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Lecturer(s)
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Janečková Miroslava, PaedDr. PhD.
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Course content
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1. Cartesian product of sets. 2. Binary relations. 3. Graphical representation of relations. 4. Additional relation. Inverse relation. 5. Properties of binary relations. 6. Binary relations in learning mathematics in primary school. 7. Equivalence relation. 8. Disjoint, sorting - a process induced equivalence relation. 9. Relation arrangement. 10. Arrangement, h-diagram. 11. Ordered sets. 12. Projection, types of projections.
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Learning activities and teaching methods
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unspecified, unspecified, unspecified
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Learning outcomes
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Subject Mathematics II contains the basic knowledge of the theory of binary relations. Provides an introduction to the mathematical theory of elementary arithmetic and geometry and the theory of teaching mathematics with a focus on special needs teacher in the first grade of primary school. Special emphasis is placed on creative and independent work with concepts, gradually building, acquiring, accurate and concise use of technical language. It introduced the most essential symbolism to allow the use of clear entries for deeper understanding and strengthen a thorough mastery of the elements of the minimum of technical language. Student is able to: - write Binary relation correctly and draw its graph, - apply either learned definitions of binary relations attributes or its graphs for determining attributes of binary relations, - state possibilities of special types binary relations usage (equivalence, arrangement, depiction) in mathematic on primary school level and can recognize these terms in mathematical tasks and also in real life, - create mathematical tasks which contain binary relations, - write decomposition of set M induced with equivalency in set M. s and didactics.
Student is able to: - write Binary relation correctly and draw its graph, - apply either learned definitions of binary relations attributes or its graphs for determining attributes of binary relations, - state possibilities of special types binary relations usage (equivalence, arrangement, depiction) in mathematic on primary school level and can recognize these terms in mathematical tasks and also in real life, - create mathematical tasks which contain binary relations, - write decomposition of set M induced with equivalency in set M. s and didactics.
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Prerequisites
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The subject requires no specific prerequisites.
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Assessment methods and criteria
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unspecified
Active participation in the seminar. Compliance test (70% pass). Seminar work.
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Recommended literature
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Bělík, M. Matematika pro kombinované studium učitelství 1. stupně ZŠ. Ústí nad Labem, 1989.
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Blažek, J. a kol. Algebra a teoretická aritmetika I, SPN, Praha. 1985.
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Divíšek J. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha, 1989.
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Drábek J. a kol. Základy elementární aritmetiky pro studium učitelství 1. st. ZŠ, SPN Praha. 1985.
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Kaslová, M. Předmatematické činnosti v předškolním vzdělávání. Praha, 2010. ISBN 978-80-86307-96-1.
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Melichar J., Svoboda J. Rozvoj matematického myšlení I pro studium učitelství pro mateřské školy, UJEP, Ústí nad Labem. Ústí nad Labem, 2003.
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Opava Z. Matematika kolem nás, Albatros Praha. 1989.
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Perný Jaroslav. Kapitoly z elementární aritmetiky I. Liberec: TU v Liberci, 2010.
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