Didactics of mathematics 1 *

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)

Review of high school mathematics syllabus.
Foundations of logic and set theory. Basic number sets. Linear function and equation. Geometry in plane and space. Powers and roots. Quadratic function. Complex numbers. Exponent and logarithm function. Area, surface and volume. Trigonometric functions. Polinoms, rational functions, conics. Combinatorics, probability and statistics. Sequences and differential calculus.
Review of curricula and examination catalogs. Analysis of textbooks.
Preparation of curricula. Cyclically students present different contents and analyze good practice in performances.

Readings

Srednješolski učbeniki in programi.
H. Freudenthal: Mathematics as an Educational Task, Springer, Berlin, 1972.
G. Polya: Mathematics and Plausible Reasoning, Princeton Univ. Press, Princeton, 1990.

Objectives and competences

Students are introduced to high school teaching programs, textbooks and catalogs of final exams. High school material is studied in detail in form of performances before the peers. Students learn important aspects of interpretation of mathematical contents and practice in public speaking.

Intended learning outcomes

In-depth knowledge and understanding of high school mathematics with emphasis on a good explanation.
Application in practical teaching.

Learning and teaching methods

Performances, discussions, analysis, consultations

Assessment

homework, project work, performances, participation in analysis, preparations, written and/or oral exam (high school syllabus), preparations, preparations' defense.

Adequate ability of professional communication in Slovenian is required.

Grading: 6-10 pass, 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]