Keywords
GeoGebra
Moodle
computer-based testing
template
test items
How to Cite
Abstract
The study explores the use of modern information and communication technologies (ICT) for the automated generation of test items in higher mathematics. It provides a detailed analysis of the development of so-called template programs in systems such as Wolfram Mathematica, GeoGebra, R, and Excel, which enable the generation of a large number of new tasks adapted to students’ level of preparation, with predefined parameters of difficulty, discriminative ability, and formatted answers.
The paper examines methods for designing and implementing such template programs. It describes the algorithms used for automatic task generation, as well as the application of the generated tasks in assessment activities conducted on the MOODLE platform. The advantages of using automated testing systems are discussed, including objective evaluation, reduced time for task creation and grading.
The impact of modern information technologies on the development of digital literacy, competence in using software tools, and the ability to integrate modern technologies into the educational process is analyzed, along with the enhancement of instructors' critical thinking and analytical skills.
The article also presents examples of successful implementation of template programs developed using Wolfram Language, GeoGebra, R, and Excel into the educational process, along with the results of their use, which demonstrate significant improvement in students’ performance and motivation in studying higher mathematics. Examples of templates and tasks generated with these programs are provided, and the suitability of different software tools for generating test items in specific branches of mathematics is explored.
Considerable attention is given to the issue of academic integrity: the authors propose strategies to prevent cheating through task variability and the use of embedded answer formats.
Empirical results show that the use of template programs significantly reduces the number of errors in tasks, shortens development time, and improves students’ learning outcomes.
The paper concludes with the recognition of the need for further development and refinement of ICT in education, as well as the active integration of innovative technologies into curricula to improve the quality of education.
References
[1] Н. В. Круглова, О. О. Диховичний, “Добір математичної моделі для аналізу тестових завдань типу «вбудовані відповіді» з математичних дисциплін”, Інформаційні технології і засоби навчання, том. 87, №. 1, с. 166–184, 2022, doi: 10.33407/itlt.v87i1.4487.
[2] А. Ф. Дудко, “Комп’ютерно орієнтована методика оцінювання якості тестів з вищої математики викладачами вищої освіти”, Автореферат дисертації на здобуття наукового ступеня кандидата педагогічних наук, Київ, 24 с., 2019.
[3] L.M. Sánchez-Ruiz, S. Moll-López, A. Nuñez-Pérez, J.A. Moraño-Fernández, and E. Vega-Fleitas, “ChatGPT Challenges Blended Learning Methodologies in Engineering Education”, A Case Study in Mathematics. Appl. Sci, vol. 13, no. 10, 2023, doi: 10.3390/app13106039. [Електронний ресурс]. Доступно: https://www.mdpi.com/2076-3417/13/10/6039.
[4] S. Nikolic, C. Sandison, R. Haque, S. Daniel, S. Grundy, M. Belkina, M.P. Neal, “ChatGPT, Copilot, Gemini, SciSpace and Wolfram versus higher education assessments: an updated multi-institutional study of the academic integrity impacts of Generative Artificial Intelligence (GenAI) on assessment, teaching and learning in engineering”, Australasian Journal of Engineering Education, 29(2), pp.126–153, 2024, doi: 10.1080/22054952.2024.2372154.
[5] М.С. Паккі, “Забезпечення надійності процедур оцінювання здобувачів в умовах онлайн навчання”, Інформаційні технології і засоби навчання, том. 88, №. 2, с. 139–151, 2022, doi:10.33407/itlt.v88i2.4476.
[6] А. Розуменко, А. Розуменко, та О. Удовиченко, “Методичні особливості навчання вищої математики студентів нематематичних спеціальностей в кризових умовах (узагальнення досвіду роботи в умовах військового стану”, Освіта. Інноватика. Практика, № 12(3), с. 70–77, 2024, doi: 10.31110/2616-650X-vol12i3-010.
[7] M. J. Gierl, H. Lai, “A process for reviewing and evaluating generated test items “, Educational Measurement: Issues and Practice, vol. 35, no. 4. pp. 6-20, 2016.
[8] D. Bodnenko, O. Lytvyn, S. Radchenko, and V. Proshkin, ”The templates methods in e-learning of higher mathematics” in E-learning in the Time of COVID-19, vol. 13, Katowice–Cieszyn, Poland: STUDIO NOA, pp. 199–209, 2021, doi: 10.34916/el.2021.13.17.
[9] V. Zaika, A. Tetiana, T. Vakaliuk, S. Semerikov, “Selection of online tools for creating math tests”, in AREdu 2021: 4th International Workshop on Augmented Reality in EducationAt: Kryvyi Rih, Ukraine, 2021, [Електронний ресурс]. Доступно: https://ceur-ws.org/Vol-2898/paper04.pdf.
[10] N. Dahal, N. K. Manandhar, L. Luitel, B. C. Luitel, B. P. Pant, & I. M. Shrestha, “Ict
tools for remote teaching and learning mathematics: a proposal for autonomy and engagements”,
Adv Mobile Learn Educ Res, vol.2(1), pp. 289-296, 2022, doi: 10.25082/AMLER.2022.01.013.
[11] M. Zainul Arifin, Agni Danaryanti, Yuni Suryaningsih, “Development of Online Learning Media Using Geogebra and LaTeX on Derivative Material”, Indonesian Journal of Science and Mathematics Education, vol. 6(1), pp.59-72, 2023, doi: 10.24042/ijsme.v6i1.15367.
[12] E. Yildiz, I. Arpaci, ” Understanding pre-service mathematics teachers’ intentions to use GeoGebra: The role of technological pedagogical content knowledge”, Educ Inf Technol, vol.29, pp.18817–18838, 2024, doi: 10.1007/s10639-024-12614-1.
[13] R. Ziatdinov, and J.R. Valles, Jr. “Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics”, Mathematics, vol.10, p. 398, 2022, doi: 10.3390/math10030398.
[14] C. Chytas, S.P.van Borkulo, P. Drijvers, et al.,”Computational Thinking in Secondary Mathematics Education with GeoGebra: Insights from an Intervention in Calculus Lessons”, Digit Exp Math Educ, vol. 10, pp. 228–259, 2024, doi: 10.1007/s40751-024-00141-0.
[15] Neisarg Dave, Riley Owen Bakes, Bart Pursel, and C. Lee Giles, “Math Multiple Choice Question Solving and Distractor Generation with Attentional GRU Networks”. In: Proceedings of The 14th International Conference on Educational Data Mining (EDM21). International Educational Data Mining Society, pp. 422-430, 2021, [Електронний ресурс]. Доступно: https://educationaldatamining.org/edm2021.
[16] Hunter McNichols, Wanyong Feng, Jaewook Lee, Alexander Scarlatos, Digory Smith, Simon Woodhead, Andrew Lan, “Automated Distractor and Feedback Generation for Math Multiple-choice Questions via In-context Learning”, arXiv:2308.03234 [cs.CL], 2023, doi: 10.48550/arXiv.2308.03234
[17] A.C. Conceição, “Dynamic and Interactive Tools to Support Teaching and Learning”, Math. Comput. Appl. 27(1), 2022, doi: 10.3390/mca27010001.
[18] Z. Chen, “Assessing introductory physics students using large open item bank created using GPT-3 and WolframAlpha “, APS April Meeting Abstracts, vol.68(6), 2023, [Електронний ресурс]. Доступно: https://meetings.aps.org/Meeting/APR23/Session/B18.4.
REFERENCES (TRANSLATED AND TRANSLITERATED)
[1] N.V. Kruglova and О. О.Dykhovychnyi, “Selecting a mathematical model for analysis of test items of the type ‘embedded answers’ for mathematical disciplines”, Information Technologies and Learning Tools, vol. 87, no. 1, pp. 166–184, 2022, doi: 10.33407/itlt.v87i1.4487. (in Ukrainian).
[2] A. F. Dudko, “Computer-oriented methodology of assessing the quality of tests in higher mathematics by teachers of higher education establishments”, Avtoreferat dysertatsii na zdobuttia naukovoho stupenia kandydata pedahohichnykh nauk, Kyiv, Ukraine, 24 р., 2019. (in Ukrainian).
[3] L.M. Sánchez-Ruiz, S. Moll-López, A. Nuñez-Pérez, J.A. Moraño-Fernández, and E. Vega-Fleitas, “ChatGPT Challenges Blended Learning Methodologies in Engineering Education”, A Case Study in Mathematics. Appl. Sci, vol. 13, no. 10, 2023, doi: 10.3390/app13106039. [Online]. Available: https://www.mdpi.com/2076-3417/13/10/6039. (in English).
[4] S. Nikolic, C. Sandison, R. Haque, S. Daniel, S. Grundy, M. Belkina, M.P. Neal, “ChatGPT, Copilot, Gemini, SciSpace and Wolfram versus higher education assessments: an updated multi-institutional study of the academic integrity impacts of Generative Artificial Intelligence (GenAI) on assessment, teaching and learning in engineering”, Australasian Journal of Engineering Education, 29(2), pp.126–153, 2024, doi: 10.1080/22054952.2024.2372154. (in English).
[5] М. С. Pakki, “Тhе ensuring of reliability of students’ assessment procedures during online learning”, Information Technologies and Learning Tools, vol. 88, no. 2, pp. 139–151, 2022, doi: 10.33407/itlt.v88i2.4476. (in Ukrainian).
[6] A. Rozumenko, A. Rozumenko, O. Udovychenko, “Methodological Features of Teaching Higher Mathematics to Non-Mathematics Major Students in Crisis Conditions (Generalization of Experience in Wartime Conditions)”, Osvita. Innovatyka. Praktyka, № 12(3), pp. 70–77, 2024, , doi: 10.31110/2616-650X-vol12i3-010. (in Ukrainian).
[7] М. С. Gierl, H.Lai, “A process for reviewing and evaluating generated test items”, Educational Measurement: Issues and Practice, vol. 35, no. 4. pp. 6-20, 2016. (in English).
[8] D. Bodnenko, O. Lytvyn, S. Radchenko, and V.Proshkin, ”The templates methods in e-learning of higher mathematics”, in E-learning in the Time of COVID-19, vol. 13, Katowice–Cieszyn, Poland: STUDIO NOA, pp. 199–209, 2021, doi: 10.34916/el.2021.13.17. (in English).
[9] V.Zaika, A.Tetiana, T.Vakaliuk, S. Semerikov, “Selection of online tools for creating math tests”, in AREdu 2021: 4th International Workshop on Augmented Reality in EducationAt: Kryvyi Rih, Ukraine, 2021, [Online]. Available: https://ceur-ws.org/Vol-2898/paper04.pdf. (in English).
[10] N. Dahal, N. K. Manandhar, L. Luitel, B. C. Luitel, B. P. Pant, & I. M. Shrestha, “Ict
tools for remote teaching and learning mathematics: a proposal for autonomy and engagements”,
Adv Mobile Learn Educ Res, vol.2(1), pp. 289-296, 2022, doi: 10.25082/AMLER.2022.01.013.(in English).
[11] M. Zainul Arifin, Agni Danaryanti, Yuni Suryaningsih, “Development of Online Learning Media Using Geogebra and LaTeX on Derivative Material”, Article in Indonesian Journal of Science and Mathematics Education, vol.6(1), pp.59-72, May 2023, doi: 10.24042/ijsme.v6i1.15367. (in English).
[12] E. Yildiz, I. Arpaci, ” Understanding pre-service mathematics teachers’ intentions to use GeoGebra: The role of technological pedagogical content knowledge”, Educ Inf Technol, vol.29, pp.18817–18838, 2024, doi: 10.1007/s10639-024-12614-1. (in English).
[13] R. Ziatdinov, and J.R. Valles, Jr. “Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics”, Mathematics, vol.10, p. 398, 2022, doi: 10.3390/math10030398. (in English).
[14] C. Chytas, S.P.van Borkulo, P. Drijvers, et al.,”Computational Thinking in Secondary Mathematics Education with GeoGebra: Insights from an Intervention in Calculus Lessons”, Digit Exp Math Educ, vol. 10, pp. 228–259, 2024, doi: 10.1007/s40751-024-00141-0. (in English).
[15] Neisarg Dave, Riley Owen Bakes, Bart Pursel and C. Lee Giles, “Math Multiple Choice Question Solving and Distractor Generation with Attentional GRU Networks”. In: Proceedings of The 14th International Conference on Educational Data Mining (EDM21). International Educational Data Mining Society,
pp. 422-430, 2021, [Online]. Available: https://educationaldatamining.org/edm2021. (in English).
[16] Hunter McNichols, Wanyong Feng, Jaewook Lee, Alexander Scarlatos, Digory Smith, Simon Woodhead, Andrew Lan, “Automated Distractor and Feedback Generation for Math Multiple-choice Questions via In-context Learning”, arXiv:2308.03234 [cs.CL], 2023, doi: 10.48550/arXiv.2308.03234. (in English).
[17] A.C. Conceição, “Dynamic and Interactive Tools to Support Teaching and Learning”, Math. Comput. Appl. 27(1), 2022, doi: 10.3390/mca27010001. (in English).
[18] Z. Chen, “Assessing introductory physics students using large open item bank created using GPT-3 and WolframAlpha “, APS April Meeting Abstracts, vol.68(6), 2023, [Online]. Available: https://meetings.aps.org/Meeting/APR23/Session/B18.4. (in English).
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