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Lecturer(s)
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Císařová Alena, PhDr. Ph.D.
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Course content
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1. RVP (Framework education program) Mathematics and its applications, TO (education area) number and variable, dependencies and data, standard tasks according to RVP 2. Natural numbers - number, digit, different meanings of natural number, divisibility 3. Integers - comparing, ordering, operations with integers, absolute value 4. Rational numbers - decimals (comparing, operations), fractions (representing, comparing, operations, equivalent fractions), mixed numbers, positive and negative integers 5. Real numbers - powers and roots, introduction, properties, operations 6. Number expressions - name and value of expression 7. Algebraic expressions - substitution, operations with polynomials, squares of binomials and other formulas for simplifying expressions 8. Rate, direct and inverse proportionality, rule of three 9. Linear equations and their systems - equivalent equations and systems, expressing an unknown from a formula 10. Preservice teacher practice - reflection - tried teaching techniques, experiences with assessment, evaluation, marking and activation of pupils 11. Word problems - stages of solution, types 12. Linear and quadratic functions - concept of function, properties of functions, graphs 13. Percentages and elements of financial math, graphs, diagrams, tables
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Learning activities and teaching methods
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Students' portfolio, Skills demonstration, Seminar classes, Individual study, Lecture, Lecture with visual aids
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Presentation preparation (report) (1-10)
- 10 hours per semester
- Contact hours
- 39 hours per semester
- Preparation for comprehensive test (10-40)
- 20 hours per semester
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| prerequisite |
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| Knowledge |
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| have knowledge corresponding to the subjects for the state bachelor's examination in Mathematics with a focus on education |
| Skills |
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| to apply knowledge and skills corresponding to the subjects for the state bachelor's examination in Mathematics with a focus on education |
| Competences |
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| N/A |
| learning outcomes |
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| Knowledge |
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| describe procedures for comparing numbers in a given number range |
| list the procedures for solving equations and systems of equations |
| distinguish between functions and other dependencies |
| Skills |
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| explain algorithms for operations with numbers in a given number field |
| express a part of a whole in different ways |
| use an appropriate method to solve a word problem |
| Competences |
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| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Lecture with visual aids |
| Self-study of literature |
| Skills |
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| Seminar classes |
| Students' portfolio |
| One-to-One tutorial |
| Competences |
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| Seminar |
| assessment methods |
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| Knowledge |
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| Test |
| Continuous assessment |
| Self-evaluation |
| Skills |
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| Test |
| Skills demonstration during practicum |
| Individual presentation at a seminar |
| Self-evaluation |
| Competences |
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| Test |
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Recommended literature
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Učebnice, sbírky úloh a další materiály pro ZŠ a nižší ročníky víceletých gymnázií.
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Etzold, Heiko; Petzschler, Ines. Nápadník aktivit a her do hodin matematiky. 1. vyd. Brno : Edika, 2013. ISBN 978-80-266-0174-6.
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Fehérová, Š., Kučinová, E., Květoň, P. Didaktika matematiky pro základní školy. Ostrava, 2006.
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HEJNÝ, M., KUŘINA, F. Dítě, škola a matematika: konstruktiv. přístupy k vyučování. Praha: Portál, 2001. ISBN 80-7178-581-4.
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Polák, J. Přehled středoškolské matematiky.. Praha : Prometheus, 2008. ISBN 978-80-7196-356-1.
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Polák, Josef. Didaktika matematiky : Jak učit matematiku zajímavě a užitečně. 1. vyd. Plzeň : Fraus, 2014. ISBN 978-80-7238-449-5.
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Starý, K. a kol. Úlohy pro rozvoj dovedností. Metodická publikace pro učitele základních škol a víceletých gymnázií. Praha: ČŠI, 2014.
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