About the “Mixture” of discourses in the use of mathematics in signal theory
Tipo de documento
Autores
Lista de autores
Hochmuth, Reinhard y Peters, Jana
Resumen
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.
Fecha
2020
Tipo de fecha
Estado publicación
Términos clave
Desde disciplinas académicas | Discurso | Epistemología | Gestión de aula | Historia de la Educación Matemática | Reflexión sobre la enseñanza
Enfoque
Idioma
Revisado por pares
Formato del archivo
Referencias
Alpers, B. 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, Kassel: Universität Kassel, p. 137-141, 2017. Antosik, P., Mikusiński, J., & Sikorski, R. Theory of distributions: the sequential approach. Amsterdam [u.a.]: Elsevier Scientific Publication, 1973. Barquero, B., Bosch, M., & Gascón, J. ‘Applicationism’ as the dominant epistemology at university. In: CERME 7-Seventh Congress of the European Society for Research in Mathematics Education, p. 1937-1948, 2011. Barquero, B., Serrano, L., & Serrano V. Creating the necessary conditions for mathematical modelling at university. In: CERME8-Eight Congress of the European Society For Research In Mathematics Education, p. 950-959, 2013. Blum, W., & Leiss, D. How do students and teachers deal with mathematical modelling problems? The example "Sugarloaf". ICTMA 12 Proceedings, p. 222-231, 2005. Bosch, M., & Gascón, J. Twenty-five years of the didactic transposition. ICMI Bulletin, 58, p. 51–65, 2006. Borzeszkowski, H. H. V., & Wahsner, R. Das physikalische Prinzip: der epistemologische Status physikalischer Weltbetrachtung. Königshausen & Neumann, 2012. Castela, C., & Romo Vázquez, A. Des mathématiques à l’automatique : étude des effets de transposition sur la transformée de Laplace dans la formation des ingénieurs. Recherches en Didactique des Mathématiques, 31(1), p. 79-130, 2011. Chevallard, Y. Fundamental concepts in didactics: Perspectives provided by an anthropological approach. Recherches en Didactique des Mathématiques Selected Papers. La Pensée Sauvage, Grenoble, p. 131-167, 1992. Chevallard, Y. L'analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques 19(2), p. 221-266, 1999. Chevallard, Y., BOSCH, M., & KIM, S. 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, p. 2614–2620, 2015. Dirac, P. A. 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), p. 621-641, 1927. Dirac, P.A.M. (1958). The principles of quantum mechanics. 4. ed. Oxford: Clarendon Press, 1958. Dirac, P.A.M. Interview with T.S. Kuhn. Archives for the History of Quantum Physics, Niels Bohr Library, AIP, New York, 1963. Fettweis, A. Elemente nachrichtentechnischer Systeme. Wiesbaden: Vieweg & Teubner Verlag, 1966. Girod, B., Rabenstein, R., & Stenger, A. K. E. Einführung in die Systemtheorie - Signale und Syteme in der Elektrotechnik und Informationstechnik. Wiesbaden: B.G. Teubner Verlag, 2007. Hochmuth, R., Biehler, R., & Schreiber, S. Considering mathematical practices in engineering contexts focusing on signal analysis. Proceedings of RUME17, p. 693-699, 2014. Hochmuth, R. & Schreiber, S. Conceptualizing Societal Aspects of Mathematics in Signal Analysis. In: Proceedings of the Eight International Mathematics Education and Society Conference Vol. 2, Portland: Ooligan Press, p. 610–622, 2015. Landers, D. & Rogge, L. Nichtstandard Analysis. Springer-Verlag, 2013. Peters, K. H. 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, 2004. Peters, J., Hochmuth, R., & Schreiber, S. 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, 2017. Purkert, W. Infinitesimalrechnung für Ingenieure—Kontroversen im 19. Jahrhundert. In: Rechnen mit dem Unendlichen, Basel: Birkhäuser, p. 179-192, 1990. Schwartz, L. Théorie des distributions et transformation de Fourier. In: Annales de l’Université de Grenoble, Vol. 23, p. 7-24, 1947. Tuminaro, J., & Redish, E. F. Elements of a cognitive model of physics problem solving: Epistemic games. Physics Education Research, 3, p. 1-22, 2007. Wahsner, R., & Borzeszkowski Von, H.-H. Die Wirklichkeit der Physik. Studien zur Idealität und Realiät in einer messenden Wissenschaft. Frankfurt/M., Berlin, Berlin: Peter Lang, 1992. Weisbach, J. L. 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, 1860.