Topics in didactics of mathematics

There are no prerequisites.

Depending on the focus and interest of students the course will follow the following chapters:

Theories of Learning:
Behavioristic, cognitive, constructivistic, interactivvistic theories of learning. The concept of mathematical knowledge. The goals of mathematics teaching. Learning of mathematics and informations management. Bruner's theory of representations. Classical and modern theories of solving of mathematical problems. Classroom practice.

Classroom motivation:
Interesting titles in the popularization of mathematics, Mathematics and Computer Sciences, Mathematics and Technology, Mathematics in Automotive Technology, Mathematics and Digital Sound Technology, Mathematics in Biology, Mathematics in Medicine, ...

Learning Technologies:
The use of Computer in Mathematics Classroom, Slides, Latex, Drawing in Latex, Internet, Interactive Web Tools, Tools for Symbolic Calculations, Dynamic Geometry Programs, Interactive Board.
Mathematical content with a computer:
Chapters in Classical Geometry with Dynamic Geometry Programs. The Geometry of Circle and Triangle. Classical Theorems: Simson, Feuerbach, Cantor, Morley, Napoleon, Apollonius, Inversion, Möbius transformations.

Other relevant contents.

1. J. Cai, ed.: Compendium for research in mathematics education, Reston (Virginia) : National Council of Teachers of Mathematics, cop. 2017.
2. T. J. Cooney, E. J. Davis, K. B. Henderson: Dynamics of teaching secondary school mathematics, Boston : Houghton Mifflin, cop. 1975.
3. B. A. Fusaro, P. C. Kenschaft, eds.: Environmental Mathematics in the Classroom, Washington : The Mathematical Association of America, cop. 2003.
4. E. A. Gavosto, S. G. Krantz, W. G. McCallum, eds.: Contemporary issues in mathematics education, Cambridge : Cambridge University, cop. 1999.
5. J. Hadamard: The mathematician's mind : the psychology of invention in the mathematical field, Princeton : Princeton University Press, 1996.
6. L. Hahn, Complex numbers and geometry, Washington : Mathematical Association of America, cop. 1994.
7. H. W. Heymann: Why teach mathematics? : a focus on general education, Dordrecht : Kluwer, cop. 2003.
8. S. G. Krantz: How to Teach Mathematics, 2nd ed., Providence : American mathematical society, cop. 1999.
9. S. Lang: The beauty of doing mathematics : three public dialogues, New York : Springer, cop. 1985.
10. J. Mason, L. Burton, K. Stacey: Thinking mathematically, Reading : Addison-Wesley, cop. 1982.
11. A. Orton: Learning mathematics : issues, theory and classroom practice, 3rd ed. - London : Continuum, 2004.
12. G. Polya: Induction and analogy in mathematics, 12th print. and 1st Princeton Paperback print. - Princeton : Princeton University Press, 1990
13. G. Polya: Patterns of plausible inference, 2nd ed. - Princeton (New Jersey) : Princeton University Press, 1968.
14. O. Skovsmose: Towards a philosophy of critical mathematics education, Dordrecht : Kluwer, cop. 1994.
15. P. Straffin, ed.: Applications of calculus : a project of the Associated Colleges of the Midwest and the Great Lakes Colleges Association, [Washington, DC] : Mathematical Association of America, cop. 1999.
16. J. S. Tanton: Solve this : math activities for students and clubs, Washington : The Mathematical Association of America, cop. 2001.

The main purpose of the subject is to provide students with the theoretical and practical background of the modern theories of learning and trends in mathematics teaching. The emphasis is given to practical mathematics teaching issues which relate to new methods, to new learning technologies and to diverse ideas of relevant mathematical contents.

Knowledge and comprehension of presented concepts. Ability to use acquired knowledge and skills.

Lectures, consultations, problem sessions

Writen exam (homeworks), oral exam

KOBAL, Damjan. The Power of Geometry in the Concept of Proof, Workshop, 13th International Congress on Mathematical Education, ICME-13, Hamburg, July 24-31, 2016.
KOBAL, Damjan. Technology and Simple Math Ideas Inspire Teaching, Workshop at 12th International Congress on Mathematics Education , Seoul, Koreja, 2012
KOBAL, Damjan, et al.. Integrating Algebra and Geometry with Complex Numbers, International Seminar in Mathematics Education, Park City Math Institute ~ Institute for Advanced Study, Park City, ZDA, 2011.