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Lecturer(s)
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Příhonská Jana, doc. RNDr. Ph.D.
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Břehovský Jiří, Mgr. Ph.D.
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Course content
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The subject is focused on the elementary concepts of arithmetic and algebra. It is taught in Czech language. The brief theoretical introduction of these topics will be performed. Basic concepts will be interpreted with focus on their application in teaching mathematics at primary school. Lectures: 1. History of mathematics, brief summary of development teaching mathematics. Tasks and aims of teaching mathematics at the 1st level of primary school. 2. Propositional calculus, truth/false proposition, connection, negation, conjunction, disjunction, implication, equivalence. Propositional form, existential and general quantifier. Axioms, mathematical theorems, definitions, evidence of mathematical theorems. 3. Introduction to the intuitive set theory. The set and its elements. Relationships between sets, subset, the set equality. Set operations and their properties, union, intersection, set difference, complement of the set. Cartesian product, Venn´s diagrams and their use in solving problems. 4. Binary relation on the set. Vertex and Cartesian graph. Supplement relation, inverse relation. Relation: reflexive, symmetrical, transitive, connective. 5. Relation of equivalence. Partition of a set, classes of partition. Examples of equivalences. 6. Relation of linear order. Composition of relations, relation from one set to other set. 7. Mapping, function as a special kind of binary relation. Domain, range. Bijection, injection, surjection. Compound mapping. Function as a mapping in the number sets. Graph of function, examples of functions at primary school. 8. Binary operation in a set, basic properties of binary operations, operation table. Commutativity, associativity, existence of neutral and inverse element. 9. Algebraic structures with one or two binary operations. Examples of number sets. 10. Natural number as a cardinal number of finite set. Primary school context. 11. Natural number as a ordinal number of well ordered finite set. 12. Natural number as an element of Peano´s set. Principle of induction. 13. Semiring (N, +, .) and its properties - dividing, divisibility criteria, prime number, composite number. 14. Recapitulation of the semester, time reserve. Seminars: We will practice the topics from lectures of the previous week. The secondary school topics will be practiced in the 1st week. Control test will be entered in 4th, 8th and 12th week and will take 45 minutes.
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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), Written assignment presentation and defence, Individual consultation, Lecture, E-learning
- Class attendance
- 28 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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The subject is an theoretical introduction into algebra (binary relation, mapping, binary operation), propositional calculus and naive set theory. The subject includes also the algebraic structures with one and two binary operations and concept of natural number (cardinal, ordinal approach, Peano's set).
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.
KMA/PMPR
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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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Bělík, M. Teorie binárních operací. [Skriptum UJEP.]. Most, 1995.
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Divíšek, J. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha, SPN, 1989.
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Drábek, J. a kol. Základy elementární aritmetiky pro učitelství 1. st. ZŠ. Praha, SPN, 1985.
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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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Kopka, J. Kapitoly o přirozených číslech. (Skriptum UJEP.). Ústí nad Labem, 2003. ISBN 80-7044-472-X.
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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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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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Perný, J. Kapitoly z elementární aritmetiky 1. (Skriptum TUL.). Liberec, 2010. ISBN 978-80-7372-698-0.
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Perný, J. Kapitoly z elementární aritmetiky 2. (Skriptum TUL.). Liberec, 2010. ISBN 978-80-7372-572-3.
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