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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. Basic mathematical concepts, mathematical symbols. 2. Mathematical thinking, mathematical logic, proposition, negation of proposition. 3. Compound statement. 4. Logically equivalent propositional formulas. 5. Propositional form, variable, compound propositional form. 6. Rules of good reasoning. 7. Expression of quantity, quantified statement, its negation. 8. The concept of a set. Expression of a set. Venn diagram. 9. Field of truth of predicate 10. Potency set. 11. Relation between sets. 12. Operations with sets. 13. Word problems for the unification of two sets with nonempty intersection. 14. Tasks requiring logical thinking in textbooks and tests for the first stage of elementary school.
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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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The subject Mathematics builds on the knowledge of mathematics that students acquired before graduation, and contains basic knowledge of mathematical logic and set theory. It provides the student with an introduction to the mathematical theories of elementary arithmetic and geometry and to the theory of teaching mathematics with a focus on the special needs of primary school teachers. The student will get acquainted with practical examples, will also work with various types of supporting materials for the development of logical thinking in teaching mathematics at the first stage of primary school (textbooks, test sets, applications, programs, interfaces for video calls and video conferencing). The student develops the ability to use mathematical logic to develop mathematical thinking. Special emphasis is placed on creative and independent work with concepts, on the gradual building, acquisition, accurate and concise use of professional language. The most necessary symbolism is introduced in order to enable the use of clear notations for a deeper understanding and to strengthen the thorough acquisition of elements of the minimum professional language. The teaching of partial topics is connected with the problems of pupils with specific disorders, especially dyscalculia and manifestations of their difficulties in mastering mathematical concepts.
The student can: - work with basic mathematical concepts, - solve problems in the field of propositional logic, - determine the field of truth of the predicate, - determine the properties of sessions and operations, - work with quantifiers
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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. Passing the credit test (success rate at least 70%).
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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. Praha: SPN, 1983.
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Divíšek J. a kol. Didaktika matematiky pro učitelství 1. stupně ZŠ. Praha, 1989.
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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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