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Lecturer(s)
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Vávrová Marcela, Doc. PaedDr. CSc.
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Císařová Alena, PhDr. Ph.D.
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Course content
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Equations and inequalities in primary school subject matter Expression of a natural number in a number system Numeric operations with natural numbers in the decimal system Numeric operations with natural numbers in the undecimal systems Posibilities for the introduction of integers
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Learning activities and teaching methods
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Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, Collaborative instruction, Cooperative instruction, Discussion, Instruction based on dialogue, Multimedia supported teaching
- Preparation for formative assessments (2-20)
- 15 hours per semester
- Preparation for an examination (30-60)
- 50 hours per semester
- Contact hours
- 39 hours per semester
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| prerequisite |
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| Knowledge |
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| Fundamental knowledge of propositional calculus, fundamental concepts of set theory and theory of relations and operations is assumed (output level of the course KMT/MSD1). Students - define fundamental properties of binary operations on a set, identify properties of the operations addition, subtraction, multiplication and division in individual sets of numbers, - identify various types of algebraic structures with one operation and algebraic structures with two operations, - explain the process of creating the concept of a natural number from the point of view of various mathematical models for primary school children, - distinguish various concepts of the introduction to natural numbers (cardinal and ordinal concepts, introduction to natural numbers as elements of a Peano-set) in terms of examples from practice and their own study of textbooks, - show various ways to compare natural numbers, - formulate the tasks of numeration in primary school mathematics, - describe various possibilities of the introduction to the operations addition, subtraction, multiplication and division of natural numbers with regard to pre-operative thinking at the level of primary school children, - illustrate ways of working with children, not leading to traditional formal methods of teaching mathematics. |
| learning outcomes |
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| Students - demonstrate different strategies for the solution of equations and inequalities that primary school children use, - illustrate the counting principles in the decimal system and numeric operations in non-decimal number systems, - apply theoretical knowledge of non-decimal number systems to mathematics education in primary school, state possibilities of the use of number systems in other science subjects, - illustrate the fundamental principles of construction of the domain of integers and fundamental principles of constructivist concepts within the introduction of integers in primary school, - prove their ability to find and create (word) problems with integers contributing to the integration of mathematics and nature sciences, - state divisibility criteria of natural numbers 2, 3, 4, 5, 8, 9, 10, 11, - distinguish individual methods of determination of the greatest common divisor and the least common positive multiple, - identify if a given number is a prime number, - solve practical problems through indeterminate equations and discuss other strategies suitable for primary pupils. Above all, learning, communication, problem-solving, professional and some aspects of civic and social competencies are being developed. With respect to profession competencies of teachers, pedagogical competencies especially are being cultivated, including diagnostic and communication skills. |
| teaching methods |
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| Lecture supplemented with a discussion |
| Interactive lecture |
| Multimedia supported teaching |
| Collaborative instruction |
| Cooperative instruction |
| Discussion |
| assessment methods |
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| Combined exam |
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Recommended literature
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Učebnice, pracovní sešity a metodické příručky matematiky pro 1. st. ZŠ.
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Coufalová, Jana. Matematika s didaktikou pro 1. ročník učitelství 1. stupně ZŠ. 4. vyd. Plzeň : Západočeská univerzita, 2004. ISBN 80-7043-277-2.
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Coufalová, Jana. Matematika s didaktikou pro 2. ročník učitelství 1. stupně ZŠ. 3. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-922-2.
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Hejný, Milan; Kuřina, František. Dítě, škola a matematika : konstruktivistické přístupy k vyučování. Vyd. 1. Praha : Portál, 2001. ISBN 80-7178-581-4.
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M. Hejný a kol. Teória vyučovania matematiky 2.. Bratislava : SPN, 1990. ISBN 80-08-01344-3.
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