<?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">10.32517/0234-0453-2022-37-2-64-77</article-id><article-id custom-type="elpub" pub-id-type="custom">infojournal-827</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>ПЕДАГОГИЧЕСКИЕ КАДРЫ</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PEDAGOGICAL STAFF</subject></subj-group></article-categories><title-group><article-title>Формирование ИКТ-компетенций будущего учителя математики при обучении стохастике в условиях цифровой трансформации образования</article-title><trans-title-group xml:lang="en"><trans-title>Formation of ICT competencies of a future mathematics teacher when teaching stochastics in the context of digital transformation of education</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0364-3098</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Латышева</surname><given-names>Л. П.</given-names></name><name name-style="western" xml:lang="en"><surname>Latysheva</surname><given-names>L. P.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Латышева Любовь Павловна, канд. пед. наук, доцент, доцент кафедры высшей математики и методики обучения математике</p><p>г. Пермь</p></bio><bio xml:lang="en"><p>Lyubov P. Latysheva, Candidate of Sciences (Education), Docent, Associate Professor at the Department of Higher Mathematics and Methods of Teaching Mathematics</p><p>Perm</p></bio><email xlink:type="simple">latisheva@pspu.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/0000-0001-9788-7514</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Скорнякова</surname><given-names>А. Ю.</given-names></name><name name-style="western" xml:lang="en"><surname>Skornyakova</surname><given-names>A. Yu.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Скорнякова Анна Юрьевна, канд. пед. наук, доцент, доцент кафедры высшей математики и методики обучения математике</p><p>г. Пермь</p></bio><bio xml:lang="en"><p>Anna Yu. Skornyakova, Candidate of Sciences (Education), Docent, Associate Professor at the Department of Higher Mathematics and Methods of Teaching Mathematics</p><p>Perm</p></bio><email xlink:type="simple">skornyakova_anna@pspu.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/0000-0003-1224-6852</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Черемных</surname><given-names>Е. Л.</given-names></name><name name-style="western" xml:lang="en"><surname>Cheremnykh</surname><given-names>E. L.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Черемных Елена Леонидовна, канд. пед. наук, доцент, и. о. зав. кафедрой высшей математики и методики обучения математике</p><p>г. Пермь</p></bio><bio xml:lang="en"><p>Elena L. Cheremnykh, Candidate of Sciences (Education), Docent, Acting Head of the Department of Higher Mathematics and Methods of Teaching Mathematics</p><p>Perm</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-3276-3793</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Лаптева</surname><given-names>Т. Д.</given-names></name><name name-style="western" xml:lang="en"><surname>Lapteva</surname><given-names>T. D.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Лаптева Татьяна Дмитриевна, студент</p><p>г. Пермь</p></bio><bio xml:lang="en"><p>Tatyana D. Lapteva, undergraduate</p><p>Perm</p></bio><email xlink:type="simple">tanyal1998@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/0000-0002-4904-267X</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Мельникова</surname><given-names>Е. В.</given-names></name><name name-style="western" xml:lang="en"><surname>Melnikova</surname><given-names>E. V.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мельникова Екатерина Викторовна, ассистент кафедры высшей математики и методики обучения математике</p><p>г. Пермь</p></bio><bio xml:lang="en"><p>Ekaterina V. Melnikova, Assistant at the Department of Higher Mathematics and Methods of Teaching Mathematics</p><p>Perm</p></bio><email xlink:type="simple">melnikova_ev@pspu.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru">Пермский государственный гуманитарно-педагогический университет<country>Россия</country></aff><aff xml:lang="en">Perm State Humanitarian Pedagogical University<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>15</day><month>07</month><year>2022</year></pub-date><volume>37</volume><issue>2</issue><fpage>64</fpage><lpage>77</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Латышева Л.П., Скорнякова А.Ю., Черемных Е.Л., Лаптева Т.Д., Мельникова Е.В., 2022</copyright-statement><copyright-year>2022</copyright-year><copyright-holder xml:lang="ru">Латышева Л.П., Скорнякова А.Ю., Черемных Е.Л., Лаптева Т.Д., Мельникова Е.В.</copyright-holder><copyright-holder xml:lang="en">Latysheva L.P., Skornyakova A.Y., Cheremnykh E.L., Lapteva T.D., Melnikova E.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/827">https://info.infojournal.ru/jour/article/view/827</self-uri><abstract><p>Включение в вузовскую подготовку специалиста педагогической сферы авторского курса по изучению функциональных возможностей Электронной пермской образовательной системы (ЭПОС) способствует развитию умения работать в цифровой среде в основном и дополнительном образовании. Преподавание обозначенного курса ориентировано на использование технологий, связанных с реализацией образовательного инжиниринга, в настоящее время вышедшего за рамки технических специальностей и распространившегося на сферу подготовки специалистов в области педагогического дизайна, проектирования образовательных программ и траекторий. Особое внимание в данном курсе уделяется формированию ИКТ-компетенций будущих учителей при разработке цифровых продуктов в процессе изучения профильных дисциплин и курсов по выбору, в частности, таких как «Теория вероятностей и математическая статистика», «Электронная пермская образовательная система», реализуемых на основе применения компетентностно-ориентированного, проектного и инжинирингового подходов. Демонстрируется возможность аккумуляции последних в работе студенческих проектных мастерских в кластере Библиотеки ЭПОС. Результатом деятельности таких мастерских предполагается востребованный в реальной практике обучения и имеющий перспективы дальнейшего использования студентом уже в роли учителя после окончания вуза цифровой образовательный продукт (ЦОП): сценарий урока, электронный тест или другой учебный контент. Формируются специальные задания для студентов, нацеленные на формирование и диагностику ИКТ-компетентности будущих учителей математики в Пермском педагогическом университете. Как правило, выполнение задания включает в себя следующие этапы: разработку аннотации, создание паспорта и предметного содержания ЦОП, организацию апробации, представление презентации, защиту и публикацию разработанных материалов в ЭПОС. Приведено описание диагностики ИКТ-компетентности будущего учителя математики по трем ее компонентам: общепользовательскому, общепедагогическому и предметно-педагогическому.</p></abstract><trans-abstract xml:lang="en"><p>The inclusion of the author’s course of studying the functionality of the “Electronic Perm Educational System” (EPES) in the university training of a pedagogical sphere specialist contributes to the development of the ability to work in a digital environment in basic and additional education. The teaching of this course is focused on the use of technologies related to the implementation of educational engineering, which has now gone beyond the scope of technical specialties and has spread to the field of training specialists in the field of pedagogical design, design of educational programs and trajectories. Particular attention in this course is paid to the formation of ICT competencies of future teachers in the development of digital products in the process of studying specialized disciplines and elective courses, in particular, such as “Probability theory and mathematical statistics”, “Electronic Perm Educational System”, implemented on the basis of competence oriented, design and engineering approaches. The possibility of accumulation of these approaches in the work of student design workshops in the EPES Library cluster is demonstrated. As a result of the activities of such workshops, a digital educational product (DEP) is supposed to be needed in real learning practice and has prospects for further use by the student already in the role of a teacher after graduation: a lesson script, an electronic test or other educational content. Special tasks for students are characterized, aimed at developing and diagnosing the ICT competence of future mathematics teachers at the Perm Pedagogical University. Usually, the solving of the task includes the following stages: development of annotations, creation of a passport and subject content of the DEP, organization of approbation, presentation, defense and publication of the developed materials in EPES. The description of diagnostics of ICT competence of a future mathematics teacher in three of its components is given: general user, general pedagogical and subject-pedagogical.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>педагогическое образование</kwd><kwd>цифровая трансформация образования</kwd><kwd>учитель математики</kwd><kwd>ИКТкомпетентность</kwd><kwd>проектная деятельность</kwd><kwd>инжиниринг</kwd></kwd-group><kwd-group xml:lang="en"><kwd>teacher education</kwd><kwd>digital transformation of education</kwd><kwd>mathematics teacher</kwd><kwd>ICT competence</kwd><kwd>project activities</kwd><kwd>engineering</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">Роберт И. В. Цифровая трансформация образования: вызовы и возможности совершенствования. Информатизация образования и науки. 2020;(3(47)):3–16.</mixed-citation><mixed-citation xml:lang="en">Robert I. V. Digital transformation of education: challenges and opportunities for improvement. Informatization of Education and Science. 2020;(3(47)):3–16. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Robert I. V., Mukhametzyanov I. Sh., Kastornova V. A. Pedagogical and ergonomic conditions for the formation of information educational space. The European Proceedings of Social &amp; Behavioural Sciences EEIA 2019. International Conference “Education Environment for the Information Age”. 2019;(16):647–654. DOI: 10.15405/epsbs.2019.09.02.74</mixed-citation><mixed-citation xml:lang="en">Robert I. V., Mukhametzyanov I. Sh., Kastornova V. A. Pedagogical and ergonomic conditions for the formation of information educational space. The European Proceedings of Social &amp; Behavioural Sciences EEIA 2019. International Conference “Education Environment for the Information Age”. 2019;(16):647–654. DOI: 10.15405/epsbs.2019.09.02.74</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Роберт И. В. Направления развития информатизации отечественного образования периода цифровых информационных технологий. Электронные библиотеки. 2020;(23(1-2)):145–164. DOI: 10.26907/1562-5419-2020-23-1-2-145-164</mixed-citation><mixed-citation xml:lang="en">Robert I. V. Directions of development of informatization of domestic education in the period of digital information technologies. Electronic libraries. 2020;(23(1-2)):145–164. (In Russian.) DOI: 10.26907/1562-5419-2020-23-1-2-145-164</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Груздев М. В., Тарханова И. Ю., Энзельдт Н. В. Образовательный инжиниринг: концептуализация понятия. Ярославский педагогический вестник. 2019;(5(110)):8–15. DOI: 10.24411/1813-145X-2019-10516</mixed-citation><mixed-citation xml:lang="en">Gruzdev M. V., Tarkhanova I. Yu., Enzeldt N. V. Educational engineering: conceptualization of the concept. Yaroslavl Pedagogical Bulletin. 2019;(5(110)):8–15. (In Russian.) DOI: 10.24411/1813-145X-2019-10516</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Anderson R. The Role of Educational Engineer. Journal of Educational Sociology. 1961;34(8):377–381.</mixed-citation><mixed-citation xml:lang="en">Anderson R. The Role of Educational Engineer. Journal of Educational Sociology. 1961;34(8):377–381.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Michael W. M., Wen-chi V. W. Educational Engineering for CALL and MALL. Epoch Making in English Language Teaching and Learning. 2016;14:115–125.</mixed-citation><mixed-citation xml:lang="en">Michael W. M., Wen-chi V. W. Educational Engineering for CALL and MALL. Epoch Making in English Language Teaching and Learning. 2016;14:115–125.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Schunn C. Engineering education Design. Educational designer. 2008;(1(1)):1–21. Available at: http://www.educationaldesigner.org/ed/volume1/issue1/article2</mixed-citation><mixed-citation xml:lang="en">Schunn C. Engineering education Design. Educational designer. 2008;(1(1)):1–21. Available at: http://www.educationaldesigner.org/ed/volume1/issue1/article2</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Зиннурова А. Ф., Габдулхаков В. Ф. Педагогические условия реализации образовательного инжиниринга в высшей школе. Современные проблемы науки и образования. 2021;1:1–5. DOI: 10.17513/spno.30447</mixed-citation><mixed-citation xml:lang="en">Zinnurova A. F., Gabdulkhakov V. F. Pedagogical conditions for the implementation of educational engineering in higher education. Modern Problems of Science and Education. 2021;1:1–5. (In Russian.) DOI: 10.17513/spno.30447</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Андрюхина Л. М. Образовательный инжиниринг в контексте цифровизации. Инновации в профессиональном и профессионально-педагогическом образовании: Материалы 24-й Международной научно-практической конференции. 2019:17–22. Режим доступа: https://elar.rsvpu.ru/bitstream/123456789/28923/1/978-5-8295-0646-9_2019_003.pdf</mixed-citation><mixed-citation xml:lang="en">Andriukhina L. M. Educational engineering in the context of digitalization. Innovations in professional and vocational pedagogical education: Materials of the 24th International Scientific and Practical Conference. 2019:17–22. (In Russian.) Available at: https://elar.rsvpu.ru/bitstream/123456789/28923/1/978-5-8295-0646-9_2019_003.pdf</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Смирнов Е. И. Фундирование опыта педагога-математика в контексте современных достижений в науке. Образование через всю жизнь: непрерывное образование в интересах устойчивого развития. Материалы второго этапа 15-й международной научно-практической конференции. 2017:225–228.</mixed-citation><mixed-citation xml:lang="en">Smirnov E. I. Foundation of the experience of a teachermathematician in the context of modern achievements in science. Lifelong learning: continuing education for sustainable development. Materials of the second stage of the 15th International Scientific and Practical Conference. 2017:225–228. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Институт развития образования. Библиотека ЭПОС. Режим доступа: http://iro.perm.ru/proekty_sub3_sub3.html [Institute of Education Development. The EPES Library. (In Russian.) Available at: http://iro.perm.ru/proekty_sub3_sub3.html]</mixed-citation><mixed-citation xml:lang="en">Institute of Education Development. The EPES Library. (In Russian.) Available at: http://iro.perm.ru/proekty_sub3_sub3.html</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Латышева Л. П., Скорнякова А. Ю., Черемных Е. Л. Цифровые инструменты повышения качества математического образования в педагогическом вузе. Развитие общего и профессионального математического образования в системе национальных университетов и педагогических вузов. Материалы 40-го Международного научного семинара преподавателей математики и информатики университетов и педагогических вузов (Брянск). 2021:181–184.</mixed-citation><mixed-citation xml:lang="en">Latysheva L. P., Skornyakova A. Yu., Cheremnykh E. L. Digital tools for improving the quality of mathematical education in a pedagogical university. Development of general and professional mathematical education in the system of national universities and pedagogical universities. Materials of the 40th International Scientific Seminar of teachers of Mathematics and Computer Science of universities and pedagogical universities (Bryansk). 2021:181–184. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Андреев Г. П., Бугаев Н. И., Михалёва О. И., Романов Н. Н. К столетию метода проектов. Школьные технологии. 2005;4:28–30.</mixed-citation><mixed-citation xml:lang="en">Andreev G. P., Bugaev N. I., Mikhaleva O. I., Romanov N. N. To the centenary of the project method. School technologies. 2005;4:28–30. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Аньшин В. М., Ильина О. Н. Управление проектами: фундаментальный курс. М.: ВШЭ; 2013. 620 с.</mixed-citation><mixed-citation xml:lang="en">Anshin V. M., Ilyina O. N. Project management: fundamental course. Moscow: HSE; 2013. 620 p. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Смирнов Е. И. Проект «Как мне стать более успешным учителем математики». Problems of quality of knowledge and personal self-actualization in terms of social transformations: Peer-reviewed materials digest (collective monograph) published following the results of the XCVI International Research and Practice Conference and I stage of the Championship in Psychology and Educational sciences. 2015:29–33.</mixed-citation><mixed-citation xml:lang="en">Smirnov E. I. Project “How can I become a more successful math teacher”. Problems of quality of knowledge and personal self-actualization in terms of social transformations: Peer-reviewed materials digest (collective monograph) published following the results of the XCVI International Research and Practice Conference and I stage of the Championship in Psychology and Educational sciences. 2015:29–33. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Smirnov E., Uvarov A. Synergy of computer modeling of lateral surface “area” of schwertz’s cylinder. 2017 European Conference on Electrical Engineering and Computer Science (EECS). 2017:76–80. DOI: 10.1109/EECS.2017.24</mixed-citation><mixed-citation xml:lang="en">Smirnov E., Uvarov A. Synergy of computer modeling of lateral surface “area” of schwertz’s cylinder. 2017 European Conference on Electrical Engineering and Computer Science (EECS). 2017:76–80. DOI: 10.1109/EECS.2017.24</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Латышева Л. П., Скорнякова А. Ю., Черемных Е. Л. Проектные решения по организации педагогической коммуникации в условиях цифровизации образования. Пермский педагогический журнал. 2020;11:48– 51. Режим доступа: https://elibrary.ru/download/elibrary_47295232_56533639.pdf</mixed-citation><mixed-citation xml:lang="en">Latysheva L. P., Skornyakova A. Yu., Cheremnykh E. L. Design solutions for the organization of pedagogical communication in the conditions of digitalization of education. Perm Pedagogical Journal. 2020;11:48–51. (In Russian.) Available at: https://elibrary.ru/download/elibrary_47295232_56533639.pdf</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Латышева Л. П., Скорнякова А. Ю., Черемных Е. Л. О цифровой грамотности будущих учителей математики. Advanced Science. 2020;(4(19)):27–30. DOI: 10.25730/VSU.0536.20.036</mixed-citation><mixed-citation xml:lang="en">Latysheva L. P., Skornyakova A. Yu., Cheremnykh E. L. On digital literacy of future mathematics teachers. Advanced Science. 2020;(4(19)):27–30. (In Russian.) DOI: 10.25730/VSU.0536.20.036</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Полат Е. С., Бухаркина М. Ю., Моисеева М. В., Петров А. Е. Новые педагогические и информационные технологии в системе образования. М.: Академия; 2002. 272 с.</mixed-citation><mixed-citation xml:lang="en">Polat E. S., Bukharkina M. Yu., Moiseeva M. V., Petrov A. E. New pedagogical and information technologies in the education system. Moscow: Academy; 2002. 272 p. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Аверкова М. А. Смешанное обучение: возможности и риски. Организация образовательного процесса по технологии на основе моделей смешанного обучения. Пенза; 2020. 44 с. Режим доступа: http://nmc-penza.com.ru/files/sborniki/2020/Аверкова_сборник_по_смешанного_обучения_2020.pdf</mixed-citation><mixed-citation xml:lang="en">Averkova M. A. Blended learning: opportunities and risks. Organization of the educational process by technology based on mixed learning models. Penza; 2020. 44 p. (In Russian.)]</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Хорн М., Стейкер Х. Смешанное обучение. Использование прорывных технологий для улучшения школьного образования. Сан-Франциско: Wiley; 2015. 308 с.</mixed-citation><mixed-citation xml:lang="en">Horn M., Staker H. Mixed learning. Using breakthrough technologies to improve school education. San Francisco: Wiley; 2015. 308 p. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Шилов А. В., Смирнов Е. И., Абатурова В. С. Методика обучения математике с использованием многоэтапных математико-информационных заданий. Математика и информатика, астрономия и физика, экономика и технология и совершенствование их преподавания. Материалы Международной конференции «Чтения Ушинского» физико-математического факультета. 2018:46–52.</mixed-citation><mixed-citation xml:lang="en">Shilov A.V., Smirnov E. I., Abaturova V. S. Methods of teaching mathematics using multi-stage mathematical and informational tasks. Mathematics and computer science, astronomy and physics, economics and technology and improving their teaching. Materials of the International Conference “Readings of Ushinsky” of the Faculty of Physics and Mathematics. 2018:46–52. (In Russian.)</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Библиотека электронных материалов. Режим доступа: https://uchebnik.permkrai.ru/catalogue</mixed-citation><mixed-citation xml:lang="en">Library of electronic materials. (In Russian.) Available at: https://uchebnik.permkrai.ru/catalogue24.	Smirnov E. I., Tikhomirov S. A., Zykova T. V. Managing of mathematics education with synergistic effects. Espacios. 2019;40(9).</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Dvoryatkina S. N., Karapetyan V. S., Dallakyan A. M., Rozanova S. A., Smirnov E. I. Synergetic effects manifestation by founding complexes deployment of mathematical tasks on the chessboard. Problems of Education in the 21st Century. 2019;(77(1)):8–21. DOI: 10.33225/PEC/19.77.08</mixed-citation><mixed-citation xml:lang="en">Dvoryatkina S. N., Karapetyan V. S., Dallakyan A. M., Rozanova S. A., Smirnov E. I. Synergetic effects manifestation by founding complexes deployment of mathematical tasks on the chessboard. Problems of Education in the 21st Century. 2019;(77(1)):8–21. DOI: 10.33225/PEC/19.77.08</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Smirnov E., Dvoryatkina S., Shcherbatykh S. Parameters and structure of neural network databases for assessment of learning outcomes. International Journal of Criminology and Sociology. 2020;9:1638–1648. DOI: 10.6000/19294409.2020.09.188</mixed-citation><mixed-citation xml:lang="en">Smirnov E., Dvoryatkina S., Shcherbatykh S. Parameters and structure of neural network databases for assessment of learning outcomes. International Journal of Criminology and Sociology. 2020;9:1638–1648. DOI: 10.6000/19294409.2020.09.188</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>
