Topics in didactics of mathematics

2022/2023
Programme:
Doctoral Programme Mathematics and Physics
Orientation:
Mathematics
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
0
Tutorial
0
Lab
0
Content (Syllabus outline)

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.

Readings

• S. G. Krantz, How to Teach Mathematics, American Mathematical Society, 1951.
• H. Freudenthal, Mathematics as an Educational Task, Dordrecht-Holland, 1973.
• J. Mason, Learning and Doing Mathematics, Macmillan, 1988.
• H. W. Heymann, Why Teach Mathematics, Kluwer, 2003.
• Orton, Learning Mathematics: Issues, Theory and Classroom Practice, London, 1992.
• Orton, G. Wain, Issues in Learning Mathematics, London 1994.
• M. P. Driscoll, Psychology of Learning for Instruction, Boston, 1993.
• L. Burton, Learning Mathematics: From Hierarchies to Networks, Kluwer 1999.
• J. Mason, Fundamental Constructs in Mathematics Education, New York, 2004.
• Bezen: Osnove didaktike, 1993.
• Burton, Mason, Stacey: Thinking Mathematically, 1985.
• Cooney, Davis, Henderson: Dynamics of Teaching Secondary School Mathematics, 1975.
• Costello: Teaching and Learning Mathematics, 1991.
• Gavosto, Krantz, McCallum: Contemporary Issues in Mathematics Education, 1999.
• J. Hadamard: The Mathematician's Mind, 1996.
• Lang: The Beauty of Doing Mathematics, 1985.
• Polya: Mathematics and plausible reasoning, 1990.
• Skovsmose: Towards a Philosophy of Critical Mathematics Education, 1994.
• Cipra & All, What's Happening in the Mathematical Sciences, 1994-2006.
• J. Tanton, Solve this – Math activities for students and clubs, MAA, 2001.
• A. Fusaro, P. C. Kenschaft, Environmental Mathematics in the Classroom, MAA, 2003.
• P. Straffin, Applications of Calculus, MAA 1999.
• L. Hahn, Complex numbers & Geometry, MAA 1994.
• M. Hohenwarter, Geogebra, http://www.geogebra.org/cms/.

Objectives and competences

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.

Intended learning outcomes

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

Learning and teaching methods

Lectures, consultations, problem sessions

Assessment

Writen exam (homeworks), oral exam

Lecturer's references

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.