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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. Mathematical thinking, mathematical logic, statement, negation of statement. 2. Composite statement. 3. Logically equivalent formula formulations. 4. Form of expression, variable, composite form. 5. Rules of Good Considerations. 6. Expression of quantity, quantified statement, its negation. 7. The concept of a set. Expression of the set. Venn diagram. 8. Field of truth of the predicate 9. Potential set. 10. Relationships between sets. 11. Set operations. 12. Verbal tasks for unification of two sets with non-empty penetration.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The Mathematics course builds on the mathematics knowledge acquired by students and includes basic knowledge of mathematical logic and set theory. It provides the student with an introduction to mathematical theories of elementary arithmetic and geometry and the theory of mathematics teaching, focusing on the special needs of a primary school teacher. The student develops the skill to use mathematical logic for the development of mathematical thinking. Particular emphasis is placed on creative and independent work with concepts, gradual building, acquisition, accurate and concise usage of the specialized language. The most necessary symbolism is introduced to allow the use of clear inscriptions for a deeper understanding and to reinforce the thorough acquisition of elements of the minimum professional language. Teaching of subtopics is connected with the problem of pupils with specific disorders, especially dyscalculia and manifestations of their difficulties in learning mathematical concepts.
Student can: - to determine the truth value of the statement, compound statement, to negate the quantified statement and to justify its solution, - to read symbolic entries of mathematical objects, to use symbols of mathematical language in written form, - to precisely formulate the definitions of established concepts and other knowledge from the basics of propositional logic and set theory to express - correctly from the point of view of linguistic and mathematical, - solving tasks using the verbal number, knowledge of sets and set operations, - show sets by the Venn diagram, - using the definitions to prove the relationship between sets.
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Prerequisites
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The subject has no prerequisites.
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Assessment methods and criteria
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unspecified
Active participation in the seminar. Completion of the credit test (success rate of at least 70%). Seminar work. Studijní opora - skripta: BĚLÍK, M. Mathematics for Combined Study of Teaching at the First Grade of Elementary School. Ústí nad Labem: UJEP, 2006.
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Recommended literature
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Bělík M. Matematika pro kombinované studium učitelství 1. stupně ZŠ, UJEP Ústí nad Labem. Ústí nad Labem, 2006. ISBN 80-7044-430-4.
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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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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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Simon, H. Dyskalkulie: jak pomáhat dětem, které mají potíže s početními úlohami.
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ZELINKOVÁ, O. Poruchy učení.. Praha: Portál, 2003.
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