Keywords
formative assessment strategies
integral calculus
self-efficacy
How to Cite
Abstract
In the context of digitalization and distance (or blended) learning, the problem of ensuring high-quality formative assessment during the study of higher mathematics is relevant. Specifically, when studying the integral calculus of a single variable function, there is a need for digital tools that are adapted to the correct display of mathematical symbols, formulas, graphs, etc., and the level of digital skills development of first-year students. The aim of the article is the theoretical substantiation and empirical establishment of the functional capabilities of Google apps (Classroom, Docs, Sheets, Forms) for the implementation of formative assessment strategies (according to Black and Wiliam) and the study of the complex impact of these services on students' self-efficacy. The expert evaluation method was used to establish the correspondence of Google apps to each of the strategies, with consistency confirmed by Kendall's W and Friedman’s tests. It is established that Google Classroom is effective for implementing three of the five strategies (formulation of goals, self- and peer-assessment), and Google Forms is effective for operative data collection on learning and providing feedback. It is statistically established that the systematic and complex application of Google apps for formative assessment during the study of integral calculus of a single variable function contributes to a statistically significant increase in the level of students' self-efficacy (Wilcoxon signed-rank test). The article substantiates the feasibility of the comprehensive and systematic application of Google apps for formative assessment during the study of integral calculus of a single variable function. The obtained results can be used by higher education institution (HEI) lecturers for the reasoned selection of Google apps, taking into account specific formative assessment strategies, the specifics of the study material, and the level of digital skills of students.
References
[1] K. Rakoczya, P. Pingera, J. Hochweberb, E. Kliemea, B. Schützec, M. Besser, “Formative assessment in mathematics: Mediated by feedback's perceived usefulness and students' self-efficacy”, Learning and Instruction, № 60, с. 154–165, 2019. https://doi.org/10.1016/j.learninstruc.2018.01.004.
[2] Н. В. Морзе, В. П. Вембер, М. А. Гладун “3D картування цифрової компетентності в системі освіти України”, Інформаційні технології і засоби навчання, т. 70, №2, с. 28-42, 2019.
[3] P. Pillay, “Online Formative Assessment іn Higher Education Post-Covid 19: a Systematic Review of Challenges and Opportuniies”, Social Sciences and Education Research Review, 11(2), рр. 283-293, 2024. https://doi.org/10.5281/zenodo.15258318.
[4] Н.В Морзе, О.В Барна., В.П. Вембер, “Формувальне оцінювання: від теорії до практики”, Інформатика та інформаційні технології в навчальних закладах, № 6, С. 45-57, 2013.
[5] P. Black, D. Wiliam, “Developing the theory of formative assessment”, Educational Assessment, Evaluation and Accountability, 21, pp. 5-31, 2009. https://doi.org/10.1007/s11092-008-9068-5.
[6] A. Speer, A. Eichler, “Developing Prospective Teachers’ Beliefs about Digital Tools and Digital Feedback”, Mathematics, MDPI, vol. 10(13), рр. 1-20, 2022. https://doi.org/10.3390/math10132192.
[7] О. Спірін, Т. Вакалюк, “Критерії добору відкритих web-opiєнтованих технологій навчання основ програмування майбутніх учителів інформатики”, Інформаційні технології і засоби навчання, т. 60, вип. 4, с. 275-287, 2017.
[8] D. J. Nicol, D. Macfarlane‐Dick, “Formative assessment and self‐regulated learning: a model and seven principles of good feedback practice”, Studies in Higher Education, 31(2), pp. 199-218, 2006. https://doi.org/10.1080/03075070600572090.
[9] О. Локшина, “Інновації в оцінюванні навчальних досягнень учнів у шкільній освіті країн Європейського союзу”, Порівняльно-педагогічні студії, № 2, с. 107-113, 2009. https://doi.org/10.31499/2306-5532.2.2009.18073.
[10] Н. Морзе, В. Вембер, М.Бойко. “Використання цифрових технологій для формувального оцінювання”, Відкрите освітнє е-середовище сучасного університету, Вип. Спецвип, с. 202-214, 2019.
[11] M. S. Mahanan, Talib C. Abdul, N. H. Ibrahim, “Online formative assessment in higher STEM education; a systematic literature review”, Asian Journal of Assessment in Teaching and Learning, 11 (1), рр. 47-62, 2021. https://doi.org/10.37134/ajatel.vol11.1.5.2021.
[12] B.R. Belland, A.E. Walker, N.J. Kim, M. Lefler, “Synthesizing results from empirical research on computer-based scaffolding in STEM education: A meta-analysis”, Review of Educational Research,. 87, pp. 309–344, 2017. doi: 10.3102/0034654316670999.
[13] L. Paleczek, E. Pölzl-Stefanec, K. Otrel-Cass, “Special Issue: Rethinking educational practices and responsibilities in the light of digitalisation”, International Journal of Educational Research, vol. 119, pр.102075, 2023. doi: 10.1016/j.ijer.2022.102075.
[14] D.T Tempelaar, B. Kuperus, H. Cuypers et al. “The Role of Digital, Formative Testing in e-Learning for Mathematics: A Case Study in the Netherlands”, Revista de Universidad y Sociedad del Conocimiento, 9, рр. 284-305, 2012. https://doi.org/10.7238/rusc.v9i1.1272.
[15] F. Azmi, M. Kankarej, “The Role of Formative Assessment in Teaching Mathematics”, International Conference for e-learning & Distance Education, рр. 1‒12, 2015. [Електронний ресурс]. Доступно: https://www.researchgate.net/publication/357397223_The_Role_of_Formative_Assessment_in_Teaching_M athematics. Дата звернення: Лип.19, 2025.
[16] P. A. Ertmer, “Teacher pedagogical beliefs: The final frontier in our quest for technology integration?” Educational Technology Research and Development, 53(4), рр. 25-40, 2005. [Електронний ресурс]. Доступно: https://www.learntechlib.org/p/67720/. Дата звернення: Лип.19, 2025.
[17] A. Haj-Yahya, S. Olsher, “Preservice teachers’ experiences with digital formative assessment in mathematics”, International Journal of Mathematical Education in Science and Technology, 53(7), рр. 1751–1769, 2020. https://doi.org/10.1080/0020739X.2020.1842527.
[18] J. Anderson, “Frequent Feedback through Google Forms”, PRIMUS, 29, pp. 124–137. 2019. doi:10.1080/10511970.2017.1411408.
[19] R. Reynaga-Chávez, Y.-L. Huamán-Romaní, J.-M. Burga-Falla et all, “The Perspective’s Analysis of Formative Assessment with University Students”, TEM Journal, vol. 12, № 2, pр. 876–882, 2023. doi: 10.18421/TEM122-33.
[20] G. F. C. Lim, N. A. Jalil, , D. S. A. Hidup, M. Omar, , F. M. Kamaruzaman, & M. Z. A. Majid, “The Use of Google Forms in Teaching and Learning based on Teachers’ Perspective”, International Journal of Academic Research in Business and Social Sciences, 13(12), рр. 3746–3761, 2023. http://dx.doi.org/10.6007/IJARBSS/v13-i12/20221.
[21] Z. Nurusshofa, E. N. Stujanna, M. Mawi, , R. A. Putranti, W. Sumartono, S. E. Purwanto, W. S. Sukary, & R. E. Edison, “Google Form or Quizizz, which is Better?” JIIP - Jurnal Ilmiah Ilmu Pendidikan, 6(10), 7791-7794, 2023. https://doi.org/10.54371/jiip.v6i10.2693.
[22] A.Bensfiya, S.Boubih, M. Madrane, & R. Janati-Idrissi, “Exploring digital alternatives for learning assessment: a comparative study of Google Forms and QCM CAM”, The International Journal of Science Didactics and Educational Engineering, 1(1), рр. 44–55, 2023. https://doi.org/10.34874/PRSM.ijsdee-vol1iss1.877.
[23] D. Kilic, “An Examination of Using Self-, Peer-, and Teacher-Assessment in Higher Education: A Case Study in Teacher Education”, Higher Education Studies, vol. 6, № 1, рр. 136-144, 2016. doi: 10.5539/hes.v6n1p136.
[24] J. König, D. J. Jäger-Biela, & N. Glutsch, “Adapting to online teaching during COVID-19 school closure: teacher education and teacher competence effects among early career teachers in Germany”, European Journal of Teacher Education, 43(4), рр. 608–622, 2020. https://doi.org/10.1080/02619768.2020.180965.
[25] Я. Б. Сікора, “Теоретико-методичні засади адаптивної системи професійної підготовки майбутніх фахівців з інформаційних технологій в умовах цифровізації,” Дис. на здобуття наук. ступеня доктора пед. наук, Житомирський державний університет імені Івана Франка, Житомир, Україна, 2025. [Електронний ресурс]. Доступно: https://eprints.zu.edu.ua/42611/1/dys-Sikora.pdf. Дата звернення: 19 Лип., 2025.
[26] І. М. Калініна, “Формувальне оцінювання навчальних досягнень здобувачів вищої освіти”, Грааль науки, 5, с. 285–290, 2021. [Електронний ресурс]. Доступно: https://ojs.ukrlogos.in.ua/index.php/grail-of-science/article/view/13126/12063. Дата звернення: Лип.19, 2025.
[27] J. Fraile, M. Monguillot, C. González-Arévalo, P. Lehane, & E. Panadero, “Investigating anonymity in formative and summative peer assessment: Effects on university students’ social-affective factors, perceptions and preference”, Studies in Educational Evaluation, 83, рр. 1-12, 2024. https://doi.org/10.1016/j.stueduc.2024.101410.
[28] A. Bandura, “Perceived Self-Efficacy in Cognitive Development and Functioning”, Educational Psychologist, 28(2), pp. 117–148, 1993. https://doi.org/10.1207/s15326985ep2802_3.
[29] E. A. Panadero, “Review of Self-regulated Learning: Six Models and Four Directions for Research”, Frontiers in Psychology, 8, 2017. doi: 10.3389/fpsyg.2017.00422. PMID: 28503157; PMCID: PMC5408091.
[30] K. Maskos, A. Schulz, S. S. Oeksuez, & K. Rakoczy,”Formative Assessment in Mathematics Education: A Systematic Review”, ZDM Mathematics Education, 57, pp. 679-693, 2025. https://doi.org/10.1007/s11858-025-01696-x.
[31] Tin, Ting Tin et al. “Exploring the Impact of Google Education Tools on Student Engagement, Learning Motivation, and Academic Performance”, Pakistan Journal of Life and Social Sciences, vol. 22, № 2, pp. 15975–15993, 2024. https://doi.org/10.57239/PJLSS-2024-22.2.001159.
REFERENCES (TRANSLATED AND TRANSLITERATED)
[1] K. Rakoczya, P. Pingera, J. Hochweberb, E. Kliemea, B. Schützec, M. Besser, “Formative assessment in mathematics: Mediated by feedback's perceived usefulness and students' self-efficacy”, Learning and Instruction, № 60, с. 154–165, 2019. https://doi.org/10.1016/j.learninstruc.2018.01.004. (in English)
[2] N. V. Morze, V. P. Vember, M. A. Gladun «3D Mapping оf Digital Competency іn Ukrainian Education System, Information Technologies and Learning Tools, vol. 70, №2, pр. 28-42, 2019. (in Ukrainian).
[3] P. Pillay, “Online Formative Assessment іn Higher Education Post-Covid 19: a Systematic Review of Challenges and Opportuniies”, Social Sciences and Education Research Review, 11(2), рр. 283-293, 2024. https://doi.org/10.5281/zenodo.15258318. (in English)
[4] N. V. Morse, O. V. Barna, V. P. Vember, “Formative assessment: from theory to practice”, Informatics and Information Technologies in Educational Establishments, (6), 45–57, 2013. (in Ukrainian)
[5] P. Black, D. Wiliam, “Developing the theory of formative assessment”, Educational Assessment, Evaluation and Accountability, 21, pp. 5-31, 2009. https://doi.org/10.1007/s11092-008-9068-5. (in English)
[6] A. Speer, A. Eichler, “Developing Prospective Teachers’ Beliefs about Digital Tools and Digital Feedback”, Mathematics, MDPI, vol. 10(13), рр. 1-20, 2022. https://doi.org/10.3390/math10132192. (in English)
[7] O. M. Spirin, T. A.Vakaliuk, «Сriteria of open web-operated technologies of teaching the fundamentals of programs of future teachers of informatics», Information Technologies and Learning Tools, vol. 60, № 4, Р. 275-287, 2017. (in Ukrainian)
[8] D. J. Nicol, D. Macfarlane‐Dick, “Formative assessment and self‐regulated learning: a model and seven principles of good feedback practice”, Studies in Higher Education, 31(2), pp. 199-218, 2006. https://doi.org/10.1080/03075070600572090. (in English)
[9] O. Lokshyna, "Innovations in Assessing Student Learning Achievements in School Education of European Union Countries", Comparative Pedagogical Studies , № 2, рр. 107-113, 2009. (in Ukrainian)
[10] N. Morze, V. Vember, M, Gladun, “Using оf digital Technologies for Formative Assessment”, Open educational e-environment of modern University, special editio, pp. 202-214, 2019. (in Ukrainian)
[11] M. S. Mahanan, Talib C. Abdul, N. H. Ibrahim, “Online formative assessment in higher STEM education; a systematic literature review”, Asian Journal of Assessment in Teaching and Learning, 11 (1), рр. 47-62, 2021. https://doi.org/10.37134/ajatel.vol11.1.5.2021. (in English)
[12] B. R. Belland, A.E. Walker, N.J. Kim, M. Lefler, “Synthesizing results from empirical research on computer-based scaffolding in STEM education: A meta-analysis”, Review of Educational Research,. 87, pp. 309–344, 2017. doi: 10.3102/0034654316670999. (in English)
[13] L. Paleczek, E. Pölzl-Stefanec, K. Otrel-Cass, “Special Issue: Rethinking educational practices and responsibilities in the light of digitalisation”, International Journal of Educational Research, vol. 119, pр.102075, 2023. doi: 10.1016/j.ijer.2022.102075. (in English)
[14] D. T Tempelaar, B. Kuperus, H. Cuypers et al. “The Role of Digital, Formative Testing in e-Learning for Mathematics: A Case Study in the Netherlands”, Revista de Universidad y Sociedad del Conocimiento, 9, рр. 284–305, 2012. https://doi.org/10.7238/rusc.v9i1.1272. (in English)
[15] F. Azmi, M. Kankarej, “The Role of Formative Assessment in Teaching Mathematics”, International Conference for e-learning & Distance Education, рр. 1‒12, 2015. [Online]. Available: https://www.researchgate.net/publication/357397223_The_Role_of_Formative_Assessment_in_Teaching_Mathematics. Accessed on: July 19, 2025. (in English)
[16] P. A. Ertmer, “Teacher pedagogical beliefs: The final frontier in our quest for technology integration?” Educational Technology Research and Development, 53(4), рр. 25-40, 2005. [Online]. Available: https://www.learntechlib.org/p/67720/. Accessed on: July 19, 2025. (in English)
[17] A. Haj-Yahya, S. Olsher, “Preservice teachers’ experiences with digital formative assessment in mathematics”, International Journal of Mathematical Education in Science and Technology, 53(7), рр. 1751–1769, 2020. https://doi.org/10.1080/0020739X.2020.1842527. (in English)
[18] J. Anderson, “Frequent Feedback through Google Forms”, PRIMUS, 29, pp. 124–137. 2019. doi:10.1080/10511970.2017.1411408. (in English)
[19] R. Reynaga-Chávez, Y.-L. Huamán-Romaní, J.-M. Burga-Falla et all, “The Perspective’s Analysis of Formative Assessment with University Students”, TEM Journal, vol. 12, № 2, pр. 876–882, 2023. doi: 10.18421/TEM122-33. (in English)
[20] G. F. C. Lim, N. A. Jalil, , D. S. A. Hidup, M. Omar, , F. M. Kamaruzaman, & M. Z. A. Majid, “The Use of Google Forms in Teaching and Learning based on Teachers’ Perspective”, International Journal of Academic Research in Business and Social Sciences, 13(12), рр. 3746–3761, 2023. http://dx.doi.org/10.6007/IJARBSS/v13-i12/20221. (in English)
[21] Z. Nurusshofa, E. N. Stujanna, M. Mawi, , R. A. Putranti, W. Sumartono, S. E. Purwanto, W. S. Sukary, & R. E. Edison, “Google Form or Quizizz, which is Better?” JIIP - Jurnal Ilmiah Ilmu Pendidikan, 6(10), 7791-7794, 2023. https://doi.org/10.54371/jiip.v6i10.2693. (in English)
[22] A. Bensfiya, S. Boubih, M. Madrane, & R. Janati-Idrissi, “Exploring digital alternatives for learning assessment: a comparative study of google forms and qcm cam”, The International Journal of Science Didactics and Educational Engineering, 1(1), рр. 44–55, 2023. https://doi.org/10.34874/PRSM.ijsdee-vol1iss1.877. (in English)
[23] D. Kilic, “An Examination of Using Self-, Peer-, and Teacher-Assessment inHigher Education: A Case Study in Teacher Education”, Higher Education Studies, vol. 6, № 1, рр. 136-144, 2016. doi: 10.5539/hes.v6n1p136. (in English)
[24] J. König, D. J. Jäger-Biela, & N. Glutsch, “Adapting to online teaching during COVID-19 school closure: teacher education and teacher competence effects among early career teachers in Germany”, European Journal of Teacher Education, 43(4), рр. 608–622, 2020. https://doi.org/10.1080/02619768.2020.180965. (in English)
[25] Y. B. Sikora, “Theoretical and methodological principles of adaptive system of professional training of future information technology specialists in the conditions of digitalization,” Ph.D. dissertation, Zhytomyr Ivan Franko State Univ., Zhytomyr, Ukraine, 2025. [Online]. Available: https://eprints.zu.edu.ua/42611/1/dys-Sikora.pdf. Accessed: 19 July, 2025. (in Ukrainian)
[26] I. M. Kalinina, "Formative Assessment of Learning Achievements of Higher Education Applicants", Grail of Science, 5, pp. 285–290, 2021. [Online]. Available: https://ojs.ukrlogos.in.ua/index.php/grail-of-science/article/view/13126/12063. Accessed on: July 19, 2025. (in Ukrainian)
[27] J. Fraile, M. Monguillot, C. González-Arévalo, P. Lehane, & E. Panadero, “Investigating anonymity in formative and summative peer assessment: Effects on university students’ social-affective factors, perceptions and preference”, Studies in Educational Evaluation, 83, рр. 1-12, 2024. https://doi.org/10.1016/j.stueduc.2024.101410. (in English)
[28] A. Bandura, “Perceived Self-Efficacy in Cognitive Development and Functioning”, Educational Psychologist, 28(2), pp. 117–148, 1993. https://doi.org/10.1207/s15326985ep2802_3. (in English)
[29] E. A. Panadero, “Review of Self-regulated Learning: Six Models and Four Directions for Research”, Frontiers in Psychology, 8, 2017. doi: 10.3389/fpsyg.2017.00422. PMID: 28503157; PMCID: PMC5408091. (in English)
[30] K. Maskos, A. Schulz, S. S. Oeksuez, & K. Rakoczy,”Formative Assessment in Mathematics Education: A Systematic Review”, ZDM Mathematics Education, 57, pp. 679-693, 2025. https://doi.org/10.1007/s11858-025-01696-x. (in English)
[31] Tin, Ting Tin et al. “Exploring the Impact of Google Education Tools on Student Engagement, Learning Motivation, and Academic Performance”, Pakistan Journal of Life and Social Sciences, vol. 22, № 2, pp. 15975–15993, 2024. https://doi.org/10.57239/PJLSS-2024-22.2.001159. (in English)
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Copyright (c) 2026 Nataliia Kuhai