Didactics of mathematics 2 *

2022/2023
Programme:
Mathematics Education
Year:
3 ali 4 year
Semester:
second
Kind:
mandatory
ECTS:
6
Language:
slovenian
Hours per week – 2. semester:
Lectures
4
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)

As a preparation and reflection on practical experiences the following topics are processed: Using the computer in mathematics. High school mathematics in the light of motivation, overburdening and discipline. Attempt to define a good teacher of mathematics. A good explanation. Art of rhetoric. Devoting to more and less talented pupils. Creativity and authority, attempt to define a good student. Between diligence and hard work. Binge work. Homeworks. Why is math so hard for many? Mathematics between Piaget and Vygotsky - Socratic method. Modern teaching methods between teaching essence and political correctness. Demystifying the definition, theorem and proof. Role and significance of (high school) graduation. Internal and external success criteria. How to measure understanding? Objective assessment between the necessity and possibility. Concrete examples as a source of motivation and understanding in mathematics. Simplification: the urgency and motivation. Analysis of curricula.
Grading. Case studies.
Problem solving. Case studies.

Readings

H. Freudenthal: Mathematics as an Educational Task, Springer, Berlin, 1972.
S. G. Krantz: How to Teach Mathematics, 2nd edition, AMS, Providence, 1999.
F. Pediček: Edukacija danes, Obzorja, Maribor, 1994.
G. Polya: Mathematics and Plausible Reasoning, Princeton Univ. Press, Princeton, 1990.
Srednješolski učbeniki.
T. Brown: Mathematics Education and Language : Interpreting Hermeneutics and Post-Structuralism, 2nd edition, Springer, New York, 2001.
H. W. Heymann: Why Teach Mathematics : A Focus on General Education, Springer, New York, 2004.
Različni primeri problemov iz Slovenije in sveta (primeri matur, sprejemnih izpitov.…)

Objectives and competences

Students learn about modern teaching problems and various forms of work in mathemaics teaching.

Intended learning outcomes

Knowing and understanding the complex relationships of teaching mathematics.
Using the ideas in the classroom.

Learning and teaching methods

Lectures, exercises, presentations, discussions, consultations

Assessment

Type: homeworks, project work, written and oral exam.
Adequate ability of professional communication in Slovenian is required.
Grading: 6-10 pass, 1-5 fail

Lecturer's references

KOBAL, Damjan. Technology and simple math ideas inspire teaching. V: ICME - 12 : the 12th International Congress on Mathematical Education, July 8-15, 2012, COEX, Seul, Korea. Cheongju: Korea National University of Education, 2012, 7 str. [COBISS-SI-ID 17151577]
KOBAL, Damjan, et al. Integrating algebra and geometry with complex numbers. V: International Seminar in Mathematics Education 2011. Park City: Park City Mathematics Institute - Institute for Advanced Study, cop. 2013, 9 str. [COBISS-SI-ID 17152345]
KOBAL, Damjan. Iluzija objektivnosti ali objektivnost odgovornosti. Obzornik za matematiko in fiziko, ISSN 0473-7466, 2007, letn. 54, št. 1, str. 18-28. [COBISS-SI-ID 14302297]
KOBAL, Damjan. Inner product space and circle power. Publicationes mathematicae, ISSN 0033-3883, 2012, vol. 81, fasc. 1-2, str. 1-9. [COBISS-SI-ID 16336473]
KOBAL, Damjan. Bijections preserving invertibility of differences of matrices on H [sub] n. Acta mathematica Sinica, English series, ISSN 1439-8516, 2008, vol. 24, no. 10, str. 1651-1654. [COBISS-SI-ID 15588441]
KOBAL, Damjan. Preserving diagonalisability on upper triangular matrices. Linear and Multilinear Algebra, ISSN 0308-1087, 2006, vol. 54, no. 3, str. 189-194. [COBISS-SI-ID 13971801]