Skip to main content

Advertisement

SpringerLink
Log in

A Call for Research that Explores Relationships between Computing and Mathematical Thinking and Activity in RUME

  • Published:
International Journal of Research in Undergraduate Mathematics Education Aims and scope Submit manuscript

Abstract

Computational thinking and activity are vital aspects of what it means to conduct scientific and mathematical work. In light of this, some propose that students’ mathematical education should include an integration of computing into their mathematical experiences, giving students opportunities to engage with computational tools as they reason about mathematical concepts. In this commentary, we make a case that the international RUME community should focus on studying the integration of computing in research in undergraduate mathematics education. We situate this discussion within existing literature. Then, we suggest ways in which researchers can incorporate ideas related to computing, and we propose ideas for how investigations into computing might practically be incorporated into our already-existing research foci. Ultimately, we hope to motivate other members of the RUME community to join us in what we consider to be a timely and exciting endeavor.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adiredja, A. P., & Andrews-Larson, C. (2017). Taking the sociopolitical turn in postsecondary mathematics education research. International Journal of Research in Undergraduate Mathematics Education, 3(3), 444–465.

    Article  Google Scholar 

  • Ayalon, M., Watson, A., & Lerman, S. (2016). Reasoning about variables in 11 to 18 year olds: Informal, schooled and formal expression in learning about functions. Mathematics Education Research Journal, 28, 379–404. https://doi.org/10.1007/s13394-016-0171-5.

    Article  Google Scholar 

  • Benton, L, Hoyles, C, Kalas, I and Noss, R. (2017). Bridging primary programming and mathematics: Some findings of design research in England. Digital Experiences in Mathematics Education, 1-24.

  • Benton, L., Saunders, P., Kalas, I., Hoyles, C., & Noss, R. (2018). Designing for learning mathematics through programming: A case study of pupils engaging with place value. International Journal of Child-Computer Interaction, 16, 68–76.

    Article  Google Scholar 

  • Blikstein, P. (2018). Pre-college computer science education: A survey of the field. Mountain View, CA: Google LLC. Retrieved from https://goo.gl/gmS1Vm

  • Broley, L., Caron, F., & Saint-Aubin, Y. (2018). Levels of programming in mathematical research and university mathematics education. International Journal of Research in Undergraduate Mathematics Education, 4(1), 38–55.

  • Buteau, C., Gueudet, G., Muller, E., Mgombelo, J., & Sacristan, A. I. (2019). University students turning computer programming into an instrument for ‘authentic’ mathematical work. International Journal of Mathematical Education in Science and Technology, 51(7), 1020–1041. 

  • Buteau, C., & Muller, E. (2017). Assessment in undergraduate programming-based mathematics courses. Digital Experiences in Mathematics Education, 3, 97–114. https://doi.org/10.1007/s40751-016-0026-4.

    Article  Google Scholar 

  • Caballero, M. D., Kohlmyer, M. A., & Schatz, M. F. (2012). Implementing and assessing computational modeling in introductory mechanics. Physical Review Special Topics – Physics Education Research, 8, 1–15. https://doi.org/10.1103/PhysRevSTPER.8.020106.

    Article  Google Scholar 

  • Cook, J. P. (2014). The emergence of algebraic structure: Students come to understand units and zero-divisors. International Journal of Mathematical Education in Science and Technology, 45(3), 349–359.

    Article  Google Scholar 

  • DeJarnette, A. F. (2019). Students’ challenges with symbols and diagrams when using a programming environment in mathematics. Digital Experiences in Mathematics Education, 5, 36–58. https://doi.org/10.1007/s40751-018-0044-5.

    Article  Google Scholar 

  • diSessa, A. A. (2000). Changing minds: Computers, learning, and literacy. Cambridge: MIT Press.

    Book  Google Scholar 

  • diSessa, A. A. (2018). Computational literacy and “the big picture” concerning computers in mathematics education. Mathematical Thinking and Learning, 20(1), 3–31. https://doi.org/10.1080/10986065.2018.1403544.

    Article  Google Scholar 

  • Fenton, W., & Dubinsky, E. (1996). Introduction to discrete mathematics with ISETL. New York: Springer-Verlag.

    Book  Google Scholar 

  • Feurzeig, W., Papert, S., & Lawler, B. (2011). Programming-languages as a conceptual framework for teaching mathematics. Interactive Learning Environments, 19(5), 487–501.

    Article  Google Scholar 

  • Guzdial, M., & Soloway, E. (2003). Computer science is more important than calculus: The challenge of living up to our potential. Association for Computing Machinery Special Interest Group on Computer Science Education Bulletin, 35(2), 5–8.

    Google Scholar 

  • Hickmott, D., Prieto-Rodriguez, E., & Holmes, K. (2018). A scoping review of studies on computational thinking in K-12 mathematics classrooms. Digital Experiences in Mathematics Education, 4, 48–69. https://doi.org/10.1007/s4075-017-0038-8.

    Article  Google Scholar 

  • Hohensee, C. (2014). Backward transfer: An investigation of the influence of quadratic functions instruction on students’ prior ways of reasoning about linear functions. Mathematical Thinking and Learning, 16(2), 135–174.

    Article  Google Scholar 

  • Hoyles, C., & Noss, R. (2015). A computational lens on design research. In S, Prediger, K. Gravemeijer, & J. Confrey, (Eds.) Design research with a focus on learning processes: an overview on achievements and challenges. ZDM, (47)6, 1039–1045.

  • Ke, F. (2014). An implementation of design-based learning through creating educational computer games: A case study on mathematics learning during design and computing. Computers & Education, 73, 26–39.

    Article  Google Scholar 

  • Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence & variable. ZDM, 37, 68–76. https://doi.org/10.1007/BF02655899.

  • Kotsopoulos, D., Floyd, L., Khan, S., Kizito Namukasa, I., Somanath, S., Weber, J., & Yiu, C. (2017). A pedagogical framework for computational thinking. Digital Experiences in Mathematics Education, 3, 154–171. https://doi.org/10.1007/s40751-017-0031-2.

    Article  Google Scholar 

  • Kuittinen, M. & Sajaniemi, J. (2004). Teaching roles of variables in elementary programming courses. Proceedings of the ninth annual SIGCSE conference on innovation and technology in computer science education, 57–61. doi:https://doi.org/10.1145/1026487.1008014.

  • Larsen, S. (2013). A local instructional theory for the guided reinvention of the group and isomorphism concepts. Journal of Mathematical Behavior, 32(4), 712–725.

  • Leyva, L. A. (2016). An intersectional analysis of Latin@ college women’s counter-stories in mathematics. Journal of Urban Mathematics Education, 9(2), 81–121.

    Google Scholar 

  • Lobato, J. (2006). Alternative perspectives on the transfer of learning: History, issues, and challenges for future research. The Journal of the Learning Sciences, 15(4), 431–449.

    Article  Google Scholar 

  • Lobato, J. (2012). The actor-oriented transfer perspective and its contributions to educational research and practice. Educational Psychologist, 47(3), 232–247.

    Article  Google Scholar 

  • Lockwood, E., DeJarnette, A. F., & Thomas, M. (2019). Computing as a mathematical disciplinary practice. Online first in Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2019.01.004.

  • Lockwood, E. & De Chenne, A. (2019). Using conditional statements in Python to reason about sets of outcomes in combinatorial problems. International Journal of Research in Undergraduate Mathematics Education.

  • Lockwood, E., Wasserman, N. H., & Tillema, E. S. (2020). A case for combinatorics: A research commentary. Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2020.100783.

  • Malthe-Sørenssen, A., Hjorth-Jensen, M., Langtangen, H. P., & Mørken, K. (2016). Integrating computation in the teaching of physics. Uniped, 38. Retrieved from http://hplgit.github.io/cse-physics/doc/pub/uniped15.html.

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer Academic Press.

    Book  Google Scholar 

  • Noss, R., Hoyles, C., & Pozzi, S. (2002). Abstraction in expertise: A study of nurses’ conceptions of concentration. Journal for Research in Mathematics Education, 33(3), 204–229.

    Article  Google Scholar 

  • Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic books.

    Google Scholar 

  • Perlis, A. (1962). The computer in the university. In M. Greenberger (Ed.), Computers and the world of the future (180–219). Cambridge: MIT Press.

    Google Scholar 

  • Rasmussen, C., Apkarian, N., & Hagman, J. E. (2019). Characteristics of precalculus through calculus 2 programs: Insights from a national census survey. Journal for Research in Mathematics Education, 50(1), 98–111.

    Article  Google Scholar 

  • Sengupta, P., Dickes, A., & Farris, A.V. (2018). Toward a phenomenology of computational thinking in STEM. In: Khine, M.S. (Ed.): Computational Thinking in STEM: Research Highlights (pp. 49-72). Springer: New York.

  • Sinclair, N., & Patterson, M. (2018). The dynamic Geometrisation of computer programming. Mathematical Thinking and Learning, 20(1), 54–74. https://doi.org/10.1080/10986065.2018.1403541.

    Article  Google Scholar 

  • Speer, N. M., Smith III, J. P., & Horvath, A. (2010). Collegiate mathematics teaching: An unexamined practice. Journal of Mathematical Behavior, 29(2), 99–114.

    Article  Google Scholar 

  • Sutherland, R., & Hoyles, C. (1988). Gender perspectives on logo programming in the mathematics classroom. In C. Hoyles (Ed.), Girls and computers: General issues and case studies of logo in the mathematics classroom, Bedford way papers 34 (pp. 40–63). University of London: London.

    Google Scholar 

  • Tallman, M. & Frank, K. (2018). Angle measure, quantitative reasoning, and instructional coherence: An examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base. Online first, Journal of Mathematics Teacher Education.

  • Tedre, M. & Denning, P. J. (2016). The long quest for computational thinking. Proceedings of the 16th Koli Calling International Conference on Computing Education Research (pp. 120-129).

  • Tuomi-Gröhn, T., & Engeström, Y. (2003). Conceptualizing transfer: From standard notions to developmental perspectives. In T. Tuomi-Gröhn & Y. Engeström (Eds.), Between school and work: New perspectives on transfer and boundary-crossing (pp. 19–38). New York: Pergamon.

    Google Scholar 

  • Vale, C. M., & Leder, G. C. (2004). Student views of computer-based mathematics in the middle years: Does gender make a difference? Educational Studies in Mathematics, 56, 287–312.

    Article  Google Scholar 

  • Wasserman, N. (Ed.) (2018). Connecting abstract algebra to secondary mathematics, for secondary teachers. Switzerland: Springer International.

  • Wawro, M., Rasmussen, C., Zandieh, M., Sweeney, G., & Larson, C. (2012). An inquiry-oriented approach to span and linear independence: The case of the magic carpet ride sequence. PRIMUS, 22(7), 1–23. https://doi.org/10.1080/10511970.2012.667516.

    Article  Google Scholar 

  • Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science and Education Technology, 25, 127–147. https://doi.org/10.1007/s10956-015-0581-5.

    Article  Google Scholar 

  • Wing, J. M. (2006). Computational thinking. Communications of the ACM., 49(3), 33–35.

    Article  Google Scholar 

  • Zanko, Z., Mladenović, M., & Boljat, I. (2019). Misconceptions about variables at the K-12 level. Education and Information Technologies, 24(2), 1251–1268. https://doi.org/10.1007/s10639-018-9824-1.

    Article  Google Scholar 

Download references

Acknowledgments

This work was funded by the National Science Foundation (1650943), by Norges Forskningsråd (288125), and by the Center for Computing in Science Education at the University of Oslo. On behalf of all authors, the corresponding author states that there is no conflict of interest.

Author information

Authors and Affiliations

  1. Department of Mathematics, Oregon State University, 064 Kidder Hall, Corvallis, OR, 97331, USA

    Elise Lockwood

  2. Center for Computing in Science Education, University of Oslo, Sem Saelands vei 24, Fysikkbygningen, 0371, Oslo, Norway

    Elise Lockwood & Knut Mørken

Authors
  1. Elise Lockwood
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Knut Mørken
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elise Lockwood.

Ethics declarations

Conflict of Interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lockwood, E., Mørken, K. A Call for Research that Explores Relationships between Computing and Mathematical Thinking and Activity in RUME. Int. J. Res. Undergrad. Math. Ed. 7, 404–416 (2021). https://doi.org/10.1007/s40753-020-00129-2

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40753-020-00129-2

Keywords

Search

Navigation