Course: Creation and solving of problems

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Course title Creation and solving of problems
Course code KMA/XTMAU
Organizational form of instruction no contact
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 30
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Tlustý Pavel, prof. RNDr. CSc.
Course content
Problem solving. Solving strategy, processual and conceptual approach to the problem. Analysis of the problem, visual ability, the right questions ability, the importance of appropriate choice of variables, decomposition into sub-problems, thought experiments, the use of induction and analogy, the use of dual strategies, use of technology for modeling and exploring issues. Creating of problems. Creativity, creating of a problem as a dual process to the solving. Advantages and disadvantages of different formulations of problem, the chains of tasks, open tasks. Motivation, inspiration, uses analogies, creation from above, creating on the basis of experiments (also thought experiments), creating by a gradual reshaping of familiar problem.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
Learning outcomes
Graduates of te teacher studies are in elementary mathematics with little experience of solving problems (ie non-standard tasks, in which is a direct way to the solution blocked). Regarding the creation of jobs, the majority can only rotate the current educational problems. The goal is to improve the situation. Content and range will be adjusted to a doctoral student profile.
Creation and solving of non-standard elementary mathematics problems.
Prerequisites
Knowledge of elementary mathematics. Knowledge of methods for solving moderately difficult types of problems from mathematical competitions.

Assessment methods and criteria
Combined exam

Knowledge of methods of creation and solving of non-standard elementary mathematics problems.
Recommended literature
  • Engel, A.:. Problem solving strategies, Springer-Verlag, New York Berlin Heidelberg 1998.
  • Hecht, T., Sklenáriková, Z.:. Metódy rešenia matematických úloh, SPN, Bratislava 1992.
  • Hejný, M., Michalcová, A.:. Skúmanie matematického riešiteľského postupu, Metodické centrum v Bratislave, Bratislava 2001.
  • Hejný M.:. Procept, In: Zborník bratislavského seminára z teórie vyučovania matematiky, Bratislava, MFF UK, Bratislava, 1999.
  • Herman, J., Kučera, J., Šimša, J.:. Metody řešení úloh I a II, MU v Brně, Brno 1996.
  • Kopka, J.:. Hrozny problémů ve školské matematice, Univerzita J. E. Purkyně, Ústí nad Labem, 1999.
  • Košč, L.:. Psychológia matematických schopností, SPN, Bratislava 1972.
  • Kuřina, F.:. Podivuhodný svět elementární matematiky, ACADEMIA, Praha 2006.
  • Kuřina, F.:. Umění vidět v matematice, SPN, Praha 1989.
  • Markides, G. a kol.:. Objevování, motivace a podpora matematických talentů na evropských školách, manuál, díl 1 - 3, MATH.EU Projekt, 2006.
  • Sternberg, R. J.:. Kognitivní psychologie, Portál, Praha 2002.
  • Švrček, J.:. Tvorba a využití gradovaných řetězců matematických úloh, UP v Olomouci, Olomouc 2008.
  • Zhouf, J.:. Tvorba diagnostických úloh z matematiky, In: Dvacet pět kapitol z didaktiky matematiky, UK v Praze, Praha 2004.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Theory of Mathematics Education (2) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -
Faculty: Faculty of Education Study plan (Version): Theory of Mathematics Education (2) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -