Impact of Informatics on Mathematics and Its Teaching
In this article, we come back to the seminal role of epistemology in didactics of sciences and particularly in mathematics. We defend that the epistemological research on the interactions between mathematics and informatics is necessary to feed didactical
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Abstract. In this article, we come back to the seminal role of epistemology in didactics of sciences and particularly in mathematics. We defend that the epistemological research on the interactions between mathematics and informatics is necessary to feed didactical research on today’s mathematics learning and teaching situations, impacted by the development of informatics. We develop some examples to support this idea and propose some perspectives to attack this issue. Keywords: Epistemology · Didactics · Education Informatics · Computer science · Interactions
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Mathematics
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Introduction
The teaching of mathematics has been questioned for more than 30 years by the development of computer science (informatics in the following) due to its strong relation with mathematics [11,14]. Today, we witness the generalization of the teaching of informatics (inside or beside mathematics), the introduction in mathematics curricula of contents shared with informatics (like algorithmics or combinatorics), and the generalization of computers as tools for teaching, especially in mathematics. Naturally, those changes raise many educational questions that have partly already been studied. Although, we want to focus on some of these questions with the point of view of epistemology and its relation to didactics. We will exemplify these questions and show how important is the epistemology of the informatics-mathematics relation in order to tackle these issues. Indeed, mathematics and informatics have strong links and a common history. More precisely, (1) they share common foundations, structured by logics, and a specific relation with proof [7], (2) there is a certain continuity between them with many fields developing at their interface, c IFIP International Federation for Information Processing 2016 Published by Springer International Publishing AG 2016. All Rights Reserved F. Gadducci and M. Tavosanis (Eds.): HaPoC 2015, IFIP AICT 487, pp. 243–255, 2016. DOI: 10.1007/978-3-319-47286-7 17
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(3) computer assisted mathematics changes the way some mathematicians work, emphasizing the experimental dimension of mathematics [22], and (4) mathematics and informatics, sometimes classified as formal sciences, have a very similar relation to other sciences through modelling and simulation (this aspect will not be discussed in details here). In the first section, we will elaborate on the role of epistemology in didactics and precise how it can be implement in the case of the interaction informaticsmathematics. In the second section, we will give examples of approaches to cope with these didactical questions and illustrate them: links between proof and algorithms, language issues, differences between mathematical and algorithmic thinkings, experimental mathematics, role of the computer and the appearance of new objects.
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The Need for Epistemological Analysis of Interactions Between Informatics and Mathematics to Feed Didactical Research
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On the Links Between Epistemology and Didactics of Sciences
Didactics of sciences
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