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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 arithmetics. 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. Complete and up-to-date information is posted on web site of the Department of mathematics and didactics of mathematics. Lectures: 1.-2. Introduction. Tasks and aims of teaching mathematics at the 1st level of primary school. Brief summary of development teaching mathematics. Current situation. Brief analysis of mathematics curriculum for primary school. Mathematics in preschool education. Mathematics at elementary and secondary school. 3. - 4. Statement logic in teaching mathematics. Verify of statements. Statement connection, negation, conjunction, disjunction, implication, equivalence. Statement formula, tautology. 5.-6. The foundations of Set theory. The set and its elements. Relationships among sets, subset, the set equality. Set operations and their properties, union, intersection, set difference, complement of the set. Graph illustration of relationship and operation. Venn?s diagrams. Cartesian product. 7.-8. Binary relation, binary relation on the set. Graph mapping, vertex and Cartesian graph. Supplement relation, inverse relation. Relation: reflexive, symmetrical, transitive, connective. Equivalence relation. Decomposition of a set. Ordering, equality, inequality. Compound relation. 9.-10. Mapping. Function. Domain, values. Bijection, injection, surjection. Compound mapping. Set comparison, number comparison. Function as mapping on number sets. Assignment of function. Graph of function. Examples of functions at primary school. 11.-12. Binary operation. The binary set operation concept. Basic properties of binary operations ? unlimited feasible operation on the set. Associativity. Commutativity. Existence of neutral and inverse element. Distributivity of operation. 13.-14. Reserve. Seminars: We will practice the topics from lectures of the previous week. The secondary school topics will be practiced in the 2nd 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), Written assignment presentation and defence
- 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 intuitive set theory
Knowledge of essential concepts of arithmetics, intuitive set theory and propositional caculus.
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Prerequisites
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Knowledge of secondary school mathematics.
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Assessment methods and criteria
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Student's performance analysis
Active participations on seminars, successfully absolved tests. Knowledge of secondary school mathematics (by curriculum of gymnasium, humanities).
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Recommended literature
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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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Hejný, M. a kol. Teória vyučovania matematiky 2. Bratislava, SPN, 1990.
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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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