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Lecturer(s)
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Břehovský Jiří, Mgr. Ph.D.
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Course content
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1. Mathematical problems and problems in school mathematics. Basic concepts: mathematical problem and mathematical problem, structure of problem solving process from the perspective of didactics of mathematics. 2. Classification of mathematical problems. Methods of solving mathematical problems. 3. Heuristic strategies - definition of the term, historical context and views on this issue (Polya, Schoenfeld, Zeitz, Kopka). Classification of mathematical problems and structure of their solution. Classification of heuristic strategies. 4. Guess - check - revise. 5. Working backwards. 6. Systematic experimentation. 7. Use of false assumption. 8. Deletion of a condition. 9. Introducing an auxiliary element. 10. Concretization and generalization. 11. Reformulation of the problem. 12. Analogy. 13. Generalization and concretization. 14. Invariant.
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Learning activities and teaching methods
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Dialogue metods(conversation,discussion,brainstorming), Active metods (simulation, situational contingency methods, drama,acting, namagerial acting )
- Class attendance
- 6 hours per semester
- Preparation for credit
- 14 hours per semester
- Home preparation for classes
- 8 hours per semester
- Semestral paper
- 10 hours per semester
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Learning outcomes
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The course is devoted to mathematical tasks, problems and methods of their solution. The primary focus is on heuristic strategies and their use in teaching mathematics at the first level of primary school. The emphasis in the exercises will be on the practical application of the presented solving strategies with regard to the future profession of the students. Seminar papers will be assigned during the semester and students will present the results of these papers in each exercise. Successful solution and presentation will be a prerequisite for credit.
Obtaining skills to develop students' geometric ideas and to teach arithmetic and geometry for pupils with SEN (special educational needs).
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Prerequisites
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Completing the course Mathematics 1 - 4, Didactics of mathematics 1,2. Using different methods of problems solving. Active use of application PowerPoint, Microsoft Excel, SMART Notebook.
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Assessment methods and criteria
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Student's performance analysis
Credit: Participation on seminars. Working out seminar work. The course is held in Czech language, the requirements are stated in the Czech version.
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Recommended literature
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ČIŽMÁR, J.. Dejiny matematiky od najstarších čias po súčasnosť. Bratislava. 2017.
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KOPKA, J. Umění řešit matematické problémy. Praha. 2013.
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KUŘINA, F. Matematika a řešení úloh. České Budějovice. 2011.
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POLYA, G.. Jak to řešit?. Praha. 2016.
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VONDROVÁ. N. Matematická slovní úloha. Praha. 2020.
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