Teaching Mathematics and Computer Science (DE-journals)
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Tétel Szabadon hozzáférhető Why is the gamma function so as it is?(2003-06-01) Gronau, DetlefThis is a historical note on the gamma function Γ. The question is, why is Γ(n) for naturals n equal to (n−1)! and not equal to n! (the factorial function n! = 1·2 · · · n) ? Was A. M. Legendre responsible for this transformation, or was it L. Euler? And, who was the first who gave a representation of the so called Euler gamma function?Tétel Szabadon hozzáférhető unity of mathematics(2003-06-01) Hilton, Peter; Pedersen, JeanWe give a sustained example, drawn largely from earlier publications, of how we may freely pursue a line of mathematical enquiry if we are not constrained, unnaturally, to confine ourselves to a single mathematical subdiscipline; and we draw conclusions from the study of this example which are relevant at many levels of mathematical instruction. We also include the statement and proof of a new result (Theorem 4.1) in linear algebra which is obviously fundamental to the geometrical investigation which constitutes the leit-motif of the paper.Tétel Szabadon hozzáférhető Gaussian iteration of mean values and the existence of 2^(1/2)(2003-06-01) Daróczy, ZoltánWe propose a method for proving the existence of √2 and finding its approximate value in secondary education.Tétel Szabadon hozzáférhető Rotation mentale et ordinateur(2004-06-01) , MáriaP. H. Maier, en se basant sur des recherches psychologiques, distingue cinq éléments d'intelligence spatiale. Dans cet article nous étudions comment l'ordinateur peut intervenir dans le développement de l'élément rotation mentale. Nous avons écrit des logiciels qui utilisent les rétroactions perspectives et nous avons effectué des expériences avec cinq groupes d'éleves. Pour pouvoir poursuivre le travail et le développement de travail de chaque éleve et pour faciliter l'examen des résultats, les tests sont au format HTML et les réponses des éleves ont été traitées par un serveur central. La statistique montre que les résultats des éleves s'améliorent au fur et a mesure.Tétel Szabadon hozzáférhető Using the computer to visualise graph-oriented problems(2004-06-01) Gyöngyösi, ErikaThe computer, if used more effectively, could bring advances that would improve mathematical education dramatically, not least with its ability to calculate quickly and display moving graphics. There is a gap between research results of the enthusiastic innovators in the field of information technology and the current weak integration of the use of computers into mathematics teaching. This paper examines what exactly the real potentials of using some mathematics computer software are to support mathematics teaching and learning in graph-oriented problems, more specifically we try to estimate the value added impact of computer use in the mathematics learning process. While electronic computation has been used by mathematicians for five decades, it has been in the hands of teachers and learners for at most three decades but the real breakthrough of decentralised and personalised micro-computer-based computing has been widely available for less than two decades. And it is the latter facility that has brought the greatest promise for computers in mathematics education. That computational aids overall do a better job of holding students' mathematical interest and challenging them to use their intellectual power to mathematical achievement than do traditional static media is unquestionable. The real question needing investigation concerns the circumstances where each is appropriate. A case study enabled a specification of advantages and obstacles of using computers in graph-oriented questions. Individual students' interviews revealed two less able students' reactions, difficulties and misinterpretations while using computers in mathematics learning. Among research outcomes is that the mathematical achievement of the two students observed improved and this makes teaching with computers an overriding priority for each defined teaching method. This paper may not have been realised without the valuable help of the Hungarian Eötvös State Grant.Tétel Szabadon hozzáférhető Illustrated analysis of Rule of Four using Maple(2003-12-01) Maróti, GyörgyRule of Four, as a basic didactic principle, was formulated among the NCTM 2000 standards (see [14]) and since then it is quoted by numerous books and publications (see [4], [9], [12]). Practically we can say it is accepted by the community of didactic experts. The usage of the Rule of Four, however, has been realized mainly in the field of calculus, in fact certain authors restrict the wording of the principle to the calculus itself (e.g. [3]). Calculus is a pleasant field, indeed. A sequence of values of a function provides us with example for numeric representation, while the formula and the graph of the function illustrate symbolic and graphical representations, respectively. In the end by wording the basic features of the function on natural language we gain textual representation. This idyllic scene, however, becomes more complex when we leave the frame of calculus. In this paper we investigate the consequences of the usage of Rule of Four outside calculus. We discuss the different types of representations and show several examples which make the multiple features of representation evident. The examples are from different fields of mathematics and are created by the computer algebra system Maple, which turns out to be an excellent tool for illustration and visualization of the maim features of mathematical objects. Next we introduce the concept of basic representation and rational representation, which is considered as the mathematical notion of "didactic usable" or "didactic rational" representation. In the end we generalize the notion of numeric representation, which leads us a more widely usable didactic principle which can be considered as a generalization of Rule of Four.Tétel Szabadon hozzáférhető Interactive web portals in mathematics(2003-12-01) Vajda, Róbert; Kovács, ZoltánMany of the recent problems in higher education (less contact seminars, the heterogeneity and the increasing number of our students) call for new instructional methods. At University of Szeged we have developed a mathematical web portal which can offer a solution for such problems among the changing circumstances. This freely available, easy-to-use web-surface supports interactive mathematical problem-solving and student self assessment. Our computer program cooperates with a lot of free software (computer algebra systems, formula parsers, converters, word processors). WebMathematics Interactive has been available for the public since June 2002 on its web page http://wmi.math.u-szeged.hu.Tétel Szabadon hozzáférhető Experiences using CAS and multimedia int teaching vectorcalculus(2003-12-01) Perjési-Hámori, IldikóThe development of informatics brings new opportunities that need reevaluating of the teaching concepts. For this reason we have performed a comprehensive educational development for engineering students. Our main goals were to work out a new educational strategy, to develop the needed package of the subject material, to introduce the strategy in the practice, to analyze and evaluate the experiences. In the developed and adapted teaching-learning strategy the teacher is the organizer, designer and the manager of the process. In this paper we summarize the concepts, the results and experiences of the 3-years-long development.Tétel Szabadon hozzáférhető Problem-solving in mathematics with the help of computers(2003-12-01) Kovács, AndrásOne of the most important tasks of the didactics of mathematics is the describing of the process of problem-solving activity and problem-solving thinking. The psychological theories concerning the problem-solving thinking leave the special demand of school subjects out of consideration, and search for connections of universal validity. In this article we attempt to connect an abstract theory of psychology concerning problem-solving thinking and a more practical conception of the problem-solving activity of mathematics, which is based on Polya's idea. In this way we can get a structure of problem-solving, which has scientific bases and at the same time it is useful in computer aided learning. Our result was developed and tested in Hungary so this is suitable especially for the Hungarian conditions of mathematics teaching.Tétel Szabadon hozzáférhető Models of impulsive phenomena(2003-12-01) Karsai, János"Take the textbook to computer" – is said quite often. Would it be so easy? If we start such a work, we meet a lot of trouble very soon. A book stored on a CD, read on the screen of computer and containing some hyperlinks does not become automatically electronic textbook. There are difficulties also in writing merely an electronic attachment to a classical book. In this paper, we deal with some important features (actually important from our point of view) of interactive mathematics textbooks, arising mathematical, didactical and technical problems. The "principles" are illustrated with examples taken from the book-CD "Models of Impulsive Phenomena".Tétel Szabadon hozzáférhető Dynamic methods in teaching geometry at different levels(2004-06-01) Árki, Tamás; Krisztin Német, IstvánIn this paper we summarize and illustrate our experiences on DGS-aided teaching geometry of the courses "Computer in mathematics" and "Mathematical software" held for students at Juhász Gyula Teacher Training College of University of Szeged. Furthermore, we show examples from our grammar school experiences too. The figures in this paper were made by using Cinderella ([19]) and Euklides ([21]).Tétel Szabadon hozzáférhető Figures to the article "Assimilation of mathematical knowledge using Maple" on pages 321-331. (color plate)(2003-12-01) Kovács, Zoltán; Kozma, LászlóColor plateTétel Szabadon hozzáférhető Proof without words(2005-12-01) Plaza, ÁngelTheorem. Let O, P and Q be three points on a line, with P lying between O and Q. Semicircles are drawn on the same side of the line with diameters OP, PQ and OQ. An arbelos is the figure bounded by these three semicircles. Draw the perpendicular…Tétel Szabadon hozzáférhető Research on IT language use at a company(2005-12-01) Juhász, Attila KálmánThe aim of the research of the IT language, used in the written documents of a company, is to contribute to the creation of a (mono- or bilingual) dictionary or encyclopaedia available for the public on the Internet, serving, among others, as a reference tool for the unified, controlled and unambiguous use of IT terms for students at various educational levels. To this ongoing work, the participation and cooperation of a panel of experts of different competences, linguists as well as IT experts, is indispensable. The methods of corpus linguistics were used to carry out the research. The IT terms were separated from the texts and then a concordance software was used to see the environment of the IT words and phrases in which they occur. So their morphological analysis became possible. The results of the research showed that a great number of Hungarian morphological language use problems stem from the way the IT terms are used in the documents. This paper lists, groups, analyses these phenomena. The conclusions of the author are: (1) If such an Internet dictionary is used generally and consulted when e.g. somebody wants to write a composition or essay, translate an article, write a newspaper article, a scientific publication or a textbook to be taught at schools of different types and levels, etc. most of the communication noises could be filtered out. (2) At the same time it could promote the use of adequate (both in linguistic and technical meaning) Hungarian terms eliminating the "Hunglish" usage. (3) It could also contribute to the prevailing use of the relevant Hungarian terminology. Such a dictionary would be indispensable, not only in educational and industrial environments but in the electronic and traditional media as well. Last but not least, it could raise the level of different teaching materials (textbooks, e-materials, etc.) used in public and higher education.Tétel Szabadon hozzáférhető Project Method and investigation in school mathematics(2005-12-01) Ujháziová, Renáta; Kopka, Ján; Šveda, Dušan; Frobisher, LeonardThe Project Method (PM) is becoming more common in the teaching of mathematics. Most of the time, Project Method means solving open and relatively wide formulated problems for the application of particular mathematical topics and the solving of everyday life problems. At present many experts in the theory of teaching mathematics advocate teaching activities as the characteristic for most mathematical work in the classroom. Thus, there is a question: whether it is possible or eventual desirable to use the PM for solving genuine mathematical problems. This paper deals with this question and discusses the connection between the PM and investigation of new mathematical knowledge for students. Our experience has shown that the PM in connection with investigations can be a useful and effective approach to teaching mathematics.Tétel Szabadon hozzáférhető "Upperview" algorithm design in teaching computer science in high schools(2005-12-01) Kátai, ZoltánIn this paper we are going to present a teaching/learning method and suggest a syllabus that help the high school students look at the algorithm design strategies from a so called "upperview": greedy, backtracking, divide and conquer, dynamic programming. The goal of the suggested syllabus is, beyond the presentation of the techniques, to offer the students a view that reveals them the basic and even the slight principal differences and similarities between the strategies. In consensus with the Comenius principle this is essential, if we want to master this field of programming ("To teach means scarcely anything more than to show how things differ from one another in their different purposes, forms, and origins. ... Therefore, he who differentiates well teaches well.").Tétel Szabadon hozzáférhető Informatics as a particular field of education(2005-12-01) Szlávi, Péter; Zsakó, LászlóInformatics education can be discussed at various levels. There is informatics education at the university, there is professional informatics training and there is public informatics education. In the following article we are going to deal with the latter, that is we are going to discuss what areas of informatics should be introduced to students within the frame of the informatics subject in primary and secondary education. Knowledge in connection with informatics can be grouped from different points of view. We consider the following points to be acceptable: according to scopes of knowledge. [1, 2]Tétel Szabadon hozzáférhető geometrische Interpretation der Ausgleichsrechnung(2005-12-01) , AndreasUsing real examples of applied mathematics in upper secondary school one has do deal with inaccurate measures. This will lead to over constrained systems of linear equations. This paper shows an instructive approach which uses methods of descriptive and computer aided geometry to get a deeper insight into the area of calculus of observations. Using a qualified interpretation one can solve problems of calculus of observations with elementary construction techniques of descriptive geometry, independent of the norm one uses.Tétel Szabadon hozzáférhető Fuzzy Datalog with background knowledge(2005-12-01) Achs, ÁgnesIn this paper we give a possible model for handling uncertain information. The concept of fuzzy knowledge-base will be defined as a triplet of a background knowledge defined by the similarity of predicates and terms; a deduction mechanism: a fuzzy Datalog program, and a decoding set of the program, which help us to determine the uncertainty level of the results.Tétel Szabadon hozzáférhető mathematics teacher trainee as an assistant teacher(2005-12-01) Szász, RékaThe experiment described in the article aims to answer two needs at once: that of assistant teachers in schools, and that of a more practical training of mathematics teachers. The answer suggested is a model of school experience where mathematics teacher trainees work as assistant teachers in schools. An attempt to realize this model is described, and it is evaluated positively.