Transition from Paper-Based Worksheets to Spreadsheets: An Exploratory Study of Opportunity to Learn in Linear Algebra Instruction
Keywords:
Opportunity to Learn, Spreadsheet-Based Learning, Linear Algebra, Learning Trajectory
Abstract
This study explores the impact of transitioning from traditional paper-based worksheets to spreadsheet-based instruction on students' Opportunity to Learn (OTL) in a Linear Algebra course. Conducted with 37 undergraduate mathematics education students, the research employed a qualitative exploratory approach to examine changes in student engagement, conceptual understanding, and pedagogical awareness. The intervention began with procedural paper-based tasks and gradually introduced spreadsheet environments designed to foster conceptual exploration and mathematical argumentation. Data were collected through observations, student artifacts, and interviews, and analyzed using content analysis and learning trajectory comparison. The findings reveal that spreadsheet-based instruction enhanced computational accuracy, facilitated independent exploration, and promoted metacognitive engagement. A comparison between the hypothetical learning trajectory (HLT) and actual learning pathway (ALT) showed that students exceeded expectations, demonstrating improved conceptual reasoning and reflective thinking. The study concludes that spreadsheet integration—when embedded in argumentation-based learning—serves as a transformative pedagogical tool, expanding instructional quality and deepening students’ opportunity to learn in higher mathematics education.
References
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Cancino, M., & Oyarzún, N. (2025). Assessing the impact of the metacognitive pedagogical cycle on adult EFL learners’ proficiency and awareness: Evidence from Chilean classrooms. Vigo International Journal of Applied Linguistics, 22, 7–34. https://doi.org/10.35869/vial.v0i22.3039
Catarino, P., & Vasco, P. (2021). Teaching Linear Algebra in Engineering Courses Using Critical Thinking. Open Education Studies, 3(1), 76–83. https://doi.org/10.1515/edu-2020-0141
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Hermans, F., Pinzger, M., & Deursen, A. Van. (2012). Detecting and Visualizing Inter-worksheet Smells in Spreadsheets. 441–451.
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Hughes, J. (2005). The Role of Teacher Knowledge and Learning Experiences in Forming Technology-Integrated Pedagogy. 13, 277–302.
Ion, T. C., & Popescu, E. (2024). An innovative distance learning platform for mathematics education in secondary schools: Design, development and preliminary studies. Education and Information Technologies, 5529–5560. https://doi.org/10.1007/s10639-024-13040-z
Kolb, D. A. (1984). Experiential Learning: Experience as The Source of Learning and Development. Prentice Hall, Inc., 1984, 20–38. https://doi.org/10.1016/B978-0-7506-7223-8.50017-4
Kop, R., & Hill, A. (2008). Connectivism: Learning theory of the future or vestige of the past? International Review of Research in Open and Distance Learning, 9(3). https://doi.org/10.19173/irrodl.v9i3.523
Kurz, A., Elliott, S. N., Lemons, C. J., Zigmond, N., Kloo, A., & Kettler, R. J. (2014). Assessing opportunity-to-learn for students with disabilities in general and special education classes. Assessment for Effective Intervention, 40(1), 24–39. https://doi.org/10.1177/1534508414522685
Lande, M. (2020). Learning trajectories through undergraduate engineering curricula and experiences. ASEE Annual Conference and Exposition, Conference Proceedings, 2020-June. https://doi.org/10.18260/1-2--34905
Lindeberg, T. (2013). A computational theory of visual receptive fields. 589–635. https://doi.org/10.1007/s00422-013-0569-z
Liu, X., & Whitford, M. (2011). Opportunities-to-Learn at Home: Profiles of Students With and Without Reaching Science Proficiency. Journal of Science Education and Technology, 20(4), 375–387. https://doi.org/10.1007/s10956-010-9259-y
Marion, S. (2020). Using Opportunity-to-Learn Data to Support Educational Equity. National Center for the Improvement of Educational Assessment, October.
Martin, D. B. (2018). Mathematics Learning and Participation as Racialized Forms of Experience: African American Parents Speak on the Struggle for Mathematics Literacy. In Urban Parents’ Perspectives on Children’s Mathematics Learning and Issues of Equity in Mathematics Education (pp. 197–229). Routledge. https://doi.org/10.4324/9780203764152-2
Mary Osei Fokuo, Nelson Opoku-Mensah, Richard Asamoah, Josephine Nyarko, Kofi Dwumfuo Agyeman, Caroline Owusu-Mintah, & Samuel Asare. (2023). The use of visualization tools in teaching mathematics in college of education: A systematic review. Open Access Research Journal of Science and Technology, 9(1), 001–009. https://doi.org/10.53022/oarjst.2023.9.1.0057
Mkundi, M. S., & Mulema, J. (2024). Awareness of Using Tablets as Potential Assistive Pedagogical Tool among Primary School Teachers in Nachingwea District. East African Journal of Education Studies, 7(2), 154–161. https://doi.org/10.37284/eajes.7.2.1898
Moore, A., & Caruso, B. (2020). Beyond the Classroom: Developing Nontraditional Learning Spaces in an Academic Library. In Innovations in Higher Education Teaching and Learning (pp. 125–146). Emerald Publishing Limited. https://doi.org/10.1108/s2055-364120200000029009
Moore, J. P., Williams, C. B., North, C., & Johri, A. (2013). Promoting conceptual understanding in engineering statics through the use of adaptive concept maps. ASEE Annual Conference and Exposition, Conference Proceedings. https://doi.org/10.18260/1-2--22383
Musa, S. N., & Zulkafly, N. A. (2017). Collaborative Virtual Environment to Enhance Learning Experience. In Proceedings of the 2017 International Conference on Education and E-Learning - ICEEL 2017. ACM Press. https://doi.org/10.1145/3160908.3160912
Nasrullah; Baharman. (2018). Exploring Practical Responses of M3LC for Learning Literacy Exploring Practical Responses of M3LC for Learning Literacy. Journal of Physics: Conference Series, 1–6. https://doi.org/10.1088/1742-6596/954/1/012007
Ng, O.-L., & Cui, Z. (2020). Examining primary students’ mathematical problem-solving in a programming context: towards computationally enhanced mathematics education. In ZDM – Mathematics Education (Vol. 53, Issue 4, pp. 847–860). Springer Science and Business Media LLC. https://doi.org/10.1007/s11858-020-01200-7
Okumus, S., & Unal, S. (2012). The Effects of Argumentation Model on Students’ Achievement and Argumentation Skills in Science. Procedia - Social and Behavioral Sciences, 46, 457–461. https://doi.org/10.1016/j.sbspro.2012.05.141
Procter, L. (2020). Fostering critically reflective thinking with first-year university students: early thoughts on implementing a reflective assessment task. Reflective Practice, 21(4), 444–457. https://doi.org/10.1080/14623943.2020.1773421
Richardson, D. S., Bledsoe, R. S., & Cortez, Z. (2020). Mindset, motivation, and teaching practice: psychology applied to understanding teaching and learning in stem disciplines. CBE Life Sciences Education, 19(3), 1–7. https://doi.org/10.1187/cbe.19-11-0238
Ruslan, R., Alimuddin, A., & Nasrullah, N. (2018). Developing Alternative Assessment of Mathematical Performance for Vocational Students. Innovation of Vocational Technology Education, 14(1), 32. https://doi.org/10.17509/invotec.v14i1.11045
Stewart, S., & Thomas, M. O. J. (2019). Student perspectives on proof in linear algebra. ZDM - Mathematics Education, 51(7), 1069–1082. https://doi.org/10.1007/s11858-019-01087-z
Street, K. E. S., Malmberg, L.-E., & Stylianides, G. J. (2017). Level, strength, and facet-specific self-efficacy in mathematics test performance. Zdm, 0(0), 0. https://doi.org/10.1007/s11858-017-0833-0
Stylianides, G., & Stylianides, A. (2009). Facilitating the Transition from Empirical Arguments to Proof. Journal for Research in Mathematics Education, 40. https://doi.org/10.5951/jresematheduc.40.3.0314
Su, H.-K., Kao, C.-C., Chang, L.-Y., Chen, Y.-F., & Sun, C.-C. (2015). Design and Implementation of Android-Based Interactive Multimedia Presentation Platform for Multiple Users. 130–131.
Sulaiman, F., Rosales, J. J., & Kyung, L. J. (2024). The effectiveness of integrated science, technology, engineering and mathematics project-based learning module. International Journal of Evaluation and Research in Education , 13(3), 1740–1754. https://doi.org/10.11591/ijere.v13i3.26676
Upu, H., Djadir, & Asyari, S. (2017). The fifth graders’ mathematisation process in solving contextual problems. World Transactions on Engineering and Technology Education, 15(2), 195–199.
Upu, H., Rusli, R., & Pratiwi, Y. (2021). Deskripsi Kemampuan Berpikir Reflektif dalam Menyelesaikan Soal High Order Thinking Skill (HOTS) ditinjau dari Kecerdasan Logis Matematis Siswa. In Issues in Mathematics Education (IMED) (Vol. 5, Issue 2, p. 127). Fakultas MIPA Universitas Negeri Makassar. https://doi.org/10.35580/imed23845
Wagner, A., & Strach, P. (2019). Internships and Applied Work‐Based Learning Experiences in Higher Education. In New Directions for Higher Education (Vol. 2019, Issue 188, pp. 51–59). Wiley. https://doi.org/10.1002/he.20345
Wang, F., Wang, Y., Liu, Y., & Leung, S. O. (2022). Investigating the Measurement of OTL in PISA 2012 and its Relationship with Self-efficacy and Mathematics Achievement: Doubly Latent Multilevel Analyses. Scandinavian Journal of Educational Research. https://doi.org/10.1080/00313831.2022.2070929
Weil, L. G., Fleming, S. M., Dumontheil, I., Kilford, E. J., Weil, R. S., Rees, G., Dolan, R. J., & Blakemore, S. J. (2013). The development of metacognitive ability in adolescence. Consciousness and Cognition. https://doi.org/10.1016/j.concog.2013.01.004
Wertsch, J. V. (2008). From Social Interaction to Higher Psychological Processes. Human Development, 51(1), 66–79. https://doi.org/10.1159/000112532
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
Yanti, I., Asiani, R. W., & Kukuh, M. (2022). STUDENTS’ MATHEMATICAL LITERACY IN SOLVING HIGHER ORDER THINKING SKILL PROBLEMS ON MATRIX MATERIAL. In Jurnal Pendidikan Matematika (JUPITEK) (Vol. 5, Issue 2, pp. 175–186). Universitas Pattimura. https://doi.org/10.30598/jupitekvol5iss2pp175-186
Alexandrovsky, D. (2018). Exploring Interactive Systems for Algebra Learning in School. October. https://doi.org/10.13140/RG.2.2.11668.35204
Anderson, T., & Dron, J. (2011). Three generations of distance education pedagogy. International Review of Research in Open and Distance Learning, 12(3), 80–97. https://doi.org/10.19173/irrodl.v12i3.890
Arslan, S. (2010). Traditional instruction of differential equations and conceptual learning. Teaching Mathematics and Its Applications, 29(2), 94–107. https://doi.org/10.1093/teamat/hrq001
Assis, R. F. de. (2021). Translating value stream maps into system dynamics models: a practical framework. International Journal of Advanced Manufacturing Technology, 114(11), 3537–3550. https://doi.org/10.1007/s00170-021-07053-y
Banks, J. A., Au, K. H., & Ball, A. F. (2011). Learning in and out of school in diverse environments. In Center for Multicultural Education (Vol. 33, Issue 8). University of Washington, Seattle. https://doi.org/10.3109/0142159X.2011.600102
Barana, A. (2022). Understanding Linear Functions in an Interactive Digital Learning Environment. Proceedings of the 15th International Conference on …, May. https://www.researchgate.net/profile/Uffe-Jankvist/publication/360642293_Proceedings_of_the_15th_international_conference_on_technology_in_mathematics_teaching_ICTMT_15_Making_and_strengthening_connections_and_connectivity_for_teaching_mathematics_with_te
Barana, A., Marchisio, M., & Sacchet, M. (2021). Interactive Feedback for Learning Mathematics in a Digital Learning Environment. In Education Sciences (Vol. 11, Issue 6, p. 279). MDPI AG. https://doi.org/10.3390/educsci11060279
Becheru, A., Calota, A., & Popescu, E. (2018). Analyzing students’ collaboration patterns in a social learning environment using StudentViz platform. In Smart Learning Environments (Vol. 5, Issue 1). Springer Science and Business Media LLC. https://doi.org/10.1186/s40561-018-0063-0
Byrnes, J. P., & Miller, D. C. (2007). The relative importance of predictors of math and science achievement: An opportunity-propensity analysis. Contemporary Educational Psychology, 32(4), 599–629. https://doi.org/10.1016/j.cedpsych.2006.09.002
Cancino, M., & Oyarzún, N. (2025). Assessing the impact of the metacognitive pedagogical cycle on adult EFL learners’ proficiency and awareness: Evidence from Chilean classrooms. Vigo International Journal of Applied Linguistics, 22, 7–34. https://doi.org/10.35869/vial.v0i22.3039
Catarino, P., & Vasco, P. (2021). Teaching Linear Algebra in Engineering Courses Using Critical Thinking. Open Education Studies, 3(1), 76–83. https://doi.org/10.1515/edu-2020-0141
Chen, X., Xie, H., Zou, D., & Hwang, G. J. (2020). Application and theory gaps during the rise of Artificial Intelligence in Education. Computers and Education: Artificial Intelligence, 1(July), 100002. https://doi.org/10.1016/j.caeai.2020.100002
Education, T., & Collection, T. (2005). The Role of Teacher Knowledge and Learning Experiences in Forming Technology-Integrated Pedagogy.
Esteve-gonzález, V. (2016). IN HIGHER EDUCATION (Issue June 2015).
Gadanidis, G., Silva, R. S. R. da, Hughes, J., Floyd, S., & Namukasa, I. (2022). Computational Literacy & Mathematics Education. In Revista Internacional de Pesquisa em Educação Matemática (Vol. 12, Issue 4, pp. 1–23). Sociedade Brasileira de Educacao Matematica. https://doi.org/10.37001/ripem.v12i4.3144
Hadianto, D., Damaianti, V. S., Mulyati, Y., & Sastromiharjo, A. (2021). Enhancing scientific argumentation skill through partnership comprehensive literacy. In Journal of Physics: Conference Series (Vol. 2098, Issue 1, p. 12015). IOP Publishing. https://doi.org/10.1088/1742-6596/2098/1/012015
Haspekian, M., & Bruillard, E. (2010). Behind Students’ Spreadsheet Competencies: Their Achievement in Algebra? a Case Study in a French Vocational School. Cerme 6 - Proceedings of the 6Th Congress of the European Society for Research in Mathematics Education, January 2009, 519–528.
Hermans, F., Pinzger, M., & Deursen, A. Van. (2012). Detecting and Visualizing Inter-worksheet Smells in Spreadsheets. 441–451.
Hirotsu, M. (2014). Using the Spreadsheet to Promote Algebraic Thinking. January.
Hughes, J. (2005). The Role of Teacher Knowledge and Learning Experiences in Forming Technology-Integrated Pedagogy. 13, 277–302.
Ion, T. C., & Popescu, E. (2024). An innovative distance learning platform for mathematics education in secondary schools: Design, development and preliminary studies. Education and Information Technologies, 5529–5560. https://doi.org/10.1007/s10639-024-13040-z
Kolb, D. A. (1984). Experiential Learning: Experience as The Source of Learning and Development. Prentice Hall, Inc., 1984, 20–38. https://doi.org/10.1016/B978-0-7506-7223-8.50017-4
Kop, R., & Hill, A. (2008). Connectivism: Learning theory of the future or vestige of the past? International Review of Research in Open and Distance Learning, 9(3). https://doi.org/10.19173/irrodl.v9i3.523
Kurz, A., Elliott, S. N., Lemons, C. J., Zigmond, N., Kloo, A., & Kettler, R. J. (2014). Assessing opportunity-to-learn for students with disabilities in general and special education classes. Assessment for Effective Intervention, 40(1), 24–39. https://doi.org/10.1177/1534508414522685
Lande, M. (2020). Learning trajectories through undergraduate engineering curricula and experiences. ASEE Annual Conference and Exposition, Conference Proceedings, 2020-June. https://doi.org/10.18260/1-2--34905
Lindeberg, T. (2013). A computational theory of visual receptive fields. 589–635. https://doi.org/10.1007/s00422-013-0569-z
Liu, X., & Whitford, M. (2011). Opportunities-to-Learn at Home: Profiles of Students With and Without Reaching Science Proficiency. Journal of Science Education and Technology, 20(4), 375–387. https://doi.org/10.1007/s10956-010-9259-y
Marion, S. (2020). Using Opportunity-to-Learn Data to Support Educational Equity. National Center for the Improvement of Educational Assessment, October.
Martin, D. B. (2018). Mathematics Learning and Participation as Racialized Forms of Experience: African American Parents Speak on the Struggle for Mathematics Literacy. In Urban Parents’ Perspectives on Children’s Mathematics Learning and Issues of Equity in Mathematics Education (pp. 197–229). Routledge. https://doi.org/10.4324/9780203764152-2
Mary Osei Fokuo, Nelson Opoku-Mensah, Richard Asamoah, Josephine Nyarko, Kofi Dwumfuo Agyeman, Caroline Owusu-Mintah, & Samuel Asare. (2023). The use of visualization tools in teaching mathematics in college of education: A systematic review. Open Access Research Journal of Science and Technology, 9(1), 001–009. https://doi.org/10.53022/oarjst.2023.9.1.0057
Mkundi, M. S., & Mulema, J. (2024). Awareness of Using Tablets as Potential Assistive Pedagogical Tool among Primary School Teachers in Nachingwea District. East African Journal of Education Studies, 7(2), 154–161. https://doi.org/10.37284/eajes.7.2.1898
Moore, A., & Caruso, B. (2020). Beyond the Classroom: Developing Nontraditional Learning Spaces in an Academic Library. In Innovations in Higher Education Teaching and Learning (pp. 125–146). Emerald Publishing Limited. https://doi.org/10.1108/s2055-364120200000029009
Moore, J. P., Williams, C. B., North, C., & Johri, A. (2013). Promoting conceptual understanding in engineering statics through the use of adaptive concept maps. ASEE Annual Conference and Exposition, Conference Proceedings. https://doi.org/10.18260/1-2--22383
Musa, S. N., & Zulkafly, N. A. (2017). Collaborative Virtual Environment to Enhance Learning Experience. In Proceedings of the 2017 International Conference on Education and E-Learning - ICEEL 2017. ACM Press. https://doi.org/10.1145/3160908.3160912
Nasrullah; Baharman. (2018). Exploring Practical Responses of M3LC for Learning Literacy Exploring Practical Responses of M3LC for Learning Literacy. Journal of Physics: Conference Series, 1–6. https://doi.org/10.1088/1742-6596/954/1/012007
Ng, O.-L., & Cui, Z. (2020). Examining primary students’ mathematical problem-solving in a programming context: towards computationally enhanced mathematics education. In ZDM – Mathematics Education (Vol. 53, Issue 4, pp. 847–860). Springer Science and Business Media LLC. https://doi.org/10.1007/s11858-020-01200-7
Okumus, S., & Unal, S. (2012). The Effects of Argumentation Model on Students’ Achievement and Argumentation Skills in Science. Procedia - Social and Behavioral Sciences, 46, 457–461. https://doi.org/10.1016/j.sbspro.2012.05.141
Procter, L. (2020). Fostering critically reflective thinking with first-year university students: early thoughts on implementing a reflective assessment task. Reflective Practice, 21(4), 444–457. https://doi.org/10.1080/14623943.2020.1773421
Richardson, D. S., Bledsoe, R. S., & Cortez, Z. (2020). Mindset, motivation, and teaching practice: psychology applied to understanding teaching and learning in stem disciplines. CBE Life Sciences Education, 19(3), 1–7. https://doi.org/10.1187/cbe.19-11-0238
Ruslan, R., Alimuddin, A., & Nasrullah, N. (2018). Developing Alternative Assessment of Mathematical Performance for Vocational Students. Innovation of Vocational Technology Education, 14(1), 32. https://doi.org/10.17509/invotec.v14i1.11045
Stewart, S., & Thomas, M. O. J. (2019). Student perspectives on proof in linear algebra. ZDM - Mathematics Education, 51(7), 1069–1082. https://doi.org/10.1007/s11858-019-01087-z
Street, K. E. S., Malmberg, L.-E., & Stylianides, G. J. (2017). Level, strength, and facet-specific self-efficacy in mathematics test performance. Zdm, 0(0), 0. https://doi.org/10.1007/s11858-017-0833-0
Stylianides, G., & Stylianides, A. (2009). Facilitating the Transition from Empirical Arguments to Proof. Journal for Research in Mathematics Education, 40. https://doi.org/10.5951/jresematheduc.40.3.0314
Su, H.-K., Kao, C.-C., Chang, L.-Y., Chen, Y.-F., & Sun, C.-C. (2015). Design and Implementation of Android-Based Interactive Multimedia Presentation Platform for Multiple Users. 130–131.
Sulaiman, F., Rosales, J. J., & Kyung, L. J. (2024). The effectiveness of integrated science, technology, engineering and mathematics project-based learning module. International Journal of Evaluation and Research in Education , 13(3), 1740–1754. https://doi.org/10.11591/ijere.v13i3.26676
Upu, H., Djadir, & Asyari, S. (2017). The fifth graders’ mathematisation process in solving contextual problems. World Transactions on Engineering and Technology Education, 15(2), 195–199.
Upu, H., Rusli, R., & Pratiwi, Y. (2021). Deskripsi Kemampuan Berpikir Reflektif dalam Menyelesaikan Soal High Order Thinking Skill (HOTS) ditinjau dari Kecerdasan Logis Matematis Siswa. In Issues in Mathematics Education (IMED) (Vol. 5, Issue 2, p. 127). Fakultas MIPA Universitas Negeri Makassar. https://doi.org/10.35580/imed23845
Wagner, A., & Strach, P. (2019). Internships and Applied Work‐Based Learning Experiences in Higher Education. In New Directions for Higher Education (Vol. 2019, Issue 188, pp. 51–59). Wiley. https://doi.org/10.1002/he.20345
Wang, F., Wang, Y., Liu, Y., & Leung, S. O. (2022). Investigating the Measurement of OTL in PISA 2012 and its Relationship with Self-efficacy and Mathematics Achievement: Doubly Latent Multilevel Analyses. Scandinavian Journal of Educational Research. https://doi.org/10.1080/00313831.2022.2070929
Weil, L. G., Fleming, S. M., Dumontheil, I., Kilford, E. J., Weil, R. S., Rees, G., Dolan, R. J., & Blakemore, S. J. (2013). The development of metacognitive ability in adolescence. Consciousness and Cognition. https://doi.org/10.1016/j.concog.2013.01.004
Wertsch, J. V. (2008). From Social Interaction to Higher Psychological Processes. Human Development, 51(1), 66–79. https://doi.org/10.1159/000112532
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
Yanti, I., Asiani, R. W., & Kukuh, M. (2022). STUDENTS’ MATHEMATICAL LITERACY IN SOLVING HIGHER ORDER THINKING SKILL PROBLEMS ON MATRIX MATERIAL. In Jurnal Pendidikan Matematika (JUPITEK) (Vol. 5, Issue 2, pp. 175–186). Universitas Pattimura. https://doi.org/10.30598/jupitekvol5iss2pp175-186
Published
2025-06-19
How to Cite
Nasrullah, Nurdin Arsyad, & Alimuddin. (2025). Transition from Paper-Based Worksheets to Spreadsheets: An Exploratory Study of Opportunity to Learn in Linear Algebra Instruction. International Journal of Education, Vocational and Social Science , 4(03), 218-234. https://doi.org/10.63922/ijevss.v4i03.1957
Contact Person +6282139474255
Email : ijevss@citakonsultindo.or.id / editor.ijevss@gmail.com
