Course: Methods of Math Problem Solving - secondary school

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Course title Methods of Math Problem Solving - secondary school
Course code UMB/030
Organizational form of instruction Lesson
Level of course Master
Year of study 2
Frequency of the course In each academic year, in the winter semester.
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Kalová Jana, doc. RNDr. Ing. Ph.D.
  • Trča Radek, Mgr.
  • Pazourek Karel, Mgr. Ph.D.
  • Vrba Zbyněk, Mgr.
  • Štěpánková Hana, Mgr. Ph.D.
Course content
Methodology for solving mathematical problems will be illustrated with specific examples from the different thematic part. 1. Basic strategy for problem solving. 2. Problems of elementary number theory. 3. Problems with parameters. 4. Problem tasks in combinatorics. 5. Inequalities. 6. Methods of solving extremal problems, optimization. 7. Polynomials and equations of higher degrees. 8. Geometry. 9. Sequences. 10. Proofs. 11. Mathematization of real situation. 12. Motivating examples, applied problem tasks. 13. Summary tasks. 14. ICT and literature for problem solving.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Projection, Work with multi-media resources (texts, internet, IT technologies)
Learning outcomes
Problem solving tasks is an essential part of teaching mathematics at all levels and types of schools. This course is an important extension of theoretical mathematics a didactics of mathematics. Course helps students to work at professional and interesting way.
A student is qualified for leading courses to the Mathematical Olympiad and mathematical competitions.
Prerequisites
Perfect knowledge of secondary school curriculum on a high-school level.

Assessment methods and criteria
unspecified
- active attendance of practicals - at least 70% points from one written test
Recommended literature
  • Herman, J., Kučera, R., Šimša, M.: Metody řešení matematických úloh I, ISBN 80-210-1202-1, 2. přepracované vydání, Herman, J., Kučera, R., Šimša, M.: Metody řešení matematických úloh I, ISBN 80-210-1202-1, 2. přepracované vydání, Herman, J., Kučera, R., Šimša, M.: Metody řešení matematických úloh I, ISBN 80-210-1202-1, 2. přepracované vydání, MU Brno, 1996..
  • Herman, J., Kučera, R., Šimša, M.: Metody řešení matematických úloh II, ISBN 80-210-3569-2, 3. přepracované vydání, MU Brno, 2004..
  • Kopka, J., Vopěnka, P.: Metody řešení matematických úloh, Projekt FRVŠ dostupný na kmd.fp.tul.cz/lide/kopka/MRU_ucebni%20text.doc, 2007..
  • Kuřina, F.: Umění vidět v matematice, SPN Praha, 1990..
  • Leischner, P.: Metody řešení úloh, učební text dostupný na http://eamos.pf.jcu.cz/amos/kat_mat/externi/kat_mat_82142/metody_reseni_uloh.pdf.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care 2 Recommended year of study:2, Recommended semester: Winter