1.Počítačové hry a explorativní přístup k výuce matematiky

Mgr. Květoslav Bártek

The article is focused on education of mathematics through utilization of computer games. Computer game gives an opportunity to use explorative methods in teaching of mathematics. The paper also presents a project "Didactic computer games in mathematics instruction and their impact on the development of pupil’s personality."

2.Netradiční úlohy o reálných číslech

Doc. RNDr. Jaroslav Beránek CSc.

This article is aimed to introducing of real numbers and solving of exercises related to real numbers. After the introductory notes there fol low arithmetic and geometric models of real numbers complemented with ten solved exercises. These deal with various aspects of real number theory, eg. decimal expansion of real numbers, decomposition of rational and irrational numbers on number scale and surds. The article is concluded by a short historical note about algebraic and transcendental numbers.

3.O dotýkajúcich sa kružniciach

RNDr. Martin Billich PhD.

Apollonius’ problem asks to construct the circle which is tangent to any three objects. The case when all three objects are circles is the most complicated case since up to eight solution circles are possible depending on the arrangement of the given circles. In addition degenerate cases of the problem of Apol lonius are discussed in this report.

4.Hrátky s matematikou

Mgr. Daniela Blažková

The paper deals with the project designate STM-Morava or more precisely with its part S006 Playing with mathematics. Conception of this project is according to principles of constructivism.

5.Pedagogická prax a didaktická príprava študentov učiteľstva matematiky pre 2. stupeň ZŠ

Doc. RNDr. Jaroslava Brincková CSc.

Scientific and technological development is fundamental for competitive knowledge society, motivating more people to choose studies and careers in the fields of Mathematics. Securing a sufficient number of qualified teachers in Mathematics subjects.

6.Same examples using IT to create the concept image of mathematical objects

Dr. Beata Bugajska - Jaszczołt, Dr. Monika Czajkowska

In this article we are discussing the complex nature of mathematical objects and specificity of construction of the mathematical knowledge. It is being demonstrated how possible it is to deepen the understanding of mathematical objects by means of using IT and also to ponder the problems that are inaccessible while using the traditional methods and demonstrative means.

7.The didactic propositions of introducing the idea of basis of linear

Dr. Beata Bugajska - Jaszczołt, Dr. Danuta Drygała

In this article we present different textbooks conceptions of introducing the concept of basis of linear space. We compare the academic handbooks of Linear Algebra for mathematics’ students. We present the handbooks` analysis in five segments. We show the didactic consequences of choosing one of them.

8.Výučbový program ako pomôcka aktualizácie učiva

Mgr. Marián Buxár

In present days IKT (information and communication technology) becomes an important part of educational systems. Different areas of education put different requirements for conception and elaboration of educational software. An important part of teaching process is repetition of knowledge before a new thematic unit. Repetition-evaluation program serves for retrieving and recapitulating of input knowledge. This process can be more effectively and less time-consuming than classical lessons. This article dissertates about input test before thematic unit Sequences and theoretic comparison between computer aided instruction and classical lessons.

9.Remarks on Euler summability method

Dr. Stanislav Domoradzki

In his clessical monograph (Théorie des opérations linéaires. Mono-grafie Matematyczne, Warszawa 1932) Stefan Banach adresses also to the problem of summability of series. The results by Euler concerning the summability were criticized by 19th century investigators as they did not correspond to the modern standards of rigor.

We conclude that the abstract formalism of functional analysis allowed to treat from the general point of view concrete calculations due to Euler. This demonstrates the diversity and reachness of interaction of mathematical ideas which sometimes have distant (also in temporal aspect) origin.

10.Przeżywanie znaków i symboli

Dr. Halina Drewniak

We need signs and symbols to understand ourselves and others. Now, human sensibility on symbols, on their recognition and discrimination is vanishing. Man is shutting on mistery and pluge into virtual reality, alone, without God and people. Man without symbol sensibility is like dead. Thus, an education of children and youth in experience with symbols is necessary. We need a didactic of symbols as an esthetic education. We need to awake sensibility on spiritual values and regenerate a symbolic ability. We need a development of symbolic imagination and symbolic thinking.

11.Úspešnosť riešenia MCRE úloh a jej vzťah s úspešnosťou žiakov v matematike

PaedDr. Ján Ďuriš

In this paper we describe MCRE (Mathematics Contra Real-life Experience) tasks and their relationship with standard mathematical tasks.

12.Skúmanie vlastností pantografu v prostredí Cabri geometria

RNDr. Radovan Engel

The paper deals with the investigation of pantograph in a microworld created in Cabri geometry. Some aspects related to usage of this program in geometry lessons including creating of microworlds and the modification of program’s environment are discussed here. Short information about history of pantograph and explanation of its principle are included in this paper, too. Finally, an experiment aimed on comparison of efficiency of mentioned microworld with classical approach is presented in this article.

13.Reťazové zlomky u Leonharda Eulera

PaedDr. Ján Gunčaga PhD.

A famous mathematician Leonhard Euler (1707-1783) was born 300 years ago. The anniversary certainly deserves to celebrate his human and mathematical achievements. In this article we present two typical examples in which Euler used continuous fractions to solve contemporary problems of mathematical analysis. Continuous fractions can serve teachers at a secondary school as a suitable topic for motivation and introduction to sequences and limits.

14.Matematický aparát fyziky

PaedDr. Ing. Peter Hanisko

Mathematics is the most important tool of physics. Use of mathematical principles is a fundamental requirement for correctness in physics; without it, formulating quantitative rules and deriving concrete numerical results from them would be impossible. This article describes the individual areas of mathematics utilized in high school physics, specifically modern physics.

15.Od skúsenosti k poznaniu

Prof. RNDr. Milan Hejný CSc.

Proces postupnej premeny aritmetickej skúsenosti na poznatok u žiaka 1. stupňa ZŠ je popísaný ako zrod a budovanie schémy aditívnej triády. Podstatou budovania schémy je tvorba najprv izolovaných a potom generických modelov triády vloženej do rôznorodých kontextov. Štúdia, ktorá je volným pokračovaním autorovho príspevku na ružomberskej konferencii v roku 2006, je založená na nových výsledkoch výskumu realizovaného spoločne s D. Jirotkovou a J. Slezákovou. Proces premeny geometrickej skúsenosti na poznatok je krátko diskutovaný v poslednej kapitole.

16.E-learning vo vyučovaní predmetu Logika, množiny, relácie

Doc. RNDr. Pavel Híc CSc., PaedDr. Milan Pokorný PhD.

Modern information and communication technologies influence mathematics teaching more and more. They help teachers to efficiently fulfill teaching aims, especially in distance learning. The paper deals with using professional e-learning courses in teaching of Logic, Sets and Relations at the Faculty of Education, Trnava University. The authors especially focus on the course Sets, which was designed in recent months.

17.Jak obohatit učivo žákům nadaným na matematiku

Mgr. Eva Hotová

The article is focused on education of the pupils gifted with mathematics. The author introduces basic approaches and methods of education of gifted children and presents some particular examples in this paper.

18.Fyzikálno-matematická aplikácia derivácie

RNDr. Klement Hrkota st., RNDr. Klement Hrkota ml.

On what kind of movement the point of intersection carries out with the axis x at regular falling of some functions in the coordinate system and the possibility of using this movement in the issue – the applying of derivation in the fonoth grade of secundary gramar schools.

19. Príklad s prvkom kognitívnej neistoty, ktorý žiakom naznačí jeden zo spôsobov zovšeobecňovania matematických poznatkov

RNDr. Klement Hrkota st., RNDr. Klement Hrkota ml.

This paper deals with some simple application of differential calculus. Is here showen some simple motivation example, which can give us necesserity to study the theory of partial derivatives.

20.O pewnym równaniu funkcyjnym charakteryzującym całkę nieoznaczoną

Dr. Antoni Chronowski, Dr. Zbigniew Powązka

Let us denote by C^∞(α,β) a family of all real-valued functions of the class C^∞ defined on the interval (α, β ) ⊂ IR. Let (C^∞(α,β), IR, +, ⋅ ) be a vector space of these functions and (H, IR, +, ⋅ ) a subspace of constant functions defined on (α,β). Consider the operator T : C^∞(α,β) →C^∞(α,β)/H such that the following condition is satisfied: T (f⋅g’) = f⋅g – T (f’⋅g), for all f, g ∈ C^∞(α,β), where f’ and g’ are derivatives of the functions f and g, respectively.

In this paper we prove that for every function f ∈ C^∞(α,β) the function T(f) is the integral of the function f. Moreover, the further properties of the operator T are proved.

21.Fibonacciho čísla na strední škole

Mgr. Martina Jarošová

In this contribution we introduce some interesting facts about Fibonacci nunbers. We wil l prove some identities using different proof methods. Than we discuss the divisibility of Fibonacci numbers, recurrent formulas and the relation between Fibonacci numbers and the Pascal triangle.

22.Stručná správa o kakurénii

Dušan Jedinák

Brief note about harmony. Didactic muse above definition of harmony in school mathematics.

23.Globalschool - moderní metoda ve výuce

Mgr. Marika Kafková

Last year Globalschool organized the first small 2-days-konference for pupils who were integrated in a determinated project called Sports complex. The article that follows describes briefly the Globalschool, informs about solved projects and describes the pupil's conference with prepared prezentations.

24.Zápis racionálnych čísel v pozičných číselných sústavách

Miroslav Kamenický

V článku sa zaoberáme menej známym spôsobom zápisu a odvodenia racionálnych čísel v pozičných číselných sústavách. Je v ňom teoreticky rozpracované ako k z-adickému rozvoju hľadať príslušné vyjadrenie zlomkom. Článok môže poslúžiť študentom vysokých škôl aj vyučujúcim na stredných školách (matematický seminár) ako ukážka iného pohľadu na vyjadrovanie racionálnych čísel v pozičných číselných sústavách.

25.First steps in introducing cooperative learning - An experiment for the application of cooperative learning

Dr. Tünde Kántor PhD., Dr. András Kovács PhD.

The authors want to present a method of cooperative learning to promote understanding in mathematical problem solving. Cooperative learning is an alternative way of teaching. The Hungarian teachers of Grammar Schools rarely apply this method in mathematical problem solving. We made videotaped teaching experiments in three Grammar Schools with different grades of students (9-11). For our investigations we chose an applied extreme value problem, which the students could solve at different levels of know ledge. It was rich in solving methods, in applying different and various strategies. In our opinion the different solutions for the same problem should get an important place, it is a very good possibility to demonstrate the connections between different mathematical topics. We investigated how the students could find more solutions of the posed problem by cooperative learning. We made four hypotheses: successfulness, problem solving strategies, sex and free choice of small groups. The completion of the experiment confirmed some statements of didactical literature.

26.Viliam Chvál – prvý dekan PF KU a iniciátor konferencií Matematika v škole dnes a zajtra v Ružomberku

Doc. RNDr. Melichar Kopas CSc., Doc. RNDr. Roman Frič DrSc.

27.Václav Šimerka a počátky matematické analýzy v české školské matematice

RNDr. Alena Kopáčková PhD.

The attention is devoted to the beginning of calculus in Czech school mathematics. The interesting personality of Václav Šimerka is commemorated in the connection with teaching calculus. The first Czech textbook on calculus, Šimerka’s Appendix to Algebra from 1863 is mentioned here; the paper deals especially with the author’s approach to the concepts of differential and derivative.

28.Zajímavé typy zkoumání (vhodné i pro začátečníky)

Prof. RNDr. Jan Kopka CSc.

Investigative work is a suitable introduction to the art of problem solving. There are several types of investigations avalable for beginners (but not only for beginners): search for patterns, iterating a certain procedure, looking for exceptions and generalizing given problem. Every type is demonstrated with the help of a simple example.

29.Výchova geometriou

Mgr. Božena Koreňová

In this paper author tries to schow possibilities to apply and to develop creative thinking in study of geometry at primary school.

30.Prístup žiakov 2. a 4. ročníka ZŠ k difúznej úlohe

Mgr. Ivana Kovárová

This paper deals with mathematical examples for pupils in the primary school.

31.Szybsze i jednakowo szybkie serie sukcesów i porazek

Dr. Ireneusz Krech

Many factors have the influence on discovering and understanding mathematics, among others intuition. The abstraction and the schematics in teaching mathematics are being confronted with the vision and perceiving of general, essential ly important mathematical structures and the quantitative and spatial relations. Our common sense i.e. our intuition is the author of any ideas, statements or hypotheses, it is he inspiration, the beginning of any discovery and the clue delivering us confidence in reasoning o any type. In the work the examples of stochastic paradoxes are presented. These paradoxes are connected with special relations defined in a set of successes and failures series, that standing against our intuitions appear to be a mean of the mathematical activation.

32.Historical Aspects in Calculus Teaching

ao. Univ. Prof. Dr. Manfred Kronfellner

This paper offers a few examples how to integrate short historical facts into calculus teaching. One the one hand these supplements contribute to an appropriate image of mathematics as a developing science and as a part of our culture whereas on the other hand the time they require in classroom is negligible.

33.Harmonický priemer a jeho praktická aplikácia

Doc. Dr. Ladislav Kulčár CSc.

The paper deals with some properties of arithmetic and harmonic means and their mutual relations. Some examples of using them are presented to better understand this topic. It should help students and teachers of various levels of schools to use these mathematical and statistical terms properly in their practice.

34.Kombinatorika

PaedDr. Ján Kuruc

This article shows some examples about combinatorics for secondary school.

35.Refleksje na temat zadań probabilistycznych formułwanych przez studentów III roku matematyki

Dr. Maciej Major

This paper presents some remarks on understanding of probability by III year students before their starting learn theory of probability.

36.Magické štvorce vo vyučovaní matematiky

PaedDr. Anna Medvecká

Magic squares belong to the oldest mathematical amusements. A magic square is a square array of integers in which the numbers in rows, columns and diagonals have the same sums respectively. Magic squares have played various roles in the mathematics classroom: as a motivational device, as a problem – solving venture. The purpose of this paper is to present 4 problems that allow students to investigate magic squares, formulate their own conjectures about these mathematical objects, look for arguments and finally establish and prove mathematical assertions. Each problem is completed with student commentary and experience from classrooms.

37.Štatistika v školskej matematikem

Mgr. Jana Mihalčová

This paper deals with school statistics. The way of teaching this concept on secondary school from the year 1945 up to present days is presented here. Several interesting tasks with the purpose to enrich school lesson are included in this article.

38.Rok s korešpondenčným seminárom

Mgr. Emília Miťková

The aim of this paper is to point one kind of mathematical competition and inform about postal math seminar effectually held in Slovakia.

39.Problematika slovných úloh na stredných školách - analýza výsledkov výskumu

RNDr. Peter Molnár

Some results of a research, related to word problems, are presented and finally analyzed in this contribution. This research was performed at 4 high schools (of different types) in 2006 and 12 math teachers and 343 students of first classes participated in it. The main aim was to find out, what are students representations of the term word problem, what are students attitudes to word problems in comparison with other types of mathematical problems, what is the essential problem of students by solving a word problem and to identify some of sources of this problem.

40.Strategie rozwiązywania zadań nietypowych stosowane przez studentów pedagogiki

Dr. Barbara Nawolska

Uncommon mathematical problems play an imp ortant role in childrens’ education in mathematics. These exercises inspire creativity in children and help them develop a sense of divergent thinking. Pedagogics students, as future teachers, must not only recognize the value of such mathematical problems, but must also be able to solve them in a simple and understandable for younger pupils way. This article is a presentation of the skills of the students in this regard.

41.Interpretacja treści zadania tekstowego a jego rozwiązanie w pracach uczniów i studentów

Dr. Barbara Nawolska, Dr. Joanna Żądło

This article is an attempt to analyse how the understanding of a problem influences the solution.

42.Počítačom podporovaná výučba matematiky na 1. stupni ZŠ

Mgr. Marta Novosadová

In recent years modern information and communication technologies influence mathematics teaching more and more. Computer supported learning help teachers to fulfill teaching aims. Educational software makes learning more interesting and enables children to play and learn at the same time. The paper deals with software designed by the author of the paper, which was created as a part of the dissertation thesis and can be used in mathematics teaching at primary school.

43.Slovní úlohy a výchova ke zdravému životnímu stylu

PhDr. Jiřina Novotná, Roman Holoubek

The paper deals with the best approach to education in primary and secondary schools with the basic consideration that mathematic can touch children mind and can give them proposals how to oriented in the day live. The problems of health and ordinary civilizations problems as a fatness’ and stress caused by lifestyle are mirrored in the mathematical issues which must be solved with mathematical skill. Key consideration is that if the young minds have good information and good mind (mathematic leads to this with better speed then other subjects) our children do not need strict rolls.

44.Błędy i trudności w nauczaniu geometrii na poziomie elementarnym

Dr. Zbigniew Nowak

Teaching geometry on the basic level faces diffculties that seem to be overmastering. Mathematicians, who are essential ly competent, often can not relay their know ledge to little children. First classes educators, that are able to relay their know ledge to little children, make basic mistakes. The article is about some of the mistakes that are widely made by the teachers and the authors of the hand-books. Realizeing gaps in the teacher’s know ledge can lead to leaving off wrong heritage of teaching geometry, otherwise next generations of the teachers and their pupils wil l make the same mistakes and that is why their career will become more diffcult.

45.O rozumieniu pojęcia funkcji w szkole średniej

Mgr. Jadwiga Orłowska

The notion of a function plays a crucial role in teaching mathematics. Unfortunately, students have big problems with understanding this notion. It is very important to search permanently tools reducing these difficulties and make attempts to activate students in the participation of defining and understanding the notion of a ‘function’.

The method of a project, which I suggest for realizing the issues connected with the understanding the notion of a function allows to activate a student in a considerable degree. After the research conducted in one of the Rzeszów secondary school it was possible to form a conclusion that active approach to a subject is an effective impulse which motivates students to act in a creative way.

Such method contributes in general recognition and development of student’s communicative skills which perfectly harmonizes with the method of a project.

46.Príprava učiteľov matematiky v nových študijných programoch

Doc. RNDr. Edita Partová CSc, Mgr. Tibor Szabó

In the article there are presented some analyzes of programmes of study in mathematics teacher preparation from the viewpoint of international document in the field of reforms in higher education in Slovakia.

47.Znamenia zverokruhu v stochastike pre učiteľov

Prof. Dr. hab. Adam Płocki

We deal with mathematical activities related to teaching probability calculus classes.The activities are inspired by observations, creating of mathematical models, calculation, and interpretations.

48.Odkrywanie regularności a myślenie algebraiczne

Mgr. Marta Pytlak

The ability to discover regularity is a starting point for a child to understand mathematics. Regularities stimulate the way of thinking that goes beyond particular cases (thinking about general regularities). In this paper I present my research concerning algebraical thinking during the process of discovering the regularity. I show analyses of work of two boys: in what way verbal language influent on to algebraical thinking during solving the task which concern discovering the regularity.

49.Develop reductive argumentation with the help of didactic games

Dr. Tadeusz Ratusiński

Computer sometimes helps pupils with their homework. But usually at home is being used as “game machine”. Pupils usually use computer for entertainment. There are many kinds of computer games such as: strategies, RPG, simulations, arcades or adventures e.t.c.. Most of such games have nice music and awesome graphic so kids like them very much. But most of them also don’t teach mathematic. Maybe can we give kids such games which can teach them “solving math problem” with fun, not only at school, but also at home? In this paper I’ll try to show the example.

I would like to present our project – pack of educational games for PC. Each of the games is such prepared to be attractive for children, but is based on educational math’s games. It uses computer properties to make mathematic more fun. Pupils playing such game even don’t notice that they are teaching mathematic. Every kid naturally want to win the game. He want to bit second player, and to do this he must solve math problem – he must discover winning strategies.

50.Vyučovanie analytickej geometrie na gymnáziách a rozvíjanie kľúčových kompetencií žiaka

RNDr. Jozef Sekerák

Teaching of analytic geometry in grammar school belongs to difficult parts of high schools mathematics. The paper deals with this problem and problem with development of key competences of students. On the basis of survey we try to answer question: In such extent does education of analytic geometry in grammar school develop key competences of students? There are characterized aim and hypothesis, sample and subject, methodology and organization of the survey. In the final part of this paper the summarization of results and recommendations are presented.

51.Úlohy z diskrétnej matematiky

RNDr. Ingrid Semanišinová PhD.

In this paper, we show utilization of discrete mathematics problems in mathematical classroom. Selected problems il lustrated different student approaches and their solution. Reasons for inclusion of such problems are formulated in conclusion.

52.Dlaczego trudno jest się porozumieć z uczniem na lekcji matematyki

Jana Slezakova, Dr. Ewa Swoboda

The main aim of this paper is to illuminate some obstacles in mathematical discourse. One of the characteristic phenomena of class communication is misunderstanding. We will describe moments of mutual misunderstandings in communication between teacher and student during math. lessons.

53.Eulerovy zásluhy o reformu goniometrie

Mgr. Radka Smýkalová

Leonhard Euler was born in Basle in 1707, three hundred years ago. He expanded and completed al l areas of mathematical thinking as wel l as if they were new ly created.

Hereinafter we’l l only deal with one scientific branch. That discipline is goniometry, the area of mathematics, which deals with goniometric functions. Part of goniometry is also trigonometry, which attends to practical use of these functions in solving different exercises about triangles.

Before we wil l talk about Euler’s activities in mentioned discipline, we’d like to give a short view about his life.

54.Výuka funkcí na základních školách v ČR a Anglii

Mgr. Anna Šlégrová

The paper is focused on function education at secondary school in Czech republic and England. It deals with curriculum documents of each country and analyzes how it works with function in each year. The second part contains two examples from English and Czech math textbook.

55.Výučba kombinatoriky, pravdepodobnosti a matematickej štatistiky na základných, stredných a vysokých školách

RNDr. Lucia Švábová

This paper presents learning of combinatorics, probability and statistics for pupils and students in the primary, secondary, high school and university.

56.O definíciach - neformálne a formálne

RNDr. Zdeno Takáč PhD.

The paper deals with the definitions. There are described definitions from informal point of view at the beginning. And in the next part of article are definitions described from formal point of view - what does it mean to give definition in the mathematical theory.

57.Počtové operácie pomocou „Napier bones“

Doc. RNDr. Štefan Tkačik PhD.

58.Zabudneme na dôkazy?

RNDr. Magdaléna Tomanová

The paper is deals with importance of proofs in mathematics teaching for primary and high schools. We join some simple exercises that are useful for both types of schools.

59.Využitie interaktívnych excelovských zošitov vo vyučovaní funkcionálnej analýzy

PaedDr. Peter Vankúš PhD.

This paper is dealing with using of interactive excel spreadsheets in teaching of mathematics with focus on teaching of function graphs. We discuss construction of interactive excel spreadsheets by easy way without knowledge of programming and the process of using of these spreadsheets in teaching of influence of parameters change on graph of function.

60.People Maths: Active Learning of Mathematics without a textbook

BA (Hons) PGCE, FHEA Robert N. Vertes

Abstract

61.Mathematics Education and Teacher Education in England

BA (Hons) PGCE, FHEA Robert N. Vertes

62.Pokus o převod výukových technik z angličtiny do matematiky

Mgr. Pavla Zagorová

The paper tries to transfer some of the teaching techniques from teaching English to teaching Mathematics and gives some examples of this attempt.

63.Zásady tvorby matematickách problémů

RNDr. Jaroslav Zhouf PhD.

The paper deals with methods how to prepare problems for using them in written leaving exams for pupils talented in mathematics, in the mathematical olympiad and in correspondence seminars. It is compared which similar and on the contrary different characteristics these methods have to have in these three fields of study. There are shown examples of such problems as well.

64.Further sequenced problems for functional equations

Ádám Zsolt,Prof. Dr. Lajkó Károly

In this paper we will create a new sequence of problems for functional equations of type
H(f (x + y ), f (x − y ), f (x), f (y ), x, y ) = 0, where H is known function and f is the unknown function to be determined. Some possible ways of generalization are also given in this note.