Task Design for Klein’s Second Discontinuity

Carl Winsløw; Rongrong  Huo

doi:10.46312/pem.v16i42.18388

Carl Winsløw University of Copenhagen https://orcid.org/0000-0001-8313-2241
Rongrong Huo University of Copenhagen https://orcid.org/0000-0002-1359-9863

DOI: https://doi.org/10.46312/pem.v16i42.18388

Keywords: Klein’s Second Discontinuity, Task Design, Anthropological Theory of the Didactic

Abstract

Since the 19th century, studies of mathematics at university have been a main component of the usual preparation for teaching at secondary level. Already around 1900, Klein pointed out that specific measures are needed to ensure that the university mathematical preparation becomes useful to the teacher, and he insisted that universities themselves must take responsibility for these measures. In this paper, we discuss this problem, as it presents itself in 2022, and we present and exemplify some principles of task design which are intended to support students’ mobilisation of university mathematical knowledge in relation to specific mathematical challenges for high school teachers.

Author Biographies

Carl Winsløw, University of Copenhagen

University of Copenhagen, IND, Faculty of Science, E-mail: winslow@ind.ku.dk. ORCID: https://orcid.org/0000-0001-8313-2241.

Rongrong Huo, University of Copenhagen

Rongrong Huo received the B.S. degree in Applied Mathematics from Jiangsu University, China in 2017 and the M.S. degree in Applied Mathematics from Suzhou University, China in 2020. She is currently working toward the Ph.D. degree in Mathematics Education with the Department of Science Education, University of Copenhagen, Denmark. Her research interests include university mathematics education, preservice high school mathematics teachers’ education and digital tools in mathematics education at high school level.

E-mail: rh@ind.ku.dk. ORCID: https://orcid.org/0000-0002-1359-9863.

References

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WINSLØW, Carl; GRØNBÆK, Niels. Klein’s double discontinuity revisited: contemporary challenges for universities preparing teachers to teach calculus. Recherches en diddactique des mathématiques, v. 34, n. 1, p. 59-86, 2014.

WINSLØW, Carl. Mathematical knowledge for the profession of upper secondary mathematics teaching. Submitted. Proceedings of the 7th international congress on ATD (CITAD7).

Task Design for Klein’s Second Discontinuity

Abstract

Author Biographies

References

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