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Lecturer(s)
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Bílá Margita, PhDr. Ph.D.
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Císařová Alena, PhDr. Ph.D.
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Chmelík Slavomil, PhDr. Ph.D.
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Hrubá Jitka, PhDr. Ph.D.
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Course content
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1. Binary operations on a set 2. Properties of binary operations 3. Algebraic structures with one operation 4. Algebraic structures with two operations 5. Cardinal numbers 6. Operations with cardinal numbers 7. Cardinal numbers in primary school subject matter 8. Ordinal numbers, ordinal numbers in primary school subject matter 9. Peano-set 10. Semiring of all natural numbers 11. Numerization 12. Addition and subtraction of natural numbers 13. Multiplication and division of natural numbers
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, Collaborative instruction, Cooperative instruction, Discussion, Instruction based on dialogue, Multimedia supported teaching, Students' portfolio
- Contact hours
- 39 hours per semester
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Presentation preparation (report) (1-10)
- 10 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| master the mathematical language at the level of the KMT/USM course output |
| explain the concept of propositional form |
| clarify the difference between a propositional form and a statement |
| define the basic properties of binary operations in a set |
| specify different types of representations in a set and between sets |
| Skills |
|---|
| determine the type of propositional formula |
| solve word problems using knowledge of sets, set operations and Venn diagrams |
| identify properties of specific types of relations |
| Competences |
|---|
| N/A |
| N/A |
| learning outcomes |
|---|
| Knowledge |
|---|
| define the basic properties of binary operations in a set |
| define the different types of algebraic structures with one and two binary operations |
| explain the process of forming the concept of natural number from the perspective of different mathematical models for children of younger school age |
| recognize different concepts of introducing natural numbers (cardinal and ordinal concepts, introduce natural numbers as elements of a Peano set) |
| explain different ways of comparing natural numbers |
| describe different ways of introducing the operations of addition, subtraction, multiplication and division of natural numbers with regard to pre-operational thinking and thinking at a specific level of pupils on primary school |
| explain ways of working with children that do not lead to formal mathematics teaching |
| Skills |
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| determine the properties of the operations of addition, subtraction, multiplication and division in individual numerical sets |
| investigate algebraic structures with one and two binary operations |
| formulate numeration problems in mathematics at primary school |
| Competences |
|---|
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Interactive lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Multimedia supported teaching |
| Collaborative instruction |
| Discussion |
| Skills |
|---|
| Interactive lecture |
| Practicum |
| Task-based study method |
| Multimedia supported teaching |
| Competences |
|---|
| Collaborative instruction |
| Discussion |
| assessment methods |
|---|
| Knowledge |
|---|
| Test |
| Self-evaluation |
| Continuous assessment |
| Skills |
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| Test |
| Skills demonstration during practicum |
| Competences |
|---|
| Continuous assessment |
| Skills demonstration during practicum |
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Recommended literature
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Učebnice, pracovní sešity a matematické příručky matematiky pro 1. st. ZŠ.
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Základy elementární aritmetiky pro učitelství 1. stupně ZŠ : Celost. vysokošk. učebnice. 1. vyd. Praha : SPN, 1985.
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Blažková, Růžena. Poruchy učení v matematice a možnosti jejich nápravy. Brno : Paido, 2000. ISBN 80-85931-89-3.
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Coufalová, Jana. Matematika s didaktikou pro 1. ročník učitelství 1. stupně ZŠ. 5. vydání. 2016. ISBN 978-80-261-0649-4.
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Coufalová, Jana. Základy elementární aritmetiky v 1. ročníku učitelství pro 1. stupeň ZŠ : Sbírka úloh. Plzeň : Pedagogická fakulta [Plzeň], 1990. ISBN 80-7043-013-3.
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Frobisher, Anne, Frobisher, Len. Didaktika matematiky: Porozumieť, riešiť, počítať. Bratislava, 2015. ISBN 978-80-8140-180-0.
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Gray, E. M., Fall, D. Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic..
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Hejný, M., Stehlíková, N. Číselné představy dětí. UK, Pedagogická fakulta, Praha, 1999.
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