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Lecturer(s)
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Posová Veronika, Mgr. et Mgr. Ph.D.
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Bílá Margita, PhDr. Ph.D.
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Course content
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1. Propositional calculus 2. Mathematization of real situation, propositional analysis of word text 3. Predicate calculus 4. Introduction to set theory, set operations 5. Venn diagrams, word problems 6. Quantified propositions 7. Proofs of mathematical theorems 8. Proofs of mathematical theorems 9. Carthesian product and binary relations on a set 10. Properties of binary relations 11. Order relations 12. Inverse and complement relations, composition of relations 13. Transformation
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, E-learning, Collaborative instruction, Cooperative instruction, Seminar classes
- Contact hours
- 39 hours per semester
- Preparation for formative assessments (2-20)
- 8 hours per semester
- Preparation for an examination (30-60)
- 40 hours per semester
- unspecified
- 15 hours per semester
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| prerequisite |
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| Knowledge |
|---|
| achieve a high school level of mathematical knowledge |
| Skills |
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| modify an algebraic expression |
| solve linear equations (including absolute value equations and equations with a parameter) |
| solve systems of linear equations |
| Competences |
|---|
| N/A |
| learning outcomes |
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| Knowledge |
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| explain the concept of propositional form |
| clarify the difference between a propositional form and a proposition |
| distinguish between a general and an existential proposition |
| 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 |
| prove mathematical theorems using different types of proofs |
| identify properties of specific types of relations |
| Competences |
|---|
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Lecture supplemented with a discussion |
| Interactive lecture |
| Collaborative instruction |
| Practicum |
| Skills |
|---|
| Practicum |
| Skills demonstration |
| Collaborative instruction |
| Competences |
|---|
| Task-based study method |
| assessment methods |
|---|
| Knowledge |
|---|
| Combined exam |
| Test |
| Continuous assessment |
| Skills |
|---|
| Combined exam |
| Test |
| Skills demonstration during practicum |
| Competences |
|---|
| Combined exam |
| Skills demonstration during practicum |
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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 1. ročník učitelství 1. stupně ZŠ. 5. vydání. 2016. ISBN 978-80-261-0649-4.
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Jirotková, Darina; Kaslová, Michaela. Sbírka úloh z elementární matematiky pro studující učitelství 1. stupně ZŠ : Určeno pro posl. fak. pedagog. Díl 1.. 1. vyd. Praha : SPN, 1985.
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Panáčová, Jitka; Beránek, Jaroslav. Základy elementární matematiky s didaktikou pro učitelství 1. stupně ZŠ. 1. vydání. 2020. ISBN 978-80-210-9863-3.
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Pisklák, Bohuslav. Matematika pro učitele primárního vzdělávání : binární relace a zobrazení :distanční text. Vyd. 1. Ostrava : Universitas Ostraviensis, 2004. ISBN 80-7368-013-0.
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Wells.D. G. Prime numbers: the most mysterious figures in math. Hoboken, 2005. ISBN 0-471-46234-9.
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