Universität Wien FIND

250034 VO School mathematics elementary geometrie and vector analysis (2019W)

2.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Tuesday 01.10. 08:00 - 09:30 Hörsaal 4 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 08.10. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 15.10. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 29.10. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 05.11. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 12.11. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 19.11. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 26.11. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 03.12. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 10.12. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 17.12. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 07.01. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 14.01. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 21.01. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß
Tuesday 28.01. 08:00 - 09:30 Hörsaal 1 Oskar-Morgenstern-Platz 1 Erdgeschoß

Information

Aims, contents and method of the course

The aim of this course is to prepare relevant content from elementary geometry and vector analysis for mathematics education. For this I would like to start each section of this lecture with a task or an example from a textbook and derive mathematical and didactical implications.

In geometry, triangles, congruence maps in the plane, congruence sentences, the theorem of Ceva, the Euler's line, the Pythagorean theorem group, quadrilaterals, elementary features of the circle, similarity, intercept theorems and the volume of solids are discussed.

The topics of vector analysis will be treated in plane and in space: linear systems of equations, the vector concept, lines, planes, circles and other conics, possibly a short section on matrix calculus.

In addition, of course, a didactical evaluation of the presented contents will be offered to make them appropriate for future lessons of the participiants.

Possibilities of a meaningful use of technology are also demonstrated.

Assessment and permitted materials

Written exam.

Electronic support such as GeoGebra is only allowed on a notebook! Smartphones or tablets are NOT allowed.
A calculator with computer algebra system and graphics can also be used.

Minimum requirements and assessment criteria

Analysis and reflection of essential matematical concepts and (subject-didactic) conceptions of geometry and vector calculation with regard to the related contents of school mathematics.

The vast majority of the tasks of the exam must be evaluated positively to complete successfully this lecture.

Examination topics

Lecture in the classical way with the possibility for discussion at the course. This defines the entire examination syllabus.

Reading list

Geometry:
Agricola, Ilka und Friedrich, Thomas: Euclidian Geometry [in German].
Expertise for study and math instruction. Vieweg, Wiesbaden 2009 (second edition).
Fraedrich, Anna Maria: The Pythagorean Theorem Group [in German]. BI
Wissenschaftsverlag, Mannheim i. a. 1994.
Holland, Gerhard: Geometry at Secondary Level [in German]. Textbooks and Monographs on Didactics of mathematics, Vol. 9. BI
Wissenschaftsverlag, Mannheim i. a. 1988.
Krauter, Siegfried: Adventure elementary geometry. A working book for independent and active discovery [in German]. Spektrum Akademischer Verlag, Munich 2005.
Weigand, Hans-Georg, Filler, Andreas, Hölzl Reinhard, Kuntze, Sebastian, Ludwig, Matthias, Roth, Jürgen, Schmidt-Thieme, Barbara and Witmann, Gerald: Didactics of Geometry at Secondary Level I [in German]. Springer Spektrum, Berlin 2018 (3., expanded and revised edition).
Wittman, Erich Ch.: Elementary Geometry and Reality. Introduction to Geometrical Literacy [in German]. Vieweg, Braunschweig 1987.

Vector Analysis:
Henn, Hans-Wolfgang and Filler, Andreas: Didactics of analytical geometry and linear algebra. Understanding algebraically ‒ visualizing and applying geometrically [in German]. Springer Spektrum, Berlin Heidelberg 2015.
Tietze, Uwe-Peter, Klika, Manfred and Wolpers, Hans (Eds.): Mathematics Education at Secondary Level II. Volume 2: Didactics of Analytical Geometry and Linear Algebra [in German], by Uwe-Peter Tietze in collaboration with Peter Schroth and Gerald Wittmann. Vieweg, Braunschweig/Wiesbaden 2000.

Textbooks Secondary Level I:
Hanisch, Günter, Benischek, Isabella, Hauer-Typpelt, Petra and Sattlberger, Eva: MatheFit 1 - 4 [in German]. Veritas (1) and Besseres Buch (2-4), Linz 2007 (1) and Vienna 2009, 2010 and 2011 (2-4).
Reichel, Hans-Christian and Humenberger, Hans (Eds.): This is Mathematics 1 - 4 [in German] by Dieter Litschauer, Herbert Groß, Vera Aue (1-4) and Erich Neuwirth (3-4). Collaboration: Stefan Götz. Thematic Sections by Rudolf Taschner. öbv, Vienna 2011 (1,2) and 2012 (3,4).

Textbooks Secondary Level II:
Götz, Stefan and Reichel, Hans-Christian (Eds.): Mathematics 5 - 8 [in German] by Robert Müller and Günter Hanisch (Collaboration: Claudia Wenzel). With an Online-Addition by Hans-Stefan Siller and Robert Müller. öbv, Vienna 2010 (5,6), 2011 (7) and 2013 (8).
Bleier, Gabriele, Lindenberg, Judith, Lindner, Andreas and Süss-Stepancik, Evelyn: Dimensions Mathematics 5 - 8 [in German]. E. Dorner, Vienna 2017 (5,8), 2015 (6) and 2016 (7).

Association in the course directory

UFMA03

Last modified: Tu 24.09.2019 09:48