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Lecturer(s)
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Course content
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The course focuses on the following topics: 1. Logical terms and sets 2. Session, display, layout 3. Operations in set, properties 4. Structures with one operation 5. Structures with two operations 6. Axiomatic theory of natural numbers 7. Content axioms of the theory of natural numbers 8. Evidence of sentences in the theory of natural numbers 9. Divisibility of natural numbers 10. Dividing the rest 11. Largest common divisor 12. Smallest multiple multiple 13. Diofant equations 14. Positional numerical systems
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Learning activities and teaching methods
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unspecified, unspecified
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Learning outcomes
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The subject Arithmetics with Didactics I together with the subject Arithmetics with Didactics II in the summer semester of the 2nd year prepares students for their teaching at the first level of elementary school in terms of gaining numerical skills and didactical methodical experience. In the lectures, the student obtains the necessary information in a comprehensive system, the exercises are used to solve mathematical problems, experiment, discovering mathematical contexts and creating mathematical problems. In the didactic aspect of the subject, the teaching is based on the principles of didactic constructivism. In the style of teaching the subject tries to transfer the elements of mathematical discovery and creation into the future pedagogical work of the students. During the course the student acquaints himself with the basic characteristics of the pupil with SPU + gifted pupil. They will learn to use non-traditional methods of teaching appropriate for the maximum involvement of these pupils in teaching. They will encounter dyscalculia.
- identify and use logic clusters, set operations, apply these skills in their own school teaching practice, - to define, recognize and present their own examples of sessions properties, display and layout, to determine the properties of standard mathematical and non-standard operations, to obtain the structure of one or two operations, to construct the theory of natural numbers, to solve and to create indeterminate equations, to understand the thought operations in these tasks used, transfer of positional numerical systems, using non-traditional forms of teaching to involve students with SPUs (dysgraphic pupils and others), - use non-traditional forms of teaching to involve talented and extraordinarily talented students.
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Prerequisites
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Graduation of Mathematics I and Mathematics II.
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Assessment methods and criteria
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unspecified
Student will pass the credit test and seminar work. The work will be handed over at the agreed date. Electronic course: https://moodle.pf.ujep.cz/course/view.php?id=599 Study materials available freely on the Department of Pre-Primary and Primary Education Department web site: http://old.pf.ujep.cz/index.php?option=com_content&view=article&id=5687&Itemid=807
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Recommended literature
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Bělík M. a kol. MATEMATIKA pro studium učitelství 1. st. ZŠ, Pedagogická fa-kulta UJEP, Ústí n.L.. 1996.
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BĚLÍK M. Dělitelnost přirozených čísel, Pedagogická fakulta UJEP, Ústí n.L..
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Bělík M., Svoboda J. Peanova aritmetika přirozeného čísla, Pedagogická fakulta UJEP, Ústí n.L.,. 1998.
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Bělík M., Svoboda J. Binární operace pro studium učitelství 1. stupně základní škol-ky, Pedagogická fakulta UJEP, Ústí n.L..
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Blažek J. a kol. Algebra a teoretická matematika, 1. díl, SPN Praha. 1983.
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Drábek J. a kol. Základy elementární aritmetiky pro studium učitelství 1. st. ZŠ, SPN Praha. 1985.
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HEJNÝ, Milan, KUŘINA, František. Dítě, škola a matematika. 2. vyd. Brno: Portál, 2009. ISBN 80-7290-189-3..
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Kopka J. Kapitoly o přirozených číslech, UJEP, Ústí nad Labem. Ústí nad Labem, 2003.
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Perný Jaroslav. Kapitoly z elementární aritmetiky I. Liberec: TU v Liberci, 2010.
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