Klein's double discontinuity revisited: contemporary challenges for universities preparing teachers to teach calculus

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Much effort and research has been invested into understanding and bridging the ‘gaps’ which many students experience in terms of contents and expectations as they begin university studies with a heavy component of mathematics, typically in the form of calculus courses. We have several studies of bridging measures, success rates and many other aspects of these “entrance transition” problems. In this paper, we consider the inverse transition, experienced by university students as they revisit core parts of high school mathematics (in particular, calculus) after completing the undergraduate mathematics courses which are mandatory to become a high school teacher of mathematics. To what extent does the “advanced” experience enable them to approach the high school calculus in a deeper and more autonomous way ? To what extent can “capstone” courses support such an approach ? How could it be hindered by deficiencies in the students’ “advanced” experience ? We present a theoretical framework, based on the anthropological theory of the didactic, for an analysis of these questions, as well as a number of critical observations and reflections on how these questions appear as challenges in the Danish institutional context.
Original languageEnglish
JournalRecherches en Didactique des Mathématiques
Issue number1
Pages (from-to)59-86
Publication statusPublished - 2014

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