Digital Technologies and Calculus: Students’ Peaks and Pits
DOI:
https://doi.org/10.46328/ijemst.5454Keywords:
Calculus education, Digital technologies, STEM retention, Students’ perspectivesAbstract
Understanding calculus students’ perspectives can provide valuable insights into their learning needs and help develop strategies to enhance persistence in STEM programs. Numerous studies have shown that the use of digital technologies (DT) influences student engagement, motivation, and mathematics achievement. In this project, we explored students’ perspectives on using DT in calculus. We interviewed eight calculus students from a midwestern doctorate-granting institution in the United States and used thematic analysis informed by the didactical tetrahedron, accounting for internal and external factors that may influence the teaching and learning process. Students reflected on their use of technology, identifying various benefits, including looking for similar problems, checking their work, and visualizing concepts. They also identified challenges, particularly with online feedback. Additionally, students shared their perceptions of how instructors utilized DT in calculus, recognizing benefits when they provided relevant course material or solved mathematical problems, and highlighted challenges related to the misalignment between course content and online homework. Finally, students described how external factors, such as classroom environments, facilities, and accessibility, impacted their use of technology. These findings offer valuable insights for faculty and institutions regarding effective DT implementation and highlight the importance of considering the specific instructional context in calculus courses.
References
American Mathematical Association of Two-Year Colleges (2018). The use of technology in the teaching and learning of mathematics. Retrieved October 15, 2024, from https://amatyc.org/page/PositionTechnology
Bedada, T. B., & Machaba, M. F. (2022). Investigation of student’s perception learning calculus with GeoGebra and cycle model. Eurasia Journal of Mathematics, Science and Technology Education, 18(10), 1-19. https://doi.org/10.29333/ejmste/12443
Bezuidenhout, J. (2001). Limits and continuity: Some conceptions of first-year students. International Journal of Mathematical Education in Science and Technology, 32(4), 487-500. https://doi.org/10.1080/00207390010022590
Blaisdell, R. (2012). Student understanding in the concept of limit in calculus: How student responses vary depending on question format and type of representation. In S. Brown, S. Larsen, K. Marrongelle, and M. Oehrtman (Eds.), Proceedings of the 15th Annual Conference on Research in Undergraduate Mathematics Education (pp. 348-353).
Boz, B., & Adnan, M. (2017). How do freshman engineering students reflect an online calculus course? International Journal of Education in Mathematics, Science and Technology, 5(4), 262-278. https://doi.org/10.18404/ijemst.83046
Braun, V., & Clarke, V. (2012). Thematic analysis. American Psychological Association.
Bressoud, D., Ghedamsi, I., Martinez-Luaces, V., Törner, G. (2016). Teaching and learning of calculus. Springer & ICME-13 Topical Surveys. https://doi.org/10.1007/978-3-319-32975-8_1
Carlson, M. P., Smith, N., & Persson, J. (2003). Developing and connecting calculus students' notions of rate-of change and accumulation: The Fundamental Theorem of Calculus. International Group for the Psychology of Mathematics Education, 2, 165-172.
Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119-142.
Crisan, C., Geraniou, E., & Hodgen, J. (2023). Educational technologies in mathematics education. The Royal Society.
Denbel, D. G. (2014). Students’ misconceptions of the limit concept in a first calculus course. Journal of Education and Practice, 5(34), 24-40.
Donnelly, D., McGarr, O., & O’Reilly, J. (2011). A framework for teachers’ integration of ICT into their classroom practice. Computers & Education, 57(2), 1469-1483. https://doi.org/10.1016/j.compedu.2011.02.014
Dorko, A. (2020). Red X’s and green checks: a model of how students engage with online homework. International Journal of Research in Undergraduate Mathematics Education, 6(3), 446-474. https://doi.org/10.1007/s40753-020-00113-w
Dorko, A. (2021). How students use the ‘see similar example’ feature in online mathematics homework. The Journal of Mathematical Behavior, 63, 100894. https://doi.org/10.1016/j.jmathb.2021.100894
Drijvers, P. (2015). Digital technology in mathematics education: Why it works (or doesn’t). In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 135-151). Springer.
Drijvers, P., Sinclair, N. (2024). The role of digital technologies in mathematics education: Purposes and perspectives. ZDM Mathematics Education, 56, 239–248. https://doi.org/10.1007/s11858-023-01535-x
Ellis, J., Fosdick, B. K., & Rasmussen, C. (2016). Women 1.5 times more likely to leave STEM pipeline after calculus compared to men: Lack of mathematical confidence a potential culprit. PloS ONE, 11(7), 1-14. https://doi.org/10.1371/journal.pone.0157447
Esparza Puga, D. S., & Aguilar, M. S. (2021). Students’ perspectives on using YouTube as a source of mathematical help: The case of ‘julioprofe.’ International Journal of Mathematical Education in Science and Technology, 54(6), 1054–1066. https://doi.org/10.1080/0020739X.2021.1988165
Ferrara, F., Pratt, D., & Robutti, O. (2006). The role and uses of technologies for the teaching of algebra and calculus. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: past, present and future (pp. 237–273). Sense Publishers.
Griffiths, B. J. (2020). Returning to campus during the COVID-19 pandemic: perceptions of calculus students in Florida. In I. Sahin & M. Shelley (Eds.), Educational practices during the COVID-19 viral outbreak: International perspectives (pp. 239-253). ISTES Organization.
Gueudet, G., & Pepin, B. (2016, March). Students' work in mathematics and resources mediation at university. In E. Nardi, C. Winsløw & T. Hausberger (Eds.), Proceedings of the First Conference of the International Network for Didactic Research in University Mathematics (pp. 444-453). University of Montpellier and INDRUM. https://hal.science/hal-01337906v 1
Habre, S., & Abboud, M. (2006). Students’ conceptual understanding of a function and its derivative in an experimental calculus course. The Journal of Mathematical Behavior, 25(1), 57-72. https://doi.org/10.1016/j.jmathb.2005.11.004
Hall, W. L. (2010). Student misconceptions of the language of calculus: Definite and indefinite integrals. In R. Beichner, D. Bressoud, A. Simpson, & P. Herbst (Eds.), Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education. Raleigh, North Carolina. Retrieved October 15, 2024, from http://sigmaa.maa.org/rume/crume2010/Archive/Hall.pdf
Higgins, K., Huscroft-D’Angelo, J., & Crawford, L. (2019). Effects of technology in mathematics on achievement, motivation, and attitude: A meta-analysis. Journal of Educational Computing Research, 57(2), 283-319. https://doi.org/10.1177/0735633117748416
Hohenwarter, M., Hohenwarter, J., Kreis, Y., & Lavicza, Z. (2008). Teaching and learning calculus with free dynamic mathematics software GeoGebra. Proceedings of the 11th International Congress on Mathematics Education. Monterrey, Mexico
Hudson, R., Porter, A., & Nelson, M. (2008). Barriers to using ICT in mathematics teaching: Issues in methodology. In J. Luca & E. Weippl (Eds.), Educational Media 2008 World Conference on Educational Multimedia, Hypermedia and Telecommunications (pp. 5765-5776). Association for the Advancement of Computing in Education.
Hunter, J. S. (2011). The effects of graphing calculator use on high-school students' reasoning in Integral Calculus (Doctoral dissertation, University of New Orleans). ProQuest. https://login.auth.lib.niu.edu/login?url=https://www.proquest.com/dissertations-theses/effects-graphing-calculator-use-on-high-school/docview/879337423/se-2
Hsu J. L., Rowland-Goldsmith M., Schwartz E. B. (2022). Student motivations and barriers toward online and in-person office hours in STEM courses. CBE-Life Sciences Education, 21(4). https://doi.org/10.1187/cbe.22-03-0048
Khan, R. N. (2022). Attendance matters: Student performance and attitudes. International Journal of Innovation in Science and Mathematics Education, 30(4), 42-63. https://doi.org/10.30722/IJISME.30.04.004
Lampe, K., & White, K. (2023). The effects of online mathematics homework on learning, attitude, and efficacy in a college calculus class: A case study. PRIMUS, 33(10), 1091-1105. https://doi.org/10.1080/10511970.2023.2235686
Liang, S. (2016). Teaching the concept of limit by using conceptual conflict strategy and Desmos graphing calculator. International Journal of Research in Education and Science, 2(1), 35-48. https://doi.org/10.21890/ijres.62743
Loch, B. (2005). Tablet technology in first year calculus and linear algebra teaching. In M. Bulmer, H. MacGillivray & C. Varsavsky (Eds.), Proceedings of the 5th Southern Hemisphere Conference on Undergraduate Mathematics and Statistics Teaching and Learning (pp. 22-26). Retrieved October 15, 2024, from https://research.usq.edu.au/item/9x78q/tablet-technology-in-first-year-calculus-and-linear-algebra-teaching
Maciejewski, W. (2016). Flipping the calculus classroom: an evaluative study. Teaching Mathematics and its Applications: An International Journal of the IMA, 35(4), 187-201. https://doi-org.auth.lib.niu.edu/10.1093/teamat/hrv019
Martinez-Planell, Rafael & Moore-Russo, Deborah. (2023). Multivariable calculus instructors' reports of resource use: Resources used and reasons for their use. In S. Cook, B. Katz, & D. Moore-Russo (Eds.), Proceedings of the 25th Annual Conference on Research in Undergraduate Mathematics Education (pp. 53-62).
Mathematical Association of America (n.d.). Best practices statements. Retrieved October 15, 2024, from https://maa.org/resource/best-practices-statements/
Muhazir, A., & Retnawati, H. (2020). The teachers’ obstacles in implementing technology in mathematics learning classes in the digital era. Journal of Physics: Conference Series, 1511(1), 12022. https://doi.org/10.1088/1742-6596/1511/1/012022
Muis, K. R. (2004). Personal epistemology and mathematics: A critical review and synthesis of research. Review of Educational Research, 74(3), 317-377. https://doi.org/10.3102/00346543074003317
National Council of Teachers of Mathematics (2023). Equitable integration of technology for mathematics learning: A position of the National Council of Teachers of Mathematics. Retrieved October 16, 2024, from https://www.nctm.org/Standards-and-Positions/Position-Statements/Equitable-Integration-of-Technology-for-Mathematics-Learning/
Ní Shé, C., Ní Fhloinn, E., & Mac an Bhaird, C. (2023). Student engagement with technology-enhanced resources in mathematics in higher education: A review. Mathematics, 11(3), 787. https://doi.org/10.3390/math11030787
Nongharnpituk, P., Yonwilad, W., & Khansila, P. (2022). The effect of GeoGebra software in calculus for mathematics teacher students. Journal of Educational Issues, 8(2), 755-770. https://doi.org/10.5296/jei.v8i2.20422
Olive, J., Makar, K., Hoyos, V., Kor, L.K., Kosheleva, O., Sträßer, R. (2009). Mathematical knowledge and practices resulting from access to digital technologies. In C. Hoyles, J. B. Lagrange (Eds.), Mathematics education and technology-rethinking the terrain (Vol. 13, pp. 133-178). Springer Science and Business Media. https://doi.org/10.1007/978-1-4419-0146-0_8
Orhun, N. (2012). Graphical understanding in mathematics education: Derivative functions and students’ difficulties. Procedia-Social and Behavioral Sciences, 55, 679-684. https://doi.org/10.1016/j.sbspro.2012.09.551
Othman, Z. S., Tarmuji, N. H., & Hilmi, Z. A. G. (2017). Students perception on the usage of PowerPoint in learning calculus. AIP Conference Proceedings, 1830(1). https://doi.org/10.1063/1.4980942
Pepin, B., & Kock, J. (2019). Towards a better understanding of engineering students’ use and orchestration of resources: Actual student study paths. Eleventh Congress of the European Society for Research in Mathematics Education, 36. Utrecht University. https://hal.science/hal-02422663v1
Pepin, B., & Kock, Z. J. (2021). Students’ use of resources in a challenge-based learning context involving mathematics. International Journal of Research in Undergraduate Mathematics Education, 7(2), 306-327. https://doi.org/10.1007/s40753-021-00136-x
Rasmussen, C., & Ellis, J. (2013). Who is switching out of calculus and why. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (pp. 73-80). PME. Retrieved October 15, 2024, from https://homepages.math.uic.edu/~bshipley/Switching.Calculus.pdf
Rasmussen, C., Marrongelle, K., & Borba, M. C. (2014). Research on calculus: what do we know and where do we need to go? ZDM, 46(4), 507–515. https://doi.org/10.1007/s11858-014-0615-x
Rasslan, S., & Tall, D. O. (2002). Definitions and images for the definite integral concept. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 89–96). IGPME. Retrieved October 15, 2024, from https://files.eric.ed.gov/fulltext/ED476065.pdf
Riegle-Crumb, C., King, B., & Irizarry, Y. (2019). Does STEM stand out? Examining racial/ethnic gaps in persistence across postsecondary fields. Educational Researcher, 48(3), 133-144. https://doi.org/10.3102/0013189X19831006
Sacristán, A. I. (2017). Digital technologies in mathematics classrooms: barriers, lessons and focus on teachers. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 90–99).
Saldaña, J. M. (2021). The Coding Manual for Qualitative Researchers (4th ed.). SAGE Publications.
Sealey, V. (2014). A framework for characterizing student understanding of Riemann sums and definite integrals. The Journal of Mathematical Behavior, 33, 230-245. https://doi.org/10.1016/j.jmathb.2013.12.002
Serhan, D. (2015). Students' understanding of the definite integral concept. International Journal of Research in Education and Science, 1(1), 84-88. https://doi.org/10.21890/ijres.00515.
Serkan, C. G. (2013). The good, the bad, and the ugly: The integration of computing technology into calculus classes (Doctoral dissertation, University of Georgia). Retrieved October 15, 2024, from https://getd.libs.uga.edu/pdfs/serkan_christopher_g_201308_phd.pdf
Sevimli, E. (2016). Do calculus students demand technology integration into learning environment? Case of instructional differences. International Journal of Educational Technology in Higher Education, 13, 1-18. https://doi.org/10.1186/s41239-016-0038-6
Sithole, A., Chiyaka, E. T., McCarthy, P., Mupinga, D. M., Bucklein, B. K., & Kibirige, J. (2017). Student attraction, persistence and retention in STEM programs: Successes and continuing challenges. Higher Education Studies, 7(1), 46-59. https://doi.org/10.5539/hes.v7n1p46
Sonnert, G., Sadler, P. M., Sadler, S. M., & Bressoud, D. M. (2014). The impact of instructor pedagogy on college calculus students’ attitude toward mathematics. International Journal of Mathematical Education in Science and Technology, 46(3), 370–387. https://doi.org/10.1080/0020739X.2014.979898
Swanson, J. A., Renes, S. L., Strange, A. T. (2020). The communication preferences of collegiate students. In P. Isaias, D. G. Sampson, & D. Ifenthaler (Eds.), Online teaching and learning in higher education. Cognition and exploratory learning in the digital age. Springer. https://doi.org/10.1007/978-3-030-48190-2_4
Takači, D., Stankov, G., & Milanovic, I. (2015). Efficiency of learning environment using GeoGebra when calculus contents are learned in collaborative groups. Computers & Education, 82, 421-431. https://doi.org/10.1016/j.compedu.2014.12.002
Tall, D. (1986). Using the computer as an environment for building and testing mathematical concepts: A tribute to Richard Skemp. Papers in Honor of Richard Skemp, 21-36. Retrieved October 15, 2024, from https://www.academia.edu/download/95495496/dot1986h-computer-skemp.pdf
Thompson, P. W. (1994). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(2), 229-274. http://www.jstor.org/stable/3482785
Vajravelu, K., & Muhs, T. (2016). Integration of digital technology and innovative strategies for learning and teaching large classes: A calculus case study. International Journal of Research in Education and Science, 2(2), 379-395. https://doi.org/10.21890/ijres.67867
VanDieren, M., Moore-Russo, D., & Seeburger, P. (2020). Technological pedagogical content knowledge for meaningful learning and instrumental orchestrations: A case study of a cross product exploration using CalcPlot3D. In J. P. Howard & J. F. Beyers (Eds.), Teaching and learning mathematics online (pp. 267-294). Chapman and Hall/CRC. https://doi.org/10.1201/9781351245586
Wagner, J. F. (2018). Students’ obstacles to using Riemann sum interpretations of the definite integral. International Journal of Research in Undergraduate Mathematics Education, 4(3), 327-356. https://doi.org/10.1007/s40753-017-0060-7
Young, J., Gorumek, F., & Hamilton, C. (2018). Technology effectiveness in the mathematics classroom: A systematic review of meta-analytic research. Journal of Computers in Education, 5(2), 133-148. https://doi.org/10.1007/s40692-018-0104-2
Yu, F. (2023). Promoting productive understandings of rate of change in calculus courses. PRIMUS, 33(9), 965-980. https://doi.org/10.1080/10511970.2023.2214891
Downloads
Published
Issue
Section
License
Copyright (c) 2026 International Journal of Education in Mathematics, Science and Technology
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Articles may be used for research, teaching, and private study purposes. Authors alone are responsible for the contents of their articles. The journal owns the copyright of the articles. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of the research material.
The author(s) of a manuscript agree that if the manuscript is accepted for publication in the journal, the published article will be copyrighted using a Creative Commons “Attribution 4.0 International” license. This license allows others to freely copy, distribute, and display the copyrighted work, and derivative works based upon it, under certain specified conditions.
Authors are responsible for obtaining written permission to include any images or artwork for which they do not hold copyright in their articles, or to adapt any such images or artwork for inclusion in their articles. The copyright holder must be made explicitly aware that the image(s) or artwork will be made freely available online as part of the article under a Creative Commons “Attribution 4.0 International” license.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
