About the “Mixture” of Discourses in the Use of Mathematics in Signal Theory<br>À propos du «mélange» de discours dans l'utilisation des mathématiques en théorie du signal
DOI:
https://doi.org/10.23925/1983-3156.2020v22i4p454-471Keywords:
Signal Theory, Dirac impulse, epistemology, ATDAbstract
Abstract
An important issue for research in university mathematics education is the use of mathematics in engineering. Here we focus on praxeologies in a course on system and signal theory (SST), which represents a typical module in electrical engineering studies in the third or fourth semester. In such courses, mathematics already studied in introductory mathematics courses will be applied, but also enriched by the introduction and development of new practices, in particular the so-called Dirac-impulse. We claim that the introduction and justification of the Dirac-impulse in SST is a convenient case where basic facets of epistemological relations between mathematics and engineering sciences might be illustrated and shown to be important for a detailed description and analysis of logos blocks of praxeologies. The background for our considerations regarding logos blocks of praxeologies that concern the introduction of the Dirac-impulse is given by philosophical studies by Wahsner and Borzeszkowski (1992, 2012) and a few illuminating remarks by Dirac.
Keywords: Signal Theory, Dirac impulse, Epistemology, ATD.
Résumé
Une question importante pour la recherche en éducation mathématique universitaire est l'utilisation des mathématiques en ingénierie. Ici, nous nous concentrons sur les praxéologies dans un cours sur la théorie du système et du signal (SST), qui représente un module typique dans les études d'ingénierie électrique au troisième ou quatrième semestre. Dans ces cours, non seulement applique-t-on les mathématiques déjà enseignées et apprises dans les cours d'introduction à la mathématique, mais on introduit et utilise aussi de nouveaux concepts mathématiques, en particulier ce que l'on appelle l'impulsion de Dirac. Nous affirmons que l'introduction et la justification de l'impulsion de Dirac dans SST est un cas pratique par lequel les facettes fondamentales des relations épistémologiques entre mathématiques et ingénierie pourraient être illustrées et démontrées importantes pour la description détaillée et l’analyse des logos blocs de praxéologies. Le contexte de nos considérations au sujet des logos blocs de praxéologies concernant l'introduction de l'impulsion de Dirac est donné par des études philosophiques de Wahsner et Borzeszkowski (1992, 2012) et quelques remarques éclairantes de Dirac.
Mots-clés: Théorie du signal, impulsion de Dirac, épistémologie, TAD.
Metrics
References
Alpers, B. (2017). Differences between the usage of mathematical concepts in engineering statics and engineering mathematics education. In Didactics of Mathematics in Higher Education as a Scientific Discipline – Conference Proceedings. khdm-Report 17-05 (pp. 137-141). Kassel: Universität Kassel.
Antosik, P., Mikusiński, J., & Sikorski, R. (1973). Theory of distributions: the sequential approach. Amsterdam [u.a.]: Elsevier Scientific Publ.
Barquero, B., Bosch, M., & Gascón, J. (2011). ‘Applicationism’ as the dominant epistemology at university. In CERME 7-Seventh Congress of the European Society for Research in Mathematics Education (pp. 1937-1948).
Barquero, B., Serrano, L., & Serrano V. (2013). Creating the necessary conditions for mathematical modelling at university. In CERME8-Eight Congress of the European Society for Research in Mathematics Education (pp. 950-959).
Blum, W., & Leiss, D. (2005). How do students and teachers deal with mathematical modelling problems? The example "Sugarloaf". ICTMA 12 Proceedings (pp. 222-231).
Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51–65.
Borzeszkowski, H. H. V., & Wahsner, R. (2012). Das physikalische Prinzip: der epistemologische Status physikalischer Weltbetrachtung. Königshausen & Neumann.
Castela, C., & Romo Vázquez, A. (2011). Des Mathematiques a l’Automatique: Etude des Effets de Transposition sur la Transformee de Laplace dans la Formation des Ingenieurs. RDM, 31(1), 79-130.
Chevallard, Y. (1992). Fundamental concepts in didactics: Perspectives provided by an anthropological approach. RDM, Selected Papers. La Pensée Sauvage, Grenoble, 131-167.
Chevallard, Y. (1999). L'analyse des practiques enseignantes en théorie anthropologique du didactique. RDM 19(2), 221-266.
Chevallard, Y., Bosch, M., & Kim, S. (2015). What is a theory according to the anthropological theory of the didactic? In CERME 9-Ninth Congress of the European Society for Research in Mathematics Education, (pp. 2614–2620).
Dirac, P. A. (1927). The physical interpretation of the quantum dynamics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 113(765), 621-641.
Dirac, P.A.M. (1958). The principles of quantum mechanics. 4. ed. Oxford: Clarendon Press.
Dirac, P.A.M. (1963). Interview with T.S. Kuhn. Archives for the History of Quantum Physics, Niels Bohr Library, AIP, New York
Fettweis, A. (1996). Elemente nachrichtentechnischer Systeme. Wiesbaden: Vieweg & Teubner Verlag.
Girod, B., Rabenstein, R., & Stenger, A. K. E. (2007). Einführung in die Systemtheorie - Signale und Syteme in der Elektrotechnik und Informationstechnik. Wiesbaden: B.G. Teubner Verlag.
Hochmuth, R., Biehler, R., & Schreiber, S. (2014). Considering mathematical practices in engineering contexts focusing on signal analysis. T. Fukawa-Connelly, G. Karakok, K. Keene & M. Zandieh. Proceedings of RUME17, 693-699.
Hochmuth, R., & Schreiber, S. (2015). Conceptualizing Societal Aspects of Mathematics in Signal Analysis. In S. Mukhopadhyay & B. Geer (Eds.), Proceedings of the Eight International Mathematics Education and Society Conference (Vol. 2, pp. 610–622). Portland: Ooligan Press.
Landers, D., & Rogge, L. (2013). Nichtstandard Analysis. Springer-Verlag.
Peters, K. H. (2004). Der Zusammenhang von Mathematik und Physik am Beispiel der Geschichte der Distributionen: Eine historische Untersuchung über die Grundlagen der Physik im Grenzbereich zu Mathematik, Philosophie und Kunst. Dissertation, Universität Hamburg.
Peters, J., Hochmuth, R., & Schreiber, S. (2017). Applying an extended praxeological ATD-Model for analyzing different mathematical discourses in higher engineering courses. In Didactics of Mathematics in Higher Education as a Scientific Discipline – Conference Proceedings. khdm-Report 17-05 (pp. 172-178). Kassel: Universität Kassel.
Purkert, W. (1990). Infinitesimalrechnung für Ingenieure—Kontroversen im 19. Jahrhundert. In Rechnen mit dem Unendlichen (pp. 179-192). Basel: Birkhäuser.
Schwartz, L. (1947). Théorie des distributions et transformation de Fourier. In Annales de l’Univ. de Grenoble, Vol. 23, 7-24.
Tuminaro, J., & Redish, E. F. (2007). Elements of a cognitive model of physics problem solving: Epistemic games. Physics Education Research, 3, 1-22.
Wahsner, R., & Borzeszkowski von, H.-H. (1992). Die Wirklichkeit der Physik. Studien zur Idealität und Realiät in einer messenden Wissenschaft. Frankfurt/M., Berlin, Berlin: Peter Lang.
Weisbach, J. L. (1860). Die ersten Grundlehren der höhern Analysis oder der Differenzial-und Integralrechnung: Für das Studium der praktischen Mechanik und Naturlehre möglichst populär. Braunschweig: Vieweg und Sohn.
Downloads
Published
How to Cite
Issue
Section
License
Autores que publicam nesta revista concordam com os seguintes termos:- Autores mantém os direitos autorais e concedem à revista o direito de primeira publicação, com o trabalho simultaneamente licenciado sob a Licença Creative Commons Attribution que permite o compartilhamento do trabalho com reconhecimento da autoria e publicação inicial nesta revista.
- Autores têm autorização para assumir contratos adicionais separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex.: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
- Autores têm permissão e são estimulados a publicar e distribuir seu trabalho online (ex.: em repositórios institucionais ou na sua página pessoal) a qualquer ponto antes ou durante o processo editorial, já que isso pode gerar alterações produtivas, bem como aumentar o impacto e a citação do trabalho publicado (Veja O Efeito do Acesso Livre).
