Abstract
There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is to frame current narratives of mathematics from a virtue-theoretic perspective. We identify the practice of mathematizing, put forward by Freudenthal’s ‘Realistic mathematics education’, as virtuous and use it to evaluate different narratives. We show that this can help to render the narratives more adequately, and to provide implications for societal organization.
Highlights
When the second author participated in an award ceremony for the local mathematics olympiads there was a greeting by the states minister of education
We argued that mathematizing is a virtuous practice, because it offers tools to grasp a larger part of reality and is beneficial for epistemically valuable ends such as understanding
Our main point is that mathematizing as a virtuous practice is a narrative which captures integral parts of mathematical practice, including the activity of research mathematicians, mathematics learners or applied scientists
Summary
When the second author participated in an award ceremony for the local mathematics olympiads there was a greeting by the states minister of education. This virtue narrative focusing on mathematizing is better than other competing narratives that are currently more present in society The latter often hide the arbitrary component factors of mathematical models which depart from the real-world context for reasons of reducing complexity or favoring simplicity of the mathematical tools for example. 2, we briefly introduce the notion of mathematizing, mostly focusing on Freudenthal’s work His approach is mainly used to understand education for primary school level children. 4, we report and analyze narratives of mathematics that we encountered during our university studies as two trained mathematicians, a series of interview studies and research conferences in the fields of mathematics, philosophy, and mathematics education In this sense, this analysis does not constitute a precise cartography of beliefs about the nature of mathematics but should be seen as contributing an exploratory exposition. We evaluate their adequacy and the problems we encounter and see how the narratives change when we add the assumption that mathematizing is the main characteristic of mathematical activity
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