kvmolurОбразование и саморазвитиеEducation and Self-Development1991-7740Казанский (Приволжский) федеральный университет10.26907/esd.21.2.13YZEQUWkvmolur-247Research ArticleСтатьиРегиональные и гендерные факторы в овладении предметным знанием (на примере математики)Regional and Gender Factors in Mastering Subject Knowledge (Using Mathematics as an Example)https://orcid.org/0000-0002-4679-0701ТуктамышовНаил К.TuktamyshovNail

Казань

Kazan

nail1954@gmail.comhttps://orcid.org/0000-0001-7136-8388ГорскаяТатьяна Ю.GorskayaTatiana

Казань

Kazan

gorskaya@kgasu.ruКазанский государственный архитектурно-строительный университетРоссияKazan State University of Architecture and Civil EngineeringRussian Federation202606072026212185198Copyright © Туктамышов Н.К., Горская Т.Ю., 20262026Туктамышов Н.К., Горская Т.Ю.Tuktamyshov N., Gorskaya T.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://kvmolur.elpub.ru/jour/article/view/247

Необходимость сокращения регионального образовательного разрыва и учет гендерных особенностей в освоении математики обусловливают актуальность работы. Данное исследование впервые объединяет гендерный и региональный аспекты в контексте математического образования. Цель исследования – изучение процесса освоения студентами математических понятий с учетом гендера и условий получения среднего образования (город или село).

В работе использована теория APOS, основанная на конструктивистских принципах. Данная теория описывает поэтапное формирование математических понятий через последовательность ментальных конструкций: действие (Action), процесс (Process), объект (Object) и схема (Schema). Эмпирический материал был получен в ходе письменного опроса, проведенного авторами в 2024 году. Для этого были опрошены студентов Казанского государственного архитектурно-строительного университета. Анализ данных показал различия в уровнях усвоения студентами предметных знаний на примере математики, оценены количественные и качественные характеристики ошибок. Сравнительный анализ допущенных ошибок на каждой стадии APOS показал, что существуют различия в понимании математических терминов у студентов в зависимости от условий получения образования, городского или сельского, и от гендерной принадлежности. Результаты, полученные в статье, помогут преподавателям вузов и учителям корректировать изложения учебного материала с учетом гендерных и региональных различий.

The necessity to reduce the regional educational gap and to consider gender differences in mastering mathematics underscores the relevance of this study. This research is the first to integrate both gender and regional aspects within the context of mathematics education. The aim of the study is to examine the process of students’ acquisition of mathematical concepts, taking into account gender and the conditions of secondary education (urban or rural areas).

This research is based on the APOS theory, which is grounded in constructivist principles. This theory describes the step-by-step formation of mathematical concepts through a sequence of mental constructions: Action, Process, Object, and Schema. The empirical material was obtained from a written survey conducted in 2024 among students of Kazan State University of Architecture and Civil Engineering. The study made it possible to determine the levels of mastery of mathematical concepts and to compare the frequency and nature of students’ errors in different regional groups. The analysis of errors at the APOS stages shows that students’ understanding of mathematical concepts differs depending on the conditions of their secondary education, urban or rural, and on gender. The findings contribute to understanding the impact of gender and regional differences on mastering mathematical concepts, providing university instructors and school teachers with valuable insights for improving instruction.

теория APOSгендерные различиярегиональные различияматематическое образованиеAPOS theorygender differencesregional differencesmathematics educationReferencesГолубовский, В. Н. Социокультурные факторы модернизации профессионального образования // Университетский педагогический журнал. – 2023. – № 1. – С. 10–17. – DOI: 10.33581/2791-2892-2023-1-10-17Arnon, I., Cottrill, J., Dubinsky, E., Oktac, A., Trigueros, S., & Weller, K. (2014). APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education. Springer. https://doi.org/10.1007/978-1-4614-7966-6Громова, Е. В., Сафуанов, И. С. Применение компьютерной математической программы Geogebra в обучении понятию функции // Образование и наука. – 2014. – № 4 (113). – С. 113–131. – DOI: 10.17853/1994-5639-2014-4-113-131Asare, B., & Larbi, E. (2025). Nexus between emotional intelligence and mathematics performance: the role of metacognitive awareness. Cogent Education, 12(1). https://doi.org/10.1080/2331186X.2025.2450117Гумерова, Ф. Ф., Амирова, Л. А., Калимуллина, Г. И., Мустаев, А. Ф., Гумерова, О. В. Определение условий повышения качества образования в сельских школах с низкими образовательными результатами // Science for Education Today. – 2023. – Т. 13. – № 1. – C. 85–107. – DOI: 10.15293/2658-6762.2301.05Azizi, H., & Herman, T. (2020). Critical thinking and communication skills of 10th grade students in trigonometry. Journal of Physics: Conference Series, 1469, 012161. https://doi.org/10.1088/17426596/1469/1/012161Далингер, В. А. Типичные ошибки учащихся по математике и их причины // Современные наукоемкие технологии. – 2014. – № 12-1. – С. 94–97.Caspi, A., & Gorsky, P. (2024). STEM career expectations across four diverse countries: motivation to learn mathematics mediates the effects of gender and math classroom environments. International Journal of STEM Education, 11, 1–15. https://doi.org/10.1186/s40594-024-00511-5Жилкина, Л. Н. Социально-географические особенности образования // Фундаментальные исследования. – 2009. – № 5. – С. 97–98.Chertkova, Y. D., & Egorova, M. S. (2013). Gender differences in mathematical abilities. Psikhologicheskie issledovaniya – Psychological Research, 6(31), 1–20. https://doi.org/10.54359/ps.v6i31.667Каплунович, И. Я. Гендерные различия в структуре визуального мышления // Международный журнал прикладных и фундаментальных исследований. – 2017. – № 11. – C. 295–299.Chesters, J., & Cuervo, H. (2022). (In)equality of opportunity: educational attainments of young people from rural, regional and urban Australia. The Australian Educational Researcher, 49, 43–61. https://doi.org/10.1007/s13384-021-00432-0Кондаурова, И. К., Шапшалова, Т. В. Гендерный подход при обучении математике в школе // Балтийский гуманитарный журнал. – 2017. – Т. 6. – № 1 (18). – С. 168–171.Cutler White, C., & Chapman, D. D. (2024). Rural Parent Viewpoints of What Makes College Possible: A Q Methodology Study. The Rural Educator, 45(2), 43–60. https://doi.org/10.55533/26439662.1399Лебедева, Н. В., Вилкова, К. А. Почему девушки не выбирают STEM: гендерные различия в мотивационных ориентирах // Мониторинг общественного мнения: экономические и социальные перемены. – 2022. – № 3. – С. 115–135. – DOI: 10.14515/monitoring.2022.3.1923Dalinger, V. A. (2014). Typical errors of students in mathematics and their causes. Sovremennye naukojmkie tekhnologii – Modern High Technologies, 12-1, 94–97.Тихомирова, Т. Н., Малых, С. Б. Половые различия в успешности школьного обучения математике и русскому языку: кросскультурное исследование // Сибирский психологический журнал. – 2023. – № 87. – С. 104–123. – DOI: 10.17223/17267080/87/6Darmaji, D., Astalini, A., Kurniawan, D., & Aldila, F. (2022). Gender and Perception: Implementation of Web-based Character Assessment in Science Learning. Journal of Educational Research and Evaluation, 6(1), 131–142. https://doi.org/10.23887/jere.v6i1.37737Туктамышов, Н. К., Горская, Т. Ю. О роли визуализации в обучении математике (на примере понятия функции) // Вектор науки Тольяттинского государственного университета. Серия: Педагогика, психология. – 2022. – № 3. – С. 51–58. – DOI: 10.18323/2221-5662-20223-51-58Dubinsky, E. (2002). Reflective Abstraction in Advanced Mathematical Thinking. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 95–126). Springer. https://doi.org/10.1007/0-30647203-1_7Туктамышов, Н. К., Горская, Т. Ю. Сравнительный анализ сформированности математических понятий у студентов через призму теории APOS: город против села // Психологическая наука и образование. – 2025. – Т. 30. – № 1. – C. 93–104. – DOI: 10.17759/pse.2025300107Dubinsky, E., & Mcdonald, M. A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.), The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 275–282). Springer. https://doi.org/10.1007/0-306-47231-7_25Черткова, Ю. Д., Егорова, М. С. Половые различия в математических способностях // Психологические исследования. – 2013. – Т. 6. – № 31. – C. 1–20. – DOI: 10.54359/ps.v6i31.667Girelli, L. (2023). What does gender has to do with math? Complex questions require complex answers. Journal of Neuroscience Research, 101, 679–688. https://doi.org/10.1002/jnr.25056Штылева, Л. В. Чем обусловлен гендерный разрыв в математическом образовании и STEM-13. занятости выпускников российских школ? // Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки. – 2018. – № 3 (51). – С. 166–173.Golubovski, V. N. (2023). Sociocultural factors of vocational education upgrade. Universitetskij pedagogicheskij zhurnal – University Pedagogical Journal, 1, 10–17. https://doi.org/10.33581/2791-2892-2023-1-10-17Arnon, I., Cottrill, J., Dubinsky, E., Oktac, A., Trigueros, S., Weller, K. APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education. – New York: Springer, 2014. – 254 p. – DOI: 10.1007/978-1-4614-7966-6Gromova, Y. V., & Safuanov, I. S. (2014). Implementation of Geogebra courseware in teaching the concept of mathematical function. Obrazovanie i nauka – The Education and Science Journal, 4(113), 113–131. https://doi.org/10.17853/1994-5639-2014-4-113-131Asare, B., Larbi, E. Nexus between emotional intelligence and mathematics performance: the role of metacognitive awareness // Cogent Education. – 2025. – Vol. 12. – No. 1. – DOI: 10.1080/2331186X.2025.2450117Gumerova, F. F., Amirova, L. A., Kalimullina, G. I., Mustaev, A. F., & Gumerova, O. V. (2023). Determining conditions for improving the quality of education in rural schools with low educational outcomes. Science for Education Today, 13(1), 85–107. https://doi.org/10.15293/26586762.2301.05Azizi, H., Herman, T. Critical thinking and communication skills of 10th grade students in trigonometry // Journal of Physics: Conference Series. – 2020. – Vol. 1469. – 012161. – DOI: 10.1088/1742-6596/1469/1/012161Hadyaoui, A., & Cheniti‐Belcadhi, L. (2023). Exploring the effects of gender in skills acquisition in collaborative learning based on the ontological clustering model. Journal of Computer Assisted Learning, 40(6), 2484–2495. https://doi.org/10.1111/jcal.12852Caspi, A., Gorsky, P. STEM career expectations across four diverse countries: motivation to learn mathematics mediates the effects of gender and math classroom environments // International Journal of STEM Education. – 2024. – Vol. 11. – Pp. 1–15. – DOI: 10.1186/s40594-024-00511-5Kaplunovich, I. Ya. (2017). Gender differences in the structure of visual thinking. Mezhdunarodnyj zhurnal prikladnyh i fundamental’nyh issledovanij – International Journal of Applied and Fundamental Research, 11, 295–299.Chesters, J., Cuervo, H. (In)equality of opportunity: educational attainments of young people from rural, regional and urban Australia // The Australian Educational Researcher. – 2022.– Vol. 49. – Pp. 43–61. – DOI: 10.1007/s13384-021-00432-0Kondaurova, I. K., & Shapshalova, T. V. (2017). Gender approach in the teaching of mathematics at school. Baltijskij gumanitarnyj zhurnal – Baltic Humanitarian Journal, 6(1(18)), 168–171.Cutler White, C., Chapman, D. D. Rural Parent Viewpoints of What Makes College Possible: A Q Methodology Study // The Rural Educator. – 2024. – Vol. 45. – No. 2. – Pp. 43–60. – DOI: 10.55533/2643-9662.1399Koricich, A., Chen, X., & Hughes, R. P. (2018). Understanding the effects of rurality and socioeconomic status on college attendance and institutional choice in the United States. The Review of Higher Education, 41(2), 281–305. https://doi.org/10.1353/rhe.2018.0004Darmaji, D., Astalini, A., Kurniawan, D., Aldila, F. Gender and Perception: Implementation of Web-based Character Assessment in Science Learning // Journal of Educational Research and Evaluation. – 2022. – Vol. 6. – No. 1. – Pp. 131–142. – DOI: 10.23887/jere.v6i1.37737Kuzniak, A., & Nechache, A. (2022). Understanding mathematical work and mathematical thinking through individuals’ actions analyses: a networking approach. In CERME12: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (pp. 2986– 2994).Dubinsky, E. Reflective Abstraction in Advanced Mathematical Thinking // In: Tall, D. (Ed.). Advanced Mathematical Thinking. – Dordrecht: Springer, 2002. – Pp. 95–126. – DOI: 10.1007/0306-47203-1_7Lebedeva, N. V., & Vilkova, K. A. (2022). Why Girls Do Not Choose STEM? Gender Differences in Motivation. Monitoring mneniya: ehkonomicheskie i social’nye issledovaniya – Monitoring of Public Opinion: Economic and Social Changes, 3, 115–135. https://doi.org/10.14515/monitoring.2022.3.1923Dubinsky, E., Mcdonald, M. A. APOS: A constructivist theory of learning in undergraduate mathematics education research // In: Holton, D., Artigue, M., Kirchgräber, U., Hillel, J., Niss, M., Schoenfeld, A. (Eds.). The Teaching and Learning of Mathematics at University Level: An ICMI Study. – Dordrecht: Springer, 2001. – Pp. 275–282. – DOI: 10.1007/0-306-47231-7_25Mali, A., Martinez, P. H., Anastasakis, M., Kouvela, E., & Treffert-Thomas, S. (2022). The interplay between person and environment, cognition and emotion: Using the concept of perezhivanie in mathematics education. In CERME12: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (pp. 3004–3012).Girelli, L. What does gender has to do with math? Complex questions require complex answers // Journal of Neuroscience Research. – 2023. – Vol. 101. – Pp. 679–688. – DOI: 10.1002/jnr.25056Nguyen, H. A., Hou, X., Richey, J., & McLaren, B. (2022). The impact of gender in learning with games: A consistent effect in a math learning game. International Journal of Game-Based Learning (IJGBL), 12(1), 1–29. https://doi.org/10.4018/IJGBL.309128Hadyaoui, A., Cheniti‐Belcadhi, L. Exploring the effects of gender in skills acquisition in collaborative learning based on the ontological clustering model // Journal of Computer Assisted Learning. – 2023. – Vol. 40. – No. 6. – Pp. 2484–2495. – DOI: 10.1111/jcal.12852Parsons, R. (2022). Moving Out to Move Up: Higher Education as a Mobility Pathway in the Rural South. RSF: The Russell Sage Foundation Journal of the Social Sciences, 8(3), 208–229. https://doi.org/10.7758/RSF.2022.8.3.09Koricich, A., Chen, X., Hughes, R. P. Understanding the effects of rurality and socioeconomic status on college attendance and institutional choice in the United States // The Review of Higher Education. – 2018. – Vol. 41. – No. 2. – Pp. 281–305. – DOI: 10.1353/rhe.2018.0004Shtyleva, L. V. (2018). What is the reason for the gender gap in mathematical education and STEM employment of Russian school graduates? Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo. Seriya: Social’nye nauki – Bulletin of N.I. Lobachevsky Nizhny Novgorod University, 3(51), 166–173.Kuzniak, A., Nechache, A. Understanding mathematical work and mathematical thinking through individuals’ actions analyses: a networking approach // CERME12: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education, Italy, February 2022. – Pp. 2986–2994.Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric functions. International Journal of STEM Education, 2, 16. https://doi.org/10.1186/s40594-015-0029-5Mali, A., Martinez, P. H., Anastasakis, M., Kouvela, E., Treffert-Thomas, S. The interplay between person and environment, cognition and emotion: Using the concept of perezhivanie in mathematics education // CERME12: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education, Italy, February 2022. – Pp. 3004–3012.Şefik, Ö., Erdem Uzun, Ö., & Dost, Ş. (2021). Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 15(2), 404–428. https://doi.org/10.17522/balikesirnef.1020526Nguyen, H. A., Hou, X., Richey, J., McLaren, B. The impact of gender in learning with games: A consistent effect in a math learning game // International Journal of Game-Based Learning (IJGBL). – 2022. – Vol. 12. – No. 1. – Pp. 1–29. – DOI: 10.4018/IJGBL.309128Tikhomirova, T. N., & Malykh, S. B. (2023). Gender Differences in School Achievement on Mathematics and Russian Language: Cross-cultural Study. Sibirskiy psikhologicheskiy zhurnal – Siberian journal of psychology, 87, 104–123. https://doi.org/10.17223/17267080/87/6Parsons, R. Moving Out to Move Up: Higher Education as a Mobility Pathway in the Rural South // RSF: The Russell Sage Foundation Journal of the Social Sciences. – 2022. – Vol. 8. – No. 3. – Pp. 208–229. – DOI: 10.7758/RSF.2022.8.3.09Tuktamyshov, N. K., & Gorskaya, T. Yu. (2025). Comparative Analysis of the Formation of Mathematical Concepts among Students through the Prism of APOS Theory: Urban vs. Rural. Psikhologicheskaya nauka i obrazovanie – Psychological Science and Education, 30(1), 93–104. https://doi.org/10.17759/pse.2025300107Siyepu, S. W. Analysis of errors in derivatives of trigonometric functions // International Journal of STEM Education. – 2015. – Vol. 2. – 16. – DOI: 10.1186/s40594-015-0029-5Tuktamyshov, N. K., & Gorskaya, T. Yu. (2022). On the role of visualization in teaching mathematics (using an example of the concept of function). Vektor nauki Tolyattinskogo gosudarstvennogo universiteta. Seriya: Pedagogika, psikhologiya – Vector of Science of Togliatti State University. Series: Pedagogy, Psychology, 3, 51–58. https://doi.org/10.18323/2221-5662-2022-3-51-58Şefik, Ö., Erdem Uzun, Ö., Dost, Ş. Content Analysis of the APOS Theory Studies on Mathematics Education Conducted in Turkey and Internationally: A Meta-Synthesis Study // Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education. – 2021. – Vol. 15. – No. 2. – Pp. 404–428. – DOI: 10.17522/balikesirnef.1020526Welsh, R. O. (2025). Does Rural Mean not Urban? Reconsidering the Conceptualization and Operationalization of Rural School Districts. Urban Education, 60(6), 1530–1565. https://doi.org/10.1177/00420859241227929Welsh, R. O. Does Rural Mean not Urban? Reconsidering the Conceptualization and Operationalization of Rural School Districts // Urban Education. – 2025. – Vol. 60. – No. 6. – Pp. 1530–1565. – DOI: 10.1177/00420859241227929Wood, R. M. (2023). A Review on Education differences in Urban and Rural Areas. International Research Journal of Educational Research, 14(2), 1–3. https://doi.org/10.14303/21415161.2023.254Wood, R. M. A Review on Education differences in Urban and Rural Areas // International Research Journal of Educational Research. – 2023. – Vol. 14. – No. 2. – Pp. 1–3. – DOI: 10.14303/21415161.2023.254Xie, F., Yang, Y., & Xiao, C. (2023). Gender-math stereotypes and mathematical performance: the role of attitude toward mathematics and math self-concept. European Journal of Psychology of Education, 38(2), 695–708. https://doi.org/10.1007/s10212-022-00631-yXie, F., Yang, Y., Xiao, C. Gender-math stereotypes and mathematical performance: the role of attitude toward mathematics and math self-concept // European Journal of Psychology of Education. – 2023. – Vol. 38. – No. 2. – Pp. 695–708. – DOI: 10.1007/s10212-022-00631-yZahl-Thanem, A., & Blekesaune, A. (2025). Social origin and educational choices: A comparative study of rural and urban students’ school track choices in Norway. Acta Sociologica, 68(3), 389–408. https://doi.org/10.1177/00016993241305615Zahl-Thanem, A., Blekesaune, A. Social origin and educational choices: A comparative study of rural and urban students’ school track choices in Norway // Acta Sociologica. – 2025. – Vol. 68. – No. 3. – Pp. 389–408. – DOI: 10.1177/00016993241305615Zhilkina, L. N. (2009). Social-geographical features of education. Fundamental’nye issledovaniya – Fundamental Research, 5, 97–98.

The authors declare that there are no conflicts of interest present.