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Lecturer(s)
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Course content
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Definition of mathematical thinking, development of mathematical thinking in primary school students. The Concept Cartoons method, building the elementary foundations of mathematical thinking. Solving a practical task in the role of a mathematics teacher. The role of numbers in our lives. The mathematical nature of selected numbers as an opportunity to develop students' mathematical thinking. Ratio in practice. Pi and the golden ratio. Natural numbers, prime numbers. Euler's number, its role in geometry, nature, and finance. Solving a practical task in the role of a mathematics teacher. Geometry in real life. Basic geometric principles in natural, technical, and social phenomena. Visual perception vs. reality. Solving a practical task in the role of a mathematics teacher. Application of mathematical thinking in solving financial problems. Basic financial products and phenomena and their understanding through mathematics. Solving a practical task in the role of a mathematics teacher.
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Learning activities and teaching methods
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Dialogic (discussion, interview, brainstorming), Demonstration, Activating (simulations, games, drama), Work with multi-media resources (texts, internet, IT technologies), Group work
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Learning outcomes
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The course is focused on the development and practical application of mathematical methods. At first, by means of particular activities, the participant will become acquainted with the basis of mathematical thinking and the methods of its development. Then, when solving specific real life situations, the participant applies selected mathematical procedures appropriate to these situations and which are also applicable in other practical situations. In order to do so, a basic knowledge of upper secondary school mathematics is sufficient. If the development of a mathematical model or the solution of a real life problem appears to be too complex, the intuitively operated mathematical software or mobile application is provided for the participant to do so. The scope of the course spans from the development of the basic processes of mathematical thinking, through the reflection of the principles of number theory and geometry in real life, to the application of mathematical methods in everyday financial issues.
Through specific activities, becomes familiar with the nature of mathematical thinking and methods for its development. Through solving real-life situations, acquires the ability to apply selected mathematical procedures that are essential for practice. Understands the nature of mathematical methods and thinking and knows how to further develop in this area. Is aware of the potential and specific ways of didactic transformation of the course content in accordance with students' educational needs. Has knowledge of geometry content and understands how to use it to support students' curiosity and motivation to learn. Acquires and practically applies approaches that promote learning-supportive behaviour and cooperation within the classroom. Is practically familiar with both physical and digital environments currently most suitable for supporting the study and teaching of mathematics. Gains practical experience with appropriate teaching methods and procedures for setting assessment criteria in mathematics. Alignment with the Competence Framework for Graduates of Teacher Training Programs (KRAU): Area 1: 1.1, 1.2 Area 2: 2.3 Area 3: 3.2, 3.3 Area 4: 4.1
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Prerequisites
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Assessment methods and criteria
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Seminar work, Interim evaluation
Active participation in discussions and completion of partial tasks during the seminar. Four seminar papers on selected topics.
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Recommended literature
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Arthur, C. J. Financial literacy education: Neoliberalism, the consumer and the citizen. 2012.
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Bogomolny, A. Cut The Knot: Interactice Mathematics Miscellany and Puzzles [online]. .
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Capiňski, M., & Zastawniak, T. Mathematics for finance: An introduction to financial engineering. 2008.
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Devlin, K. Introduction to Mathematical Thinking. .
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Kirkby, D. Go Further With Investigations. 1996.
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Kirkby, D. More Investigations. 1995.
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MŠMT. Kompetenční rámec absolventa a absolventky učitelství. Praha. 2023.
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Samková, L. Metoda Concept Cartoons. České Budějovice. 2020.
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Stacey, K. et al. Specific mathematics assessments that reveal thinking. Smart tests research and development project. .
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Ulm, V. Inquiry-based mathematics education for gifted children in primary school. 2011.
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