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Lecturer(s)
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Bímová Daniela, Mgr. Ph.D.
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Pirklová Petra, RNDr. Ph.D.
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Břehovský Jiří, Mgr. Ph.D.
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Příhonská Jana, doc. RNDr. Ph.D.
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Course content
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In the lectures, a brief theoretical introduction to the mentioned topics is outlined and an introduction to the basic terms from a didactic point of view is made. All concepts will be presented from the point of view of their application in the teaching of mathematics at the 1st grade of primary school, while the accuracy of the interpretation will be subordinated to this point of view. In the exercises, the subject matter explained in the lecture is practiced, supplemented by practical applications related to the contents of the 1st grade arithmetic curriculum. Thematic areas 1. Number systems, writing a number in a system with a given base. 2. Mutual conversions between number entries in different systems, arithmetic operations in number systems 3. Expanding the range of natural numbers - whole numbers, arrangement on the number line, absolute value 4. Numerical operations in Z, divisibility in Z, common divisor, common multiple 5. Expanding the field of whole numbers - rational numbers, fractions, decimal numbers, finite and periodic development. 6. Conversions between individual expressions of rational numbers, work with decimal numbers and fractions in the 1st grade of elementary school. 7. Irrational numbers, examples of irrational numbers, square roots. 8. Equations and inequalities as propositional forms and their solutions, equivalent modifications of equations and inequalities. 9. Diophantine equations, word problems solved using Diophantine equations. 10. Combinatorics - rule of sum and product, combination, variation, permutation, simple problems. 11. Basics of probability - classic definition, simple problems that can be solved in the 1st grade. 12. Word problems, simple and complex word problems, phases of solving a simple word problem. 13. Methods of solving word problems usable in the 1st grade, graphic solutions. 14. Reserve.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Dialogue metods(conversation,discussion,brainstorming), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Individual consultation, Lecture, E-learning
- Class attendance
- 12 hours per semester
- Preparation for credit
- 14 hours per semester
- Home preparation for classes
- 18 hours per semester
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Learning outcomes
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In the lectures, a brief theoretical introduction to the mentioned topics is outlined and an introduction to the basic terms from a didactic point of view is made. All concepts will be presented from the point of view of their application in the teaching of mathematics at the 1st grade of elementary school, while the accuracy of the interpretation will be subject to this point of view. In the exercises, the material explained in the lecture is practiced, supplemented with practical applications related to the contents of the geometry and arithmetic curriculum of the 1st grade of elementary school.
Knowledge of the essential concepts of arithmetics, intuitive set theory and propositional calculus. Insight into the concept of natural number defined by means of different ways.
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Prerequisites
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Knowledge of secondary school mathematics, successful completion of the subject MPRP.
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Assessment methods and criteria
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Combined examination, Student's performance analysis
Active participations on seminars, successfully absolved tests. Knowledge of secondary school mathematics (by curriculum of gymnasium, humanities). Successful completion of the subject MPRP.
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Recommended literature
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Učebnice matematiky pro 1. st. ZŠ - různé řady.
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Divíšek, J. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha, SPN, 1989.
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Gábor, O. a kol. Teória vyučovania matematiky 1. Bratislava, 1989. ISBN 80-08-00285-9.
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Hejný, M. a kol. Teória vyučovania matematiky 2. Bratislava, SPN, 1990.
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Hejný, M. a kol. Vyučování matematice orientované na budování schémat:aritmetika 1. st.. Praha, 2014. ISBN 978-80-7603-343-6.
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Kopka, J. Kapitoly o přirozených číslech. (Skriptum UJEP.). Ústí nad Labem, 2003. ISBN 80-7044-472-X.
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Kopka, J. Katitoly o celých číslech. (skriptum UJEP). Ústí nad Labem, 2004. ISBN 80-7044-562-9.
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Križalkovič, K. a kol. Didaktika matematiky na 1. stupni ZŠ. Bratislava, SPN, 1990.
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Križalkovič, K. a kol. Základy elementárnej aritmetiky. Bratislava, SPN, 1991.
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Kuřina, F., Vondrová, N. 15 pohledů na školskou matematiku. Jak to vidíme.. Praha, 2022. ISBN 978-80-7603-343-6.
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Malinová, E. Kapitoly z elementární aritmetiky. Praha, SPN, 1986.
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Malinová, E. Teorie vyučování matematiky v 1.-4. r. ZŠ - část 1 (Aritmetika). Praha, SPN, 1978.
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