Drawing on a computer algorithm to advance future teachers’ knowledge of real numbers: A case study of task design

Rongrong Huo 1 *
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1 Department of Science Education, University of Copenhagen, København, DENMARK
* Corresponding Author
EUR J SCI MATH ED, Volume 11, Issue 2, pp. 283-296. https://doi.org/10.30935/scimath/12640
Published Online: 14 November 2022, Published: 01 April 2023
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ABSTRACT

In our investigation of university students’ knowledge about real numbers in relation to computer algebra systems (CAS) and how it could be developed in view of their future activity as teachers, we used a computer algorithm as a case to explore the relationship between CAS and the knowledge of real numbers as decimal representations. Our work was carried out in the context of a course for university students who aim to become mathematics teachers in high schools. The main data consists of students’ written responses to an assignment of the course and interviews to clarify students’ perspectives in relation to the responses. The analysis of students’ work is based on the anthropological theory of the didactic (ATD). Our results indicate that simple CAS-routines have a potential to help university students (future teachers) to apply their university knowledge on certain problems related to the decimal representation of real number which are typically encountered but not well explained in high school.
Keywords: CAS, ATD, real numbers, future teachers

CITATION

Huo, R. (2023). Drawing on a computer algorithm to advance future teachers’ knowledge of real numbers: A case study of task design. European Journal of Science and Mathematics Education, 11(2), 283-296. https://doi.org/10.30935/scimath/12640

REFERENCES

  • Barquero, B., & Winsløw, C. (2022). Preservice secondary school teachers revisiting real numbers: a striking instance of Klein’s second discontinuity [Manuscript submitted for publication]. University of Copenhagen.
  • Bergé, A. (2010). Student’s perception of completeness property of the set of real numbers. International Journal of Mathematical Education in Science and Technology, 41(2), 217-227. https://doi.org/10.1080/00207390903399638
  • Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima Journal of Mathematics Education, 12, 71-114.
  • Durand-Guerrier, V. (2016). Conceptualization of the continuum, an educational challenge for undergraduate students. International Journal of Research in Undergraduate Mathematics Education, 2, 338-361. https://doi.org/10.1007/s40753-016-0033-2
  • Forsythe, G. E. (1959). The role of numerical analysis in an undergraduate program. The American Mathematical Monthly, 66(8), 651-662. https://doi.org/10.2307/2309339
  • González, M. F., Kuzniak, A., Delgadillo, E., & Vivier, L. (2019). Two situations for working key properties of R. In U. T. Jankvist, M. Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the 11th Congress of the European Society for Research in Mathematics Education (pp.2492-2493). ERME.
  • González-Martín, A. S., Giraldo, V., & Souto, A. M. (2013). The introduction of real numbers in secondary education: An institutional analysis of textbooks. Research in Mathematics Education, 15(3), 230-248. https://doi.org/10.1080/14794802.2013.803778
  • Gyöngyösi, E., Solovej, J. P., & Winsløw, C. (2011). Using CAS based work to ease the transition from calculus to real analysis. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the 7th Congress of the European Society for Research in Mathematics Education (pp. 2002-2011). ERME.
  • Hill, H. C., Rowan, B., & Ball, D.L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
  • Klein, F. (2016). Elementary mathematics from a higher standpoint: Volume I: Arithmetic, algebra, analysis (G. Schubring, Trans.). Springer. https://doi.org/10.1007/978-3-662-49439-4
  • Krainer, K., Hsieh, F. J., Peck, R., & Tatto, M. (2015). The TEDS-M: Important issues, results and questions. In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 99-121). Springer. https://doi.org/10.1007/978-3-319-12688-3_10
  • Lagrange, J. B. (2005). Using symbolic calculators to study mathematics: The case of tasks and techniques. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 113-135). Springer. https://doi.org/10.1007/0-387-23435-7_6
  • Schmidt, W. H., Houang, R., & Cogan, L. S. (2011). Preparing future math teachers. Science, 332(6035), 1266-1267. https://doi/10.1126/science.1193855
  • Sultan, A., & Artzt, A. F. (2018). The mathematics that every secondary school math teacher needs to know. Routledge. https://doi.org/10.4324/9781315391908
  • Winsløw, C. (2011). Anthropological theory of didactic phenomena: Some examples and principles of its use in the study of mathematics education. In M. Bosch, J. Gascón, A. Ruiz-Olarría, M. Artaud, A. Bronner, Y. Chevallard, G. Cirade, C. Ladage, & M. Larguier (Eds.), Un panorama de la TAD [An overview of the TAD] (pp. 117-140). Centre de Recerca Matemàtica [Center for Mathematical Research].
  • Winsløw, C. (2013). The transition from university to high school and the case of exponential functions. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of 8th Congress of the European Society for Research in Mathematics Education (pp. 2476-2485). ERME.
  • Winsløw, C., & Grønbæk, N. (2014). Klein’s double discontinuity revisited: Contemporary challenges for universities preparing teachers to teach calculus. Recherches en Didactique des Mathématiques [Research in Didactics of Mathematics], 34(1), 59-86.
  • Zazkis, R., & Sirotic, N. (2004). Making sense of irrational numbers: Focusing on representation. In M. Høines, & A. B. Fugelstaed (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (pp. 497-504). PME.