The Legacy of Felix Klein by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783319993867
Publisher: Springer International Publishing

8.2 History of Mathematics in Mathematics Education

The topic of “the use of the history of mathematics in mathematics teaching” is gaining popularity in the international discourse of mathematics education. Possible reasons for this might be the introduction of topics from the history mathematics in the curricula in such countries as Denmark, Austria or Great Britain, or likewise the new interest in concept development from a mathematical perspective and the historical genetic method in the style of Toeplitz (1949).

There are numerous publications on the variety of ways of using the history of mathematics in teaching mathematics as well as on the promotion of mathematical interests which range from theoretical material for classification (e.g. Jankvist 2009; Kronfellner 1998) to concrete descriptions of their realizations in teaching practices (e.g. Fauvel and van Maanen 2000; Katz and Michalowicz 2000; Jahnke 2006; Shell-Gellasch 2007; Glaubitz 2011). It is important to note whether the history of mathematics and mathematics education is used to inspire new perspectives on the teaching of mathematics and concept development or whether the history of a mathematical idea, an authority or an institution are the subject of investigation. The latter especially presumes methodology and knowledge of the history of mathematics.

A special challenge is presented by the use of original historical sources in order to teach a mathematical idea as well as its historical conceptual development. In this case, on top of the use of representations and mathematical languages that are different to those the students are used to, problems may also occur due to a foreign or ancient language or to different translations of the original source. On the other hand, working with artefacts bearing contemporary witness to a past period is particularly attractive. The mathematical exploration of historical sources is often easier if related to models, instruments, equipment or also mathematical toys, and even better if accompanied by appropriate texts and descriptions of the experiments. The mathematical concept development also benefits from the use of mathematical instruments and visualizing models. Vollrath illustrates how this can be done with a non-historical approach to historical drawing and measuring instruments in his book “Verborgene Ideen” (en.: hidden ideas) (Vollrath 2013).

There is no doubt that it is important for future mathematics teachers to know some of the history of their own discipline, that is, the history of mathematics, but also the history of their own profession, i.e. the history of mathematics education. Both topics are scientific disciplines with specialized knowledge and methodology. Do student teachers have the prerequisites and capabilities to look into the history of a mathematical concept in order to teach it later on with historical awareness?

To include the contents of the history of mathematics in their teaching, teachers are required to have developed a particular interest in this field and to therefore gladly accept the challenge of teaching mathematics in a way that also embraces perspectives of the humanities. Hardly any German university offers canonical lectures on the cultural history of mathematics or on selected topics on the history of mathematics. Therefore,

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