Abstract:

Engineering mathematics: an ongoing debate:
In May 1979 Robert D. Strum and Donald E. Kirk published a paper on IEEE TRANSACTIONS ON EDUCATION titled “Engineering Mathematics: Who Should Teach It and How?” [1]. In this paper the authors complained about the mathematical deficiencies of engineering students and, in order to provide pedagogical recommendation, they elaborate on the following points: a) who should be responsible for Engineering Mathematics, the mathematician or the engineer? b) What is the role of rigor and abstraction in the early courses? c) Which kind of mathematics should be taught to undergraduate students? More than forty years later the issues raised by Strum and Kirk are still relevant and not fully resolved [2]. In the first part of this paper we will reconsider those themes in the light of the recent evolution in the following areas:
a) the increasingly blurring boundaries between pure and applied mathematics;
b) the growing role of technology in education and society in general;
c) the flexibility required by new generations of engineers to copy with a volatile and fast-changing industrial and service sector.

Pure Vs “application-driven” mathematics:
At the origin of this debate there is a perceived dichotomy in which two ideas of mathematics are contrasted: pure mathematics (abstract, proof-based) vs. application-driven mathematics (modelling and equation-solving activity). We argue that this opposition is outdated and misleading for the following reasons: a) some theoretical abstractions (like "set" or "function") and theorems (like the binomial formula) are necessary both for developing an analytical "forma mentis" and for proceeding to more advanced techniques commonly used in engineering; b) it is difficult to predict which kind of mathematics will be “useful”, and which will have an impact on the engineering practice of the future, so the engineering student needs to be equipped with tools that allows him/her to approach new mathematics if needed and this require a strong theoretical foundation.

Experimenting with mathematics:
Based on our ten-year teaching experience of teaching undergraduate mathematics to engineering students we elaborate an educational philosophy in which we stress the importance of transmitting a core mathematical theoretical knowledge combined with the promotion of an experimental attitude towards mathematical manipulation. With this we mean a teaching approach that fosters and rewards creative, alternative ways of reaching a given mathematical result. In this way, on one hand we oppose to the widespread opinion - common between students - that mathematics is only a dry application of formulas. On the other hand, the stress on experimentation as exploration of different paths encourages a research attitude, forces a critical self-reflection on what has been learned and pave the way for further developments and applications of mathematics in different areas.

References:
[1] R. D. Strum and D. E. Kirk, "Engineering Mathematics: Who Should Teach It and How?," in IEEE Transactions on Education, vol. 22, no. 2, pp. 85-88, May 1979, doi: 10.1109/TE.1979.4321299.
[2] G. H. Gomes, A. S. González-Martín. Mathematics in Engineering: The professors’ vision. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, Charles University in Prague, Faculty of Education; ERME, Feb 2015, Prague, Czech Republic. pp.2110-2116. hal-0128858.

Keywords:

Engineering Mathematics, Applied and pure mathematics, Experimentation.