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Note on the use of Camassa-Holm equations for simulation of incompressible fluid turbulence
Caggio, Matteo; Bodnár, Tomáš
2017 - English
The aim of this short communication is to briefly introduce the Camassa-Holm equations as a working model for simulation of incompressible fluid turbulence. In particular we discuss its application for turbulent boundary layer flows. This model (and related models) is studied for several years in mathematical community, starting from Leray [23]. It can be understood as a generalization of some classical fluid models (Navier-Stokes equations, Prandtl boundary layer equations), showing some interesting mathematical properties in the analysis of the behavior of it's solution (e.g. Layton and Lewandowski [22]). It has been found however, that the model predictions can lead to surprising extensions of the use of the model in technical applications, namely in simulating the turbulent fluid flows. This brief paper should be understood as an introductory note to this novel class of models for applied scientists.
Keywords:
Camassa-Holm equations; turbulent boundary layer
Available on request at various institutes of the ASCR
Note on the use of Camassa-Holm equations for simulation of incompressible fluid turbulence
The aim of this short communication is to briefly introduce the Camassa-Holm equations as a working model for simulation of incompressible fluid turbulence. In particular we discuss its application ...
Znovuobjevování geometrických konstrukcí
Roubíček, Filip
2016 - Czech
Článek je věnován uplatnění principů badatelsky orientovaného vyučování matematice v didaktickém semináři určeném studentům učitelství prvního stupně základní školy, konkrétně aktivitě zaměřené na konstruování známých geometrických útvarů v prostředí překládaného papíru. V článku je popsáno sedm studentských postupů konstrukce čtverce. The paper deals with the application of principles of inquiry based mathematics education in seminars of didactics for future primary school teachers, specifically with the activity focused on construction of known geometrical figures in the environment of folding paper. Seven students´ construction procedures of a square are presented in the paper.
Keywords:
mathematics education; inquiry; elementary geometry
Available at various institutes of the ASCR
Znovuobjevování geometrických konstrukcí
Článek je věnován uplatnění principů badatelsky orientovaného vyučování matematice v didaktickém semináři určeném studentům učitelství prvního stupně základní školy, konkrétně aktivitě zaměřené na ...
Badatelsky orientované vzdělávání jako jedna z cest ke zkvalitňování profesionality učitelů
Tichá, Marie; Samková, L.
2016 - Czech
Příspěvek je zaměřen na badatelsky orientované vzdělávání jako možnou cestu rozvíjení a zkvalitňování profesionality v přípravě učitelů 1. stupně základní školy. Vzhledem k tomu, že proces bádání vede k domněnkám, hypotetickým odpovědím a ty je třeba ověřit, zaměřili jsme se v poslední době také na rozvíjení uvědomování si potřeby argumentovat, vědomě zařazovat odůvodňování do vyučování matematice. This contribution focuses on inquiry-based education as one of the ways to develop and improve professionalism of future primary school teachers. Since the process of inquiry leads to conjectures and hypotheses that need to be verified, we recently turned our attention also to developing awareness of the need of proper argumentation and its incorporation into mathematics lessons.
Keywords:
inquiry-based education; teachers professionalism; primary school; argumentation
Available on request at various institutes of the ASCR
Badatelsky orientované vzdělávání jako jedna z cest ke zkvalitňování profesionality učitelů
Příspěvek je zaměřen na badatelsky orientované vzdělávání jako možnou cestu rozvíjení a zkvalitňování profesionality v přípravě učitelů 1. stupně základní školy. Vzhledem k tomu, že proces bádání vede ...
Badatelské aktivity s geometrickým obsahem v přípravě studentů učitelství
Roubíček, Filip
2016 - Czech
Příspěvek je věnován otázkám uplatnění badatelského přístupu v semináři z didaktiky matematiky určených budoucím učitelům prvního stupně základní školy. Studentům byly předkládány badatelské výukové situace, jejichž základem bylo specifické geometrické prostředí. Studenti se zabývali řešením neurčitých geometrických úloh, které umožňovalo uplatnění badatelských postupů, jako jsou kladení otázek, navrhování postupů, experimentování, usuzování, ověřování, diskutování závěrů aj. V příspěvku jsou prezentovány tři ukázky badatelských aktivit realizovaných se studenty a jejich reflexe bádání. The paper deals with the issue of implementation of inquiry-based approach into seminars of didactics of mathematics for future primary school teachers. Inquiry -stimulating teaching situations based on specific geometrical environments were presented to students. Students engaged in the solving of undefined geometrical problems that enables application od inquiry procedures, such as posing of questions, designing of solving processes, making experiments, reasoning, verification, discussion of findings and others. Three illustrations of inquiry activities realised with students and their reflection of inquiry are presented in the paper.
Keywords:
inquiry activities; geometrical problems; preservice teacher education
Available on request at various institutes of the ASCR
Badatelské aktivity s geometrickým obsahem v přípravě studentů učitelství
Příspěvek je věnován otázkám uplatnění badatelského přístupu v semináři z didaktiky matematiky určených budoucím učitelům prvního stupně základní školy. Studentům byly předkládány badatelské výukové ...
Error patterns in computation in concept cartoons
Samková, L.; Tichá, Marie; Hošpesová, A.
2015 - English
The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to prepare Concept Cartoons displaying various mental computation strategies and error patterns.
Keywords:
concept Cartoons; error patterns; mental computation strategies
Available at various institutes of the ASCR
Error patterns in computation in concept cartoons
The paper focuses on an educational tool called Concept Cartoons, and its possible usage in primary school mathematics, especially in promoting discussion in the classroom. We show in detail how to ...
Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task
Roubíček, Filip
2015 - English
The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster describes communicative situations in solving of inquiry based problems and presents examples of pupils’ solutions and discussion in the classroom.
Keywords:
inquiry based education; teaching of geometry; problem solving; mathematical discourse
Available at various institutes of the ASCR
Reasoning of pupils in the solving process of a geometrical inquiry-stimulating task
The poster focuses on the issue of solving geometrical problems in the context of inquiry based education, namely on the use of inquiry by pupils and on classroom mathematics discourse. The poster ...
Badatelské úlohy ve vyučování geometrii
Roubíček, Filip
2015 - Czech
Podnětem badatelských aktivit ve vyučování geometrii je geometrická úloha, která popisuje neznánou, neurčitou nebo nejednoznačnou situaci a požaduje její komplexní prozkoumání. V příspěvku je popsáno šest badatelských úloh z různých oblastí elementární geometrie. The stimulus of inquire activities in the teaching of geometry is a geometrical problem which describes an unknown, undefined or ambiguous situation and requires its complexe exploration. Six inquiry-stimulating problems of various areas of elementary geometry are described in the paper.
Keywords:
inquiry-based teaching; inquiry activities; geometrical problem
Available at various institutes of the ASCR
Badatelské úlohy ve vyučování geometrii
Podnětem badatelských aktivit ve vyučování geometrii je geometrická úloha, která popisuje neznánou, neurčitou nebo nejednoznačnou situaci a požaduje její komplexní prozkoumání. V příspěvku je popsáno ...
Separable reductions and rich families in theory of Fréchet subdifferentials
Fabian, Marián
2015 - English
We consider important properties of Fréchet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; all statements being considered in Fréchet sense. Given a nonseparable Banach space X, we show how the validity of these statements is implied by the validity of them in every separable subspace of X. Such a reasoning is called “separable reduction”. We show that, behind this approach, there is a modern and powerful concept of rich subfamily of the family of all separable subspaces of X.
Keywords:
Fréchet subdifferentials
Available on request at various institutes of the ASCR
Separable reductions and rich families in theory of Fréchet subdifferentials
We consider important properties of Fréchet subdifferentials, in particular: the non-emptiness of subdifferentials, the non-zeroness of normal cones, the fuzzy calculus, and the extremal principle; ...
Talk about patterns in the mathematics classroom
Roubíček, Filip
2015 - English
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical patterns in a triangle grid and their transformation into arithmetic patterns or algebraic functions. It shows how pupils/students reason about relationships in these patterns and among these patterns, how they describe and express their generalizations in words or symbols.
Keywords:
discourse; mathematics classroom; patterns
Available on request at various institutes of the ASCR
Talk about patterns in the mathematics classroom
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical ...
How primary school teachers posed problems for inquiry based mathematics education
Hošpesová, A.; Samková, L.; Tichá, Marie; Roubíček, Filip
2015 - English
The paper reports on a survey whose aim is to contribute to the research in the area of inquiry based mathematics education (IBME), primary school teacher training, and problem posing. The core of the study is an empirical survey with a qualitative design. We let pre-service and in-service primary school teachers pose problems which they believe enable IBME, perform the problems with pupils, and write self-reflections on this activity. We investigated the nature of the posed problems in relation to the self-reflections.
Keywords:
inquiry based mathematics education; posing problems; primary school teacher training; pre-service and in-service teachers
Available at various institutes of the ASCR
How primary school teachers posed problems for inquiry based mathematics education
The paper reports on a survey whose aim is to contribute to the research in the area of inquiry based mathematics education (IBME), primary school teacher training, and problem posing. The core of the ...
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