Promoting antiderivative calculation through perceptual learning: digital games and instrumental orchestrations
DOI:
https://doi.org/10.29352/mill0223e.42500Keywords:
antiderivative calculation, perceptual learning, digital games, instrumental orchestrations, mathematics educationAbstract
Introduction: The calculation of antiderivatives is often identified as a challenge for students. Perceptual Learning (PL), combined with the use of digital artifacts such as games and appropriate instrumental orchestrations, can foster a better understanding of expression structures and facilitate this learning.
Objective: To determine how digital artifacts based on PL principles, integrated into instrumental orchestrations, contribute to students’ fluency and accuracy in calculating antiderivatives.
Methods: A Design Science Research methodology was followed across three iterations. Participants were 12th- grade Portuguese students. Digital games focused on identifying structures of basic antiderivatives were developed. Data collection included tests, observations, and interactions with the games, analyzed using qualitative and quantitative methods.
Results: Students showed improvement in both discovery and fluency in computing antiderivatives. The combination of games, teacher mediation, and conceptual understanding activities enhanced learning. The progressive integration of the games into a single application, with features such as immediate feedback and life-based constraints, helped prevent trial-and-error strategies. Despite the pandemic context, a tendency toward collaborative work was observed.
Conclusion: Digital games designed according to PL principles, when embedded in appropriate orchestrations, prove effective in teaching antiderivatives. Teacher mediation is essential for these artifacts to become true epistemic tools.
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Almeida, M., Queiruga-Dios, A., & Cáceres, M. (2021). Differential and integral calculus in first-year engineering students: A diagnosis to understand the failure. Mathematics, 9(1), 1–18. https://doi.org/10.3390/math9010061
Araújo, F., Lopes, J., Soares, A., & Cravino, J. (2019). Eficácia da mediação do professor no ensino da estrutura corpuscular da matéria. Comunicações Piracicaba, 26(2), 259-276. https://shre.ink/32YF
Bardin, L. (2021). Análise de conteúdo (Edição Revista e atualizada). Edições 70.
Cavanagh, P. (2011). Visual cognition. Vision Research, 51(13), 1538–1551. https://doi.org/10.1016/j.visres.2011.01.015
Chen, P., Hwang, G., Yeh, S., Chen, Y., Chen, T., & Chien, C. (2022). Three decades of game‑based learning in science and mathematics education: an integrated bibliometric analysis and systematic review. Journal of Computers in Education, 9(3), 455–476. https://doi.org/10.1007/s40692-021-00210-y
Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education (8th ed). Routledge.
Domondon, C., Pardo, C., & Rin, E. (2022). Analysis of difficulties of students in learning calculus. Science International (Lahore), 34(6),1-4. https://shre.ink/3UTA
Drijvers, P., Doorman, M., Boom, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: instrumental orchestrations in the technology mathematics classroom. Educational Studies in Mathematics, 75, 213-234. https://doi.org/10.1007/s10649-010-9254-5
Drijvers, P., Grauwin, S., & Trouche, L. (2020). When bibliometrics met mathematics education research: the case of instrumental orchestration. ZDM – Mathematics Education, 52,1455–1469. https://doi.org/10.1007/s11858-020-01169-3
Erhel, S., & Jamet, E. (2013). Digital game-based learning: Impact of instructions and feedback on motivation and learning effectiveness. Computers & Education, 67, 156–167. https://doi.org/10.1016/j.compedu.2013.02.019
Eyrikh, N., Bazhenov, R., Gorbunova, T., & Masyagin, V. (2020). Implementing interactive information technologies when learning integral calculus in teaching further Mathematics. In V. Ermolayev, F. Mallet, R. Chbeir, V. Peschanenko, & A. Kravets (Eds.), Communications in Computer and Information Science, 1201, 163–172.
Frangou, P., Emir, U., Karlaftis, V., Nettekoven, C., Hinson, E., Larcombe, S., Bridge, H., Stagg, C., & Kourtzi, Z. (2019). Learning to optimize perceptual decisions through suppressive interactions in the human brain. Nature Communications, 10, 474. https://doi.org/10.1038/s41467-019-08313-y
Hui, H., & Mahmud, M. (2023). Influence of game-based learning in mathematics education on the students' cognitive and affective domain: A systematic review. Frontiers in Psychology, 14, Article 1105806. https://doi.org/10.3389/fpsyg.2023.1105806
Kellman, P., Massey, C., Roth, Z., Burke, T., Zucker, J., Saw, A., Aguero, K., & Wise, J. (2008). Perceptual learning and the technology of expertise - Studies in fraction learning and algebra. Pragmatics & Cognition, 16(2), 356-405. https://files.eric.ed.gov/fulltext/ED547776.pdf
Kellman, P., Massey, C., & Son, J. (2010). Perceptual learning modules in mathematics: Enhancing students’ pattern recognition, structure extraction, and fluency. Topics in Cognitive Science, 2(2), 285–305. https://doi.org/10.1111/j.1756-8765.2009.01053.x
Kellman, P. J., & Massey, C. M. (2013). Perceptual learning, cognition, and expertise. The Psychology of Learning and Motivation, 58, 117–165. https://doi.org/10.1016/B978-0-12-407237-4.00004-9
Khalid, I., Abdullah, M., & Fadzil, H. (2025). A Systematic Review: Digital Learning in STEM Education. Journal of Advanced Research in Applied Sciences and Engineering Technology, 51(1) 98-115. https://doi.org/10.37934/araset.51.1.98115
Küchelmann, T., Velentzas, K., Essig, K., Koester, D., & Schack, T. (2022). Expertise-dependent perceptual performance in chess tasks with varying complexity. Frontiers in Psychology, 13, 986787. https://doi.org/10.3389/fpsyg.2022.986787
Li, V., Julaihi, N., & Eng, T. (2017). Misconceptions and errors in learning integral calculus. Asian Journal of University Education (AJUE), 13(1), 17–39.https://files.eric.ed.gov/fulltext/EJ1207815.pdf
Lopes, J. B., Cravino, J., & Silva, A. (2010). Effective Teaching for Intended Learning Outcomes in Science and Technology (Metilost). Nova Science Publishers.
Lopes, J. B., & Costa, C. (2019). Digital resources in science, Mathematics and technology teaching – How to convert them into tools to learn. Digital Resources in Science, Mathematics and Technology Teaching (pp. 243-255). Springer Nature.
Lopes, J. B., & Costa, C. (2021). Converting digital resources into epistemic tools enhancing STEM learning. In A. Reis, J. Barroso, J. B. Lopes, T. Mikropoulos, & C.-W. Fan (Eds.), Technology and innovation in learning, teaching and education (pp. 3–20). Springer.
Mahathir, I., Hong, J., Hui, K., Han, C., & Juan, L. (2024). The critical factors associating to high failure rate in calculus among university students. In J.C. Hong (Ed.), New technology in education and training. AEIT 2024. Lecture notes in educational technology (pp. 303-310). Springer.
Monroe Community College. (2024). MTH 2020 Calculus I. https://shre.ink/3cmH
Moyer-Packenham, P., Lommatsch, C., Litster, K., Ashby, J., Bullock, E., Roxburgh, A., Shumway, J., Speed, E., Covington, B., Hartmann, C., Clarke-Midura, J., Skaria, J., Westenskow, A., MacDonald, B., Symanzik, J., & Jordan, K. (2019). How design features in digital math games support learning and mathematics connections. Computers in Human Behavior, 91, 316-332. https://doi.org/10.1016/j.chb.2018.09.036
Pramuditya, S., Sulaiman, H. & Wahyudin. (2019). Development of instructional media game education on integral and differential calculus. Journal of Physics: Conference Series, 1280(042049), 1-6. https://doi.org/10.1088/1742-6596/1280/4/042049
Peffers, K., Tuunanen, T., Rothenberger, M., & Chatterjee, S. (2008). A design science research methodology for information systems research. Journal of Management Information Systems, 24(3), 45-77. https://doi.org/10.2753/MIS0742-1222240302
Rau, M., & Wu, S. (2018). Combining instructional activities for sense-making processes and perceptual-induction processes involved in connection making among multiple visual representations, Cognition and Instruction, 36(4), 361-395. https://doi.org/10.1080/07370008.2018.1494179
Tabach, M. (2011). A mathematics teacher’s practice in a technological environment: A case study analysis using two complementary theories. Technology, Knowledge and Learning, 16, 247–265. https://doi.org/10.1007/s10758-011-9186-x
Tokac, U., Novak, E. & Thompson, C. (2019). Effects of game‐based learning on students' mathematics achievement: A meta‐analysis. Journal of Computer Assisted Learning, 35(3). https://doi.org/10.1111/jcal.12347
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