|
Lecturer(s)
|
|
|
|
Course content
|
1. Cardinal numbers. Equivalence of sets. Definition of a cardinal number. Equality of cardinal numbers. Natural numbers as cardinal numbers of finite sets. Cardinal numbers of infinite sets. 2. Properties of cardinal numbers. Addition and multiplication of cardinal numbers. Inequalities of cardinal numbers. Commutative semiring with addition and multiplication operations on a set of cardinal numbers and its properties. 3. Word problems about sets with non-empty intersection and ways to solve them. 4. Ordinal numbers. A well-arranged set. Similarity of sets. Equality of ordinal numbers. A natural number as an ordinal number. Ordinal numbers of infinite well-ordered sets. The difference between ordinal and cardinal numbers in mathematical theory and in the teaching of mathematics. 5. Properties of ordinal numbers. Addition and multiplication of ordinal numbers. Convention on the organization of unification and the cartesian product of two well-ordered sets. Semiring with addition and multiplication operations on a set of ordinal numbers and its properties. 6. Extension of numerical fields. Hierarchy of algebraic structures of numerical fields of natural, integer, rational and decimal numbers. 7. Introduction of integers. Equality of ordered pairs of natural numbers representing integers. Decomposition classes of ordered pairs of natural numbers representing integers, their graphical interpretation. 8. Definition of addition and multiplication of ordered pairs of natural numbers representing integers. Properties of ordered pairs of natural numbers representing integers. 9. Commutative ring with addition and multiplication operations on a set of ordered pairs of natural numbers representing integers. Derivation of integers. Integers and their designation. Negative numbers, counting with negative numbers. 10. Introduction of rational numbers. Equality of ordered pairs of integers representing rational numbers. Decomposition classes of ordered pairs of integers representing rational numbers, their graphical interpretation. 11. Definition of addition and multiplication of ordered pairs of integers representing rational numbers. Properties of ordered pairs of integers representing rational numbers. 12. Commutative division ring with addition and multiplication operations on a set of ordered pairs of integers representing rational numbers. Derivation of rational numbers and their notation. Fractions, counting fractions. 13. Decimal numbers. Definition of decimal numbers. Decimal representations. Finite and infinite repeating representations of rational numbers. Commutative ring of decimal numbers and its properties. 14. Extension of the division ring of rational numbers. Irrational numbers. Real numbers.
|
|
Learning activities and teaching methods
|
|
unspecified, unspecified
|
|
Learning outcomes
|
The subject Arithmetic with Didactics II together with the subject Arithmetic with Didactics I in the winter semester of the 2nd year prepares students for their pedagogical work at the first stage of primary school in terms of acquiring mathematical knowledge, skills and didactic-methodological insight into the issue. In the lectures the student will obtain the necessary information in a comprehensive system, exercises are used to solve mathematical problems, experimentation, discovering mathematical contexts, creating mathematical problems and demonstrations of modern didactic methods. Increased attention is paid to the central concept of the whole subject, which is the concept of number. In accordance with the didactic constructivism to which the teaching of the subject applies, the knowledge bases are first created, on which the concept of number is gradually constructed during both semesters. Elements of mathematical discovery, research methods, etc. are used so that students not only build a comprehensive mathematical theory, but that the constructivist teaching style becomes a natural model for future pedagogical work of students in mathematics. The shown teaching methods will be supplemented by work with a textbook, didactic aids, computer technology, mathematical applications and extended by practical examples.
|
|
Prerequisites
|
unspecified
KPR/7830
|
|
Assessment methods and criteria
|
unspecified
Active participation for min. 80 % of seminars. Successful completion of credit tests (success rate 50 %).
|
|
Recommended literature
|
-
Bělík M. Přirozená čísla jako čísla kardinální a ordinální, Pedagogická fakulta UJEP, Ústí n.L.. 1998.
-
Bělík M., Svoboda J. Celá čísla, Pedagogická fakulta UJEP, Ústí n.L.. 1998.
-
Bělík M., Svoboda J. Racionální čísla, PF UJEP, Ústí nad Labem. Ústí nad Labem, 1998.
-
Drábek J.a kol. Základy elementární aritmetiky pro studium učitelství 1. st. ZŠ, SPN Praha,. 1985.
-
Kopka, J. Kapitoly o celých číslech, Ped. F. UJEP, Ústí nad Labem 2002.
-
Kopka J. Kapitoly o přirozených číslech, UJEP, Ústí nad Labem. Ústí nad Labem, 2003.
|