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Lecturer(s)
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Císařová Alena, PhDr. Ph.D.
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Chmelík Slavomil, PhDr. Ph.D.
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Bílá Margita, PhDr. Ph.D.
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Hrubá Jitka, PhDr. Ph.D.
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Course content
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1. Equations and inequalities in primary school subject matter 2. Expression of a natural number in a number system 3. Numeric operations with natural numbers in the decimal system 4. Numeric operations with natural numbers in systems of base 10 5. Posibilities for the introduction of integers 6. Integral domain of integers 7. Numeric operations with integers 8. Ordered integral domain of integers 9. Absolute value of an integer 10. Divisibility of integers, symbols of divisibility 11. Greatest common divisor 12. Least common (positive) multiple 13. Prime numbers, prime decomposition into a product of prime 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
- Preparation for formative assessments (2-20)
- 15 hours per semester
- Preparation for an examination (30-60)
- 50 hours per semester
- Contact hours
- 39 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| to master the basics of propositional logic (KMT/USM exit level) |
| to explain the basic concepts of set theory |
| to explain the basic concepts of relation theory |
| to define individual mathematical operations (KMT/MSD1 exit level) |
| to define the basic properties of binary operations in a set |
| to define individual types of algebraic structures with one and two binary operations |
| to explain the process of forming the concept of natural number from the perspective of various mathematical models for children of younger school age |
| to recognize the different concepts of introducing natural numbers (cardinal and ordinal concepts, introducing natural numbers as elements of a Peano set) |
| to explain the different ways of comparing natural numbers |
| to describe the different ways of introducing the operations of addition, subtraction, multiplication and division of natural numbers with respect to pre-operational thinking and thinking at a specific level of students on primary school |
| to explain ways of working with children that do not lead to formal mathematics teaching |
| Skills |
|---|
| determine the properties of the operations of addition, subtraction, multiplication and division in individual numerical sets |
| investigate the type of algebraic structure with one and two binary operations |
| formulate numeration problems in mathematics at the 1st level of primary school |
| Competences |
|---|
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| to explain the principles of counting in the decimal system |
| to explain the principles of numerical operations in non-decimal number systems |
| to summarize the possibilities of using number systems in other science subjects |
| to explain the basic principles of the construction of the field of integrity of integers |
| to summarize the basic principles of the constructivist concept of introducing integers in elementary school |
| to summarize and describe the criteria for the divisibility of natural numbers by 2, 3, 4, 5, 8, 9, 10, 11 |
| to distinguish the different ways of determining the greatest common divisor |
| to distinguish the different ways of determining the least common multiple |
| Skills |
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| demonstrate different strategies for solving equations and inequalities with regard to the knowledge of children at primary school |
| apply theoretical knowledge of non-integer number systems to the mathematics curriculum at primary school |
| search for and create problems with integers leading to the integration of mathematics and science |
| decide whether a given number is a prime number |
| solve practical problems using indefinite equations and evaluate other methods suitable for primary school |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Interactive lecture |
| Lecture supplemented with a discussion |
| Practicum |
| Multimedia supported teaching |
| Collaborative instruction |
| Skills |
|---|
| Interactive lecture |
| Lecture with visual aids |
| Practicum |
| Task-based study method |
| Competences |
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| Practicum |
| Discussion |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Test |
| Continuous assessment |
| Skills |
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| Combined exam |
| Test |
| Continuous assessment |
| Competences |
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| Continuous assessment |
| Combined exam |
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Recommended literature
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Učebnice, pracovní sešity a metodické příručky matematiky pro 1. st. ZŠ.
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Coufalová, Jana. Matematika s didaktikou : pro 2. ročník učitelství 1. stupně ZŠ. 5. vydání. 2016. ISBN 978-80-261-0650-0.
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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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Frobisher, Anne, Frobisher, Len. Didaktika matematiky: Porozumieť, riešiť, počítať. Bratislava, 2015. ISBN 978-80-8140-180-0.
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Hejný, Milan; Kuřina, František. Dítě, škola a matematika : konstruktivistické přístupy k vyučování. Vyd. 1. Praha : Portál, 2001. ISBN 80-7178-581-4.
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M. Hejný a kol. Teória vyučovania matematiky 2.. Bratislava : SPN, 1990. ISBN 80-08-01344-3.
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