Universität Wien

250030 VO School mathematics analysis (2021W)

2.00 ECTS (2.00 SWS), SPL 25 - Mathematik
REMOTE
Moodle

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Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Start: October 5, 2021 online as a collaboration session on Moodle.

  • Tuesday 05.10. 11:30 - 13:00 Digital
  • Tuesday 12.10. 11:30 - 13:00 Digital
  • Tuesday 19.10. 11:30 - 13:00 Digital
  • Tuesday 09.11. 11:30 - 13:00 Digital
  • Tuesday 16.11. 11:30 - 13:00 Digital
  • Tuesday 23.11. 11:30 - 13:00 Digital
  • Tuesday 30.11. 11:30 - 13:00 Digital
  • Tuesday 07.12. 11:30 - 13:00 Digital
  • Tuesday 14.12. 11:30 - 13:00 Digital
  • Tuesday 11.01. 11:30 - 13:00 Digital
  • Tuesday 18.01. 11:30 - 13:00 Digital
  • Tuesday 25.01. 11:30 - 13:00 Digital

Information

Aims, contents and method of the course

Content: Real and complex numbers, sequences and series - convergence, continuous functions, elementary transcendent functions, calculus.

Aim: The aim of this course is to connect these themes with characteristic aspects of school mathematics. Those links are either intended to be intergrated directly in mathematics education or they are supposed to play an important role in the background knowledge of the teachers. Calculus is an essential part of school mathematics all over the world. It should not be restricted to execute some well known algorithm. At the end of the course you should be became aware of the meaning of the central conceptions of real analyis in one variable in order to integrate these insights in your personal knowledge spectrum as a future teacher.

Method: if possible, lecture as a face-to-face event, otherwise online presentation with script.
It is strongly recommended that you have attended the lecture "Analysis in one variable for the teaching profession (analysis in einer Variable für das Lehramt)" before attending this course.

Assessment and permitted materials

If possible, written colloquium in presence: calculator, CAS, spreet sheet.

If not: written digital open book exam. (Students are allowed to use their learning materials and all available aids. For this reason, the examination tasks do not aim at the reproduction of knowledge, but at transfer and application achievements.)

Minimum requirements and assessment criteria

Analysis and reflection of important concepts and conceptions of calculus in one variable with respect to corresponding contents of school mathematics.

On site: Each question will be rated from "Sehr gut" to "Nicht genügend". The median of these grades is then the overall assessment.

Online: Twelve multiple-choice questions. Each with four response options. One point per question. This is only awarded if exactly the right answers and statements, respectively, are ticked: "all or nothing model".
Grading scale: 6 points "sufficient", 7 and 8 points "satisfactory", 9 and 10 points "good", 11 and 12 points "very good".

Examination topics

Lecture given in a classical way with the option to discuss also during the course. The total content of the lectures is what you have to learn to pass the written exam. There is a script.

Reading list

The following books are all in German.

Appell, J.: Analysis in Beispielen und Gegenbeispielen. Eine Einführung in die Theorie reeller Funktionen. Springer, Berlin u. a. 2009.
Blum, W. und Törner, G.: Didaktik der Analysis. Vandenhoeck & Ruprecht, Göttingen 1983.
Bruder, R., Hefendehl-Hebeker, L., Schmidt-Thieme, B. und Weigand, H.-G. (Hrsg.): Handbuch der Mathematik-Didaktik. Springer Spektrum, Berlin Heidelberg 2015 (Teil II, Abschnitt 6: Analysis: Leitidee Zuordnung und Veränderung von R. vom Hofe, J. Lotz und A. Salle).
Danckwerts, R. und Vogel, D.: Analysis verständlich unterrichten. Mathematik Primar- und Sekundarstufe. Elsevier Spektrum Akademischer Verlag, München 2006.
Götz, S. und Reichel, H.-C. (Hrsg): Mathematik 5-8. Von R. Müller, G. Hanisch und C. Wenzel. öbv, Wien 2010 bis 2012.
Greefrath, G., Oldenburg, R., Siller, H.-St., Ulm, V. und Weigand, H.-G.: Didaktik der Analysis. Aspekte und Grundvorstellungen zentraler Begriffe. Springer-Verlag, Berlin Heidelberg 2016.
Knoche, N. und Wippermann, H.: Vorlesungen zur Methodik und Didaktik der Analysis. Lehrbücher und Monographien zur DIdaktik der Mathematik, Band 4. B.I.-Wissenschaftsverlag, Mannheim u. a. 1986.
Kütting, H.: Elementare Analysis. Band 1: Reelle Zahlen, reelle Zahlenfolgen und unendliche Reihen. Band 2: Stetigkeit, Differentiation und Integration reeller Funktionen. B.I.-Hochschultaschenbuch Band 653 und 654. B.I.-Wissenschaftsverlag, Mannheim u. a. 1992.
Riede, H.: Die Einführung des Ableitungsbegriffs. Thema mit Variationen. Lehrbücher und Monographien zur Didaktik der Mathematik, Band 27. B.I.-Wissenschaftsverlag, Mannheim u. a. 1994.
Scheid, H.: Folgen und Funktionen. Eine Einführung in die Analysis. WTM Verlag für wissenschaftliche Texte und Medien, Münster 2007.
Tietze, U.-W., Klika, M. und Wolpers, H.: Mathematikunterricht in der Sekundarstufe II. Band 1: Fachdidaktische Grundfragen. Didaktik der Analysis. Vieweg, Braunschweig/Wiesbaden 1997.
Weigand, H.-G.: Zur Didaktik des Folgenbegriffs. Lehrbücher und Monographien zur Didaktik der Mathematik, Band 21. B.I.-Wissenschaftsverlag, Mannheim u. a. 1993.

Association in the course directory

UFMA04

Last modified: Fr 12.05.2023 00:21