New technological possibilities in future teachers' education of mathematics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23420%2F16%3A43932010" target="_blank" >RIV/49777513:23420/16:43932010 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

New technological possibilities in future teachers' education of mathematics

Popis výsledku v původním jazyce

At present time, it is necessary to use computer technology in preparation of mathematics teachers. The article covers three areas of this preparation, namely the area of mathematical statistics, algebra and solving mathematical problems with graphic method. The immediate access to imaging methods, understandable processes and interesting examples plays an important role in teaching statistics (not only for mathematics but also for other branches). On our department, we started to use software tool Mathematica which allows us to use the essential resources that are needed in statistics for creating interactive models. The second part of the article deals with LLL algorithm. The Gram-Schmidt process for orthonormalising a set of vectors is familiar to everyone who passed university mathematical studies. The orthonormal basis acquired this way is not usually “nice” although the original vectors had integer coordinates. The LLL algorithm in its common modification is able to produce certain reduced basis of integer lattice, in fact it is a integer approximation of Gram-Schmidt process. Many of its applications are quite interesting even in the ordinary school education (for example, finding rational approximations of real numbers, etc.). In the third part of the article, graphic method of solving mathematical problems is reminded. Sometime, this method is being neglected but in some cases, it is quite easy and effective way of finding the solution. Especially in solving word problems about the movement (or simple optimizing word problems, too), it can be used not only as a supplement to classical solving process, but even completely separately. Using some dynamic geometry software might be an advantage in the case, allowing the teacher or the student to change (in a certain level of interactivity) the input conditions and variables and then watch the changing output.

Název v anglickém jazyce

New technological possibilities in future teachers' education of mathematics

Popis výsledku anglicky

At present time, it is necessary to use computer technology in preparation of mathematics teachers. The article covers three areas of this preparation, namely the area of mathematical statistics, algebra and solving mathematical problems with graphic method. The immediate access to imaging methods, understandable processes and interesting examples plays an important role in teaching statistics (not only for mathematics but also for other branches). On our department, we started to use software tool Mathematica which allows us to use the essential resources that are needed in statistics for creating interactive models. The second part of the article deals with LLL algorithm. The Gram-Schmidt process for orthonormalising a set of vectors is familiar to everyone who passed university mathematical studies. The orthonormal basis acquired this way is not usually “nice” although the original vectors had integer coordinates. The LLL algorithm in its common modification is able to produce certain reduced basis of integer lattice, in fact it is a integer approximation of Gram-Schmidt process. Many of its applications are quite interesting even in the ordinary school education (for example, finding rational approximations of real numbers, etc.). In the third part of the article, graphic method of solving mathematical problems is reminded. Sometime, this method is being neglected but in some cases, it is quite easy and effective way of finding the solution. Especially in solving word problems about the movement (or simple optimizing word problems, too), it can be used not only as a supplement to classical solving process, but even completely separately. Using some dynamic geometry software might be an advantage in the case, allowing the teacher or the student to change (in a certain level of interactivity) the input conditions and variables and then watch the changing output.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

50301 - Education, general; including training, pedagogy, didactics [and education systems]

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

EDULEARN16 : 8th International Conference on Education and New Learning Technologies : Conference Proceedings

ISBN

978-84-608-8860-4

ISSN

2340-1117

e-ISSN

neuvedeno

Počet stran výsledku

10

Strana od-do

4794-4803

Název nakladatele

IATED

Místo vydání

Barcelona

Místo konání akce

Barcelona

Datum konání akce

4. 7. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000402955904129