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On basis of knowledge gained from previous mathematical courses the environments suitable for the development of pupils mathematical understanding will be extended and completed with particular respect to solving strategy and solving methods. The core of the work will be development of the ability to solve submitted tasks using different methods (including restricted tools). We will focus on the following areas: modelling, representation, choice of strategy, creating and realization of solving plan, interpretation of findings. Another course of study will be creating and posing such tasks which are possible to solve using given method.
Last update: Esserová Kateřina, DiS. (24.09.2019)
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1. To use problem solving as a tool to develop cognitive structure of students. Focusing on solving strategies the students' meta-cognition will be systematically developed.
2. To give the students direct experience with constructivistic way of teaching in those areas with which they have not got their own school experience.
3. To enable students to diagnose their own mathematical abilities and knowledge and to offer them possibility of re-education (particularly concerning the main mathematical concepts) if necessary.
Last update: Esserová Kateřina, DiS. (24.09.2019)
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Online sessions are taken place here: https://meet.google.com/uec-vkom-utr?authuser=1 Last update: Jirotková Darina, doc. RNDr., Ph.D. (10.02.2021)
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Opava, Z.: Matematika kolem nás, Albatros
Hejný M., Stehlíková N.: Číselné představy dětí (skriptum PedF UK)
Hruša a kol.: Aritmetika pro pedagogické instituty (starší učebnice)
Wittmann, E. Ch. , Müller, G. N.: Handbuch produktiver Rechenübungen, Band 1 (Von Einspluseins zum Einmaleins, 1990), Band 2 (Von halbschriftlichen zum schriftlichen Rechnen, 1992)
Koman, M.: Pravidelnosti aritmetiky a geometrie číselných dvojčat, In Dvacetpět kapitol z didaktiky matematiky (2004).
Koman, M.: Rozšiřování číselných oborů (Užití čtvercových sítí), (skriptum UK Praha, 1975) Last update: Esserová Kateřina, DiS. (24.09.2019)
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Seminars will be led consequently in constructivistic ways. The main teaching tool will be problems and their solutions by students. Students will be guided to create autonomously cascades of tasks with respect to individual need of pupils.
Last update: Esserová Kateřina, DiS. (24.09.2019)
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Requirements for examination: Active presence Seminar work Essey about how to make use the content of the course at home university Last update: Jirotková Darina, doc. RNDr., Ph.D. (10.02.2021)
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1. Method of modelling (interpretation of a task: story, objects, relationships, model). 2. Method of dramatization (from dramatization to simulation and to tables, development of procept). 3. Method od decomposition: a) chaining, b) classification. 4. Series of specific methods (simplification, from the end, set of points with particular attribute, analogy etc.). 5. Discovering of patterns in different environments using method: progression, tables, graphs (processual grasping of patterns using recursion and conceptual grasping using relationships. 6. Method of releasing invariables as a tool for generalization in geometrical, arithmetical, algebraical and combinatorial environments.
Last update: Esserová Kateřina, DiS. (24.09.2019)
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