It is very difficulty to discovery organisation principle of elements choice from base set during solving of combination problems with pupils at primary schools from methodical point of view. A teacher is able to create adequate application problems if he knows individual types of intelligentsia of his pupils. He teaches them to discovery strategies of solving combinations problems. This article is dealing with various views on teaching interesting combination problems.
In this article we present some theoretical approaches in mathematics education especially in Poland and Hungary with practical examples. We describe also some aspects of using ICT in mathematics education.
The informatisation of schools will have effective education processes. A research realized with centred on edifying tasks of education in term of resourcespupil tp learn and teacher to teach on the lesson in mathematics or geometry on the 2nd degree of a primary school by ICT (computers, computer programs, computer geometry, computer graphics). The innovation methods of constructivism paedeutics show appropriate for application. From deductions of research are concluded applications for effective using in praxis.
The artickle treats of the using of the interactive board SMART Board during the teaching of mathematics at college or secondary school. The project has run last year in May at a grammar school in České Budějovice. There participated second year students and by this interactive board they were getting known a new and not allways loved scope of Mathematics - combinatorics.
In our research we investigate probabilistic thinking of pupils of the 8th class of an elementary school. We have found out that only few of pupils were able to construct corresponding discrete probability space when solving probabilistic tasks. However, our analysis shows that low level of probabilistic thinking is not always the reason.
Vyučovaniu matematiky sa často vyčíta, že je pre žiaka abstraktné, nezaujímavé a málo spojené so životom. Existuje viacero jednoduchých experimentov, ktoré nie sú náročné na pomôcky ani čas a dajú sa realizovať priamo na vyučovacej hodine. Je to jedna z možností, ako urobiť hodinu matematiky zaujímavejšou, zábavnejšou a žiakovi ukážu, načo potrebuje matematiku.
A typical method of investigating a mathematical situation follows this sequence of processes: Mathematical situation - experimentation - conjecture - test - proof - mathematical theorem. The central activity during the investigation of many mathematical problem situations is that of conjecturing. A conjecture is a statement which appears reasonable, but whose truth has not yet been established. Conjecturing forms the backbone of mathematical thinking and reasoning. We look at a number of famous and interesting conjectures associated with positive integers which can be explored at different levels in elementary and secondary schools.
Využívaniu digitálnych technológií vo vyučovacom procese sa v súčasnosti venuje veľká pozornosť.Vyučovanie matematiky s podporou digitálnych technológií a s e-learningovou podporou bolo predmetom výskumu realizovaného na strednej obchodnej akadémii. Príspevok chce oboznámiť s realizáciou a poukázať na niektoré zaujímavé výsledky tohto projektu.
The mathematical base of our examples comes from the book Calculus of Variations written by Lavrent’ev and Lyusternik. We can read here about the J-hyperbolas. As well-nown, we proceed at the normal definition of the hyperbola from given two points. In complete analogy now two lines are given. These two lines take the role from the two points. In this presentation different cases (in respect of signs) are discussed with the help of computers. Finally it turns out that eight rays occur. So a mistake, an incompleteness in the mentioned book was discovered. At the end of the lecture a new problem is posed. What about the case that the two points both are circles or one point is a circle and the other is a line?
The subject of this paper concerns the deliberation on the use of school mathematical knowledge by pupils in the process of solving maths problems. The deliberation has been conducted on the notion of even parity. This paper shows, among other things, results of research on the knowledge and skills that pupils posses, as well as their intuition concerning the discussed notion.
In his article it is presented how one can make use of the notion of calculus of probability such as expected value, variance, standard deviation, semi-variance and semi-standard deviation in order to make the optimal decision as to the choice of a gambling game.
We say that the combinatorial problem is elementary if it can be solved using one combinatorial operation (permutations, combinations, variations with or without repetition). Elementary combinatorial problems may be classified into three different combinatorial models (selection, partition and distribution). In this paper, we describe the effect of the implicit combinatorial model for understanding the problem, the choice of strategies for solving and the accuracy of student’s solutions. We consider also the most common errors in the solutions of the problems. Based on our results we formulate ideas of the selection of combinatorial problems for mathematics lessons.
The paper deals with effectivity of digital whiteboard in mathematics teaching. There are presented some results of investigations from using of this tool in teacher training and their comparation with literature. There are presented some examples and suggestions for elementary teachers how improve the interactivity and effectivity of their teaching by digital whiteboard.
Kombinatorika v škole je prezentovaná ako hotový príspevok matematiky (definícia - veta - úlohy). Nikto nevie komu a na čo (prečo) sú potrebné kombinatorické pojmy a vety. Prednáška prezentuje: a) kombinatorické pojmy ako zvláštne prostriedky riešení mimomatematických problémov (kombinatorika okolo nás); b) kombinatorické vzorce ako vety objavované na hodinách matematiky; c) zvláštnu argumentáciu ako prostriedok tohto matematického objavovania. Prednáška sa týka fázy matematizácie pri riešení praktických problémov (ide o proces aplikácie matematiky a kombinatorické pojmy ako prostriedky matematizácie). V máji 2010 vo vedeckom vydavateľstve Novum v Plocku (Poľsko) vyšla farebná monografia Adam Plocki, Pavel Tlustý "Kombinatorika okolo nás". Prednáška sa týka istej "filozofie" výučby kombinatoriky a kombinatorického aspektu matematického vzdelávania v rámci matematiky pre každého, predstavenej v tejto knihe. Farba je v tejto knihe dôležitým prostriedkom argumentácie.
The main aim of this paper is the investigation of students’ understanding of statistical concepts at secondary school level. Our investigation was carried through the tasks motivated by secondary school curriculum and based on report of OECD PISA 2003. At the end we summarize the observations and we suggest possible improvements in process of data analysis teaching.
In this paper we will bring out different views on key mathematical competences and possibilities of their development through different types of mathematical tasks. It is appropriate to focus primarily on some key competences among the varieties of topics included in school mathematics teaching content. In our contribution we focus on Combinatorics and key competence Visualization, description of mathematical objects and situations, representation.
In this paper we present examples of introducing basic concepts of mathematical analysis. We especially accent didactical operations which have been used to facilitate understanding of those concepts to students.
One of fundamental part of maths teaching is teaching of reasoning. Reduction is a method “moving from end to beginning”. It is very useful in process of solving mathematical problems, but it's hard to teach reduction in natural way at school. Maybe special kind of maths problem can help with it. Educational computer game can be such problem. It can discreetly provoke situation, when pupils discover reductive method to win the game.
The paper deals with a need of lifelong learning mathematics teachers in the field of school education programs. The goal of the article is to propose criteria for the creation of training programs for teachers of Mathematics.
The paper presents research result conducted at lower secondary school level focusing on the language aspects of the initial phase of implementation of the CLIL method into mathematics lessons.
Už v staroveku sa objavili metódy, ktoré stáli pri zrode integrálneho počtu. Jednou z prvotných myšlienok boli Demokritové hypotézy, ktoré znamenali dve odlišné pohľady na integrálny počet. Prvý pohľad sa spája s menami Cavalieri, Newton a Leibnitz. Druhý pohľad- exhaustačná metóda sa rozvinuli prostredníctvom Eudoxa, Archiméda a Oresmeho. Tento pohľad však nenašiel odozvu v integrálnom počte. Cieľom tohto článku je ukázať, že aj druhý pohľad môže viesť k integrálnemu počtu ešte zrozumiteľnejšou a jednoduchšou metódou, ktorú je možné zovšeobecniť na Lebesgueov integrál. Je založený na sumovateľnosti postupnosti a má niekoľko vhodných didaktických prístupov. Je definovaný bez použitia teórie miery a je jednoduchší ako Riemannov integrál. Ukážeme niekoľko príkladov a otvorených problémov.
Cieľom príspevku je ukázať niektoré možnosti využitia informačno-komunikačných technológií a softvéru GeoGebra vo vyučovaní matematiky na základnej škole. Príspevok obsahuje tri metodické listy pre učiteľa využívajúce program GeoGebra pri výučbe geometrie. Prvý metodický list predstavuje základy práce so samotným softvérom, druhý sa venuje problematike dokazovania existencie trojuholníka z troch strán. Tretí metodický list je zameraný na prácu s významnými prvkami trojuholníka – výšky, ťažnice a stredné priečky. V práci sú uvedené prepojenia na videosekvencie zverejnené v priestore Windows Live s návodmi pre prácu v programe GeoGebra. V závere je zhodnotený prínos GeoGebry k skvalitneniu vyučovania geometrie na základnej škole. V prílohe práce je k dispozícii niekoľko pracovných listov pre žiakov a zoznam videosekvencií.
Keď sa pozorne pozriete na (štandardnú) futbalovú loptu môžete ľahko zistiť, že je zošitá z 32 kúskov kože, ktoré majú tvar 5-uholníkov a 6-uholníkov, pričom v každom bode sa spájajú najviac tri kúsky kože. V minulosti sa používali aj iné typy lôpt. Prirodzeným spôsobom vzniká otázka, z koľkých a akých počtov stien sa skladá lopta? Vychádzajúc z klasickej Eulerovej formuly pre konvexné mnohosteny, budeme sa zaoberať kombinatorickými vlastnosťami rôznych lôpt. V prednáška budeme rozvíjať fakty, ktoré sú uvedené v práci [1], ktorá je prístupná aj v elektronickej verzii.
This paper deals with research on pupils’ attitudes towards mathematics and its teaching. We study theoretical framework of attitudes and results of our research. Mainly we focus on influences on pupils’ attitudes made by the teacher and teaching - learning styles.