Design of a didactic situation – mathematical experiments in linear algebra
DOI:
https://doi.org/10.7146/nomad.v12i4.148045Abstract
We describe how we used Brousseau’s theories of didactic 1 situations and didactic engineering as a framework for the development of an exam project in a first year mathematics course at a life science university. The main learning goals of the project were to (re)discover eigenvalues and eigenvectors partly by studying the asymptotic behaviour of matrix models for population growth and to understand the role eigenvalues play in such models. Moreover, the students would gain experience with mathematical experiments with the use of computers and with drawing conclusions from such experiments.
References
Artigue, M. (1994). Didactical engineering as a framework for the conception of teaching products. In R. Biehler et al. (Eds.), Didactics of mathematics as a scientific discipline (pp. 27-39). Dordrecht: Kluwer.
Bloch, I. (2005). Dimension adidactique et connaissance nécessaire: un exemple de 'retournement' d'une situation. In M.-H. Salin et al. (Eds.), Sur la théorie des situations didactiques (pp.143-152). Grenoble: La Pensée Sauvage.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 10 3 -131. https://doi.org/10.1007/s10649-006-0400-z
Gravemeijer, K. & Terwel, T. (2000). Hans Freudenthal: a mathematician on didactics and curriculum theory. Journal of Curricullum Studies, 32(6), 777-796. https://doi.org/10.1080/00220270050167170
Grønbæk, N. & Winsløw, C. (2007). Developing and assessing specific competencies in a first course on real analysis. In F. Hitt et al. (Eds.), Research in collegiate mathematics education VI (pp.99-138). Providence, RI: American Mathematical Society. https://doi.org/10.1090/cbmath/013/04
Harel, G. (2000). Three principles of learning and teaching mathematics. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp.177-189). Dordrecht: Kluwer. https://doi.org/10.1007/0-306-47224-4_6
Niss, M. & Jensen, T. H. (Eds.) (2002). Kompetencer og matematiklæring: ideer og inspiration til udvikling af matematikundervisning i Danmark (Uddannelsesstyrelsens temahæfteserie no. 18. In Danish). København: Undervisningsministeriet.
Pedersen, T. V. (2005). Attaining mathematical competencies via the use of other subjects in a first year mathematics course at an agricultural university. In M. Anaya & C. Michelsen (Eds.), Relations between mathematics and other subjects of science or art. Proceedings of Topic Study Group 21 at ICME-10, the 10th International Congress on Mathematics Education, Copenhagen, Denmark, 2004 (pp.38-44). Odense: University of Southern Denmark.
Sierpinska, A. (1999). Lectures on the theory of didactic situations (Lecture notes). Retrieved November 12, 2007 from http://www.asjdomain.ca/TDS-lectures.html
Sierpinska, A. (2000). On some aspects of students' thinking in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp.209-246). Dordrecht: Kluwer. https://doi.org/10.1007/0-306-47224-4_8
Svendsen, T. S., Hansen, P. E., Sommer, C., Martinussen, T., Grønvold, J. et al. (2005). Life history characteristics of lumbricus terrestris and effects of the veterinary antiparasitic compounds ivermectin and fenbendazole. Soil Biology & Biochemistry, 37 (5), 927-936. https://doi.org/10.1016/j.soilbio.2004.10.014
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