–162. EDN: QYXAMT.</mixed-citation><mixed-citation xml:lang="en">Valuyeva E. A., Lapteva E. M. The phenomenon of hint in problem solving: A creativity psychology point of view. Part 2. Hint effects in complex cognitive tasks. Psychology. Journal of Higher School of Economics. 2012;9(3):140–162. (In Russian.) EDN: QYXAMT.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Соколова Т. Н., Гусятников В. Н., Безруков А. И., Каюкова И. В. Методика оценки набора компетенций на основе результатов тестирования. Фундаментальные исследования. 2020;(12):209–215. EDN: IHYEON. DOI: 10.17513/fr.42935.</mixed-citation><mixed-citation xml:lang="en">Sokolova T. N., Gusyatnikov V. N., Bezrukov A. I., Kayukova I. V. Methodology for assessing a set of competencies based on testing results. Fundamental’nyye Issledovaniya. 2020;(12):209–215. (In Russian.) EDN: IHYEON. DOI: 10.17513/fr.42935.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Маслак А. А. Теория и практика измерения латентных переменных в образовании. М.: Юрайт; 2020. 255 с. EDN: RQBLAY.</mixed-citation><mixed-citation xml:lang="en">Maslak A. A. Theory and practice of measuring latent variables in education. Moscow, Yurayt; 2020. 255 p. (In Russian.) EDN: RQBLAY.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Родионов А. В., Братищенко В. В. Применение IRT­-моделей для анализа результатов обучения в рамках компетентностного подхода. Современные проблемы науки и образования. 2014;(4):1–11. EDN: STRMVH.</mixed-citation><mixed-citation xml:lang="en">Rodionov A. V., Bratischenko V. V. Application IRT-model for the analysis training results within the competence approach. Sovremennye Problemy Nauki i Obrazovaniya. 2014;(4):1–11. (In Russian.) EDN: STRMVH.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Кондрашова Е. В. Применение методов математической статистики при проведении педагогического эксперимента. Современные наукоемкие технологии. 2021;(2):162–169. EDN: MOXZVO. DOI: 10.17513/snt.38512.</mixed-citation><mixed-citation xml:lang="en">Kondrashova E. V. Application of mathematical statistics methods in a pedagogical experiment. Sovremennyye Naukoyemkiye Tekhnologii. 2021;(2):162–169. (In Russian.) EDN: MOXZVO. DOI: 10.17513/snt.38512.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
