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Difference lists in Prolog
73-87Views:164Prolog is taught at Bradford University within the two-semester module Symbolic and Declarative Computing/Artificial Intelligence. Second year undergraduate students are taught here the basics of the functional and the logic programming paradigms, the latter by using the Linux implementation of SWI Prolog [6]. The topic 'Difference lists' is mentioned in traditional textbooks such as [2] and [5] but it was felt that the available texts do not quite serve our purposes. We present here a lecture handout and a laboratory sheet for the teaching sessions on Difference lists. It is believed that the lectures and lab sessions together with the handouts shown here are a gentle, self-contained and reasoned introduction into the topic. The figures here shown to illustrate the concepts are considered a special feature of the handouts which in this form do not seem to be well known. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2020 Sárospatak, Hungary
243-271Views:242The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Sárospatak, Hungary, on the Comenius Campus of the Eszterházy Károly University, from the 24th to the 26th of February, 2020. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen and the Eszterházy Károly University. The 76 participants – including 15 PhD students – came from 9 countries, 23 cities and represented 33 institutions of higher and secondary education. There were 4 plenary, 48 session talks and 4 poster presentations in the program.
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Probabilistic thinking, characteristic features
13-36Views:129This paper is the first step in a series of a general research project on possible development in probability approach. Our goal is to check with quantitative methods how correct our presumptions formulated during our teaching experience were. In order to get an answer to this question, we conducted a survey among third-year students at our college about their general and scientific concepts as well as about the way they typically think. -
Compositions of dilations and isometries in calculator-based dynamic geometry
257-266Views:129In an exploratory study pre-service elementary school teachers constructed dilations and isometries for figures drawn and transformed using dynamic geometry on calculators. Observational and self assessments of the constructed images showed that the future teachers developed high levels of confidence in their abilities to construct compositions of the geometric transformations. Scores on follow-up assessment items indicated that the prospective teachers' levels of expertise corresponded to their levels of confidence. Conclusions indicated that dynamic geometry on the calculator was an appropriate technology, but one that required careful planning, to develop these future teachers' expertise with the compositions. -
The mathematics textbook as an aid to differentiation: a first Hungarian example
35-53Views:108Differentiation is a way of teaching where each student is taught according to his/her personal needs. This technique is not widely used in Hungary yet, although this would be necessary due to the introduction of the two-level final examination and to a growing concern for equal opportunities and integrated teaching. One of the most significant aids to differentiation is an appropriate textbook, and that is why a group of professionals wrote a set of textbooks that supports this technique. The paper examines the requirements for a differentiated textbook, and the extent to which the textbook in question meets them. -
Bernd Zimmermann (1946-2018)
155-159Views:159Our great friend, the always helpful supporter of the Hungarian mathematics didactics, Bernd Zimmermann, the retired mathematics didactics professor of Friedrich Schiller University of Jena, passed away on 19th of July 2018. After a short chronology of his life, we remember some of the many areas of his work with strong Hungarian connections. -
Teaching probability theory by using a web based assessment system together with computer algebra
81-95Views:153In the course of Maths Basics 2, the Faculty of Economic Science students of Kaposvár University learn the classical chapters of Probability Theory, namely random variables and the well-known probability distributions. Our teaching experiences show that students' achievement is weaker in case of problems concerning continuous random variables. From school year 2012/13 we have had an opportunity to take Maple TA, the web-based test- and assessment system, into the course of education. It is sufficient for the users of Maple TA to have a browser. Maple computer algebra system, which runs on the server, assesses students' answers in an intelligent way, and compares them with the answers that are considered correct by the teacher. In our presentation we introduce some elements of Maple TA system, the didactic considerations the test sheets were made by, as well as our research results concerning the use of Maple TA. -
Expressiveness of programming languages and environments: a comparative study
111-141Views:162In written and oral communication tools, the support of the understanding of our message have an important role: we can increase the expressiveness and the level of understanding of our topic by approaching it in several ways, i.e. in written methods by highlighting the important parts; in oral by changing tone and other elements of non-verbal communication. In this paper programming languages and developing environments are compared with each other in terms of their methods and their level of support to the solution of programming tasks.
There is a need to have these tools in programming and, of course, in teaching programming. What are the factors that define the distinctness and the legibility of a program? What are the basic principles which give an instrument in programmers' and students' hands in order to create a properly working program from already existing algorithms in the most efficient way? We search for the answers to these questions in this paper. -
The mathematics teacher trainee as an assistant teacher
295-306Views:148The 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. -
Pólya’s influence on (my) research
161-171Views:273In this article, I outline the influence of George Pólya's work on research in different areas and especially on mathematics education, namely heuristics and models of the problem-solving process. On a more personal note, I will go into some details regarding Pólya's influence on my own work in mathematical problem solving with a focus on the research project for my PhD thesis.
Subject Classification: 97xxx
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Report of conference XXXVIII. National Conference on Teaching Mathematics, Physics and Computer Sciences: August 25-27, 2014 Pécs, Hungary
281-303Views:143The XXXVIII. National Conference on Teaching Mathematics, Physics and Computer Sciences (MAFIOK) was held in Pécs, Hungary between 25 and 27 August, 2014 at the Pollack Mihály Faculty of Engineering and Information Technology. It was organized by the Engineering Mathematics Department. The 65 participants – including 4 invited lecturers and 53 lecturers – came from 2 countries and represented 14 institutions of higher education. -
Dressed up problems - the danger of picking the inappropriate dress
77-94Views:225Modelling and dressed-up problems play an inevitably unavoidable role in mathematics education. In this study we would like to point out how dangerous is it to dress up mathematical problems. We go back to the principle of De Lange: The problem designer is not only dressing up the problem, but he is the solution designer, as well. We show three examples selected from Hungarian high school textbooks where the intended solution does not solve the problem, because the dressing changes the context and changes the problem itself. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 25-27, 2013 Oradea, Romania
123-143Views:164The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Oradea, Romania from the 25th to the 27th of January, 2013 at the Partium Christian University. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Partium Christian University in Oradea. The meeting was supported by the project: TAMOP-4.2.2/B/10/1-2010-0024.
The 61 participants – including 50 lecturers and 21 PhD students – came from 5 countries, 22 cities and represented 35 intstitutions of higher education. -
Sequenced problems for functional equations
179-192Views:140There are many possible methods to solve equations of the form H(f(x + y), f(x − y), f(x), f(y), x, y) = 0 (x, y 2 R), where H is a known function and f is the unknown function to be determined. Here we will create a sequence of problems for equations of type (1) (see on the next page). These sequenced problems are appropriate for the fostering of talented students on different level of mathematical education. -
Forming the concept of congruence II.
1-12Views:148This paper is a continuation of the article Forming the concept of congruence I., where I gave theoretical background to the topic, description of the traditional method of representing the isometries of the plane with its effect on the evolution of congruence concept.
In this paper I describe a new method of representing the isometries of the plane. This method is closer to the abstract idea of 3-dimensional motion. The planar isometries are considered as restrictions of 3-dimensional motions and these are represented with free translocations given by flags.
About the terminology: I use some important concepts connected to teaching of congruence, which have to be distinguished. My goal is to analyse different teaching methods of the 2-dimensional congruencies. I use the term 3-dimensional motion for the orientation preserving (direct) 3-dimensional isometry (which is also called rigid motion or rigid body move). When referring the concrete manipulative representation of the planar congruencies I will use the term translocation. -
Über den Vergleich des mathematischen bzw. mathematikdidaktischen Vektorbegriffs durch den Galois-Graphen
1-12Views:158In this article we show how to apply the method of Galois-graph – one of the means of the formal concept-analysis in order to coordinate the mathematical and didactical requirements. As an example we have chosen the concept of the "vector". As a result of the analysis it is proved that, in elaborating the right vector concept the geometric and algebraic foundations are both needed. The analysis also points out that the geometric model, based on the concept of the "directed segment" is unnecessarily overemphasized in the East-European education. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 26-28, 2018 Hajdúszoboszló, Hungary
131-153Views:175The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Hajdúszoboszló, Hungary from the 26th to the 28th of January, 2018. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen.
The 61 participants – including 47 lectures and 17 PhD students – came from 8 countries, 21 cities and represented 37 institutions of higher and secondary education. -
Central axonometry in engineer training and engineering practice
17-28Views:147This paper is concerned with showing a unified approach for teaching central and parallel projections of the space to the plane giving special emphasis to engineer training. The basis for unification is provided by the analogies between central axonometry and parallel axonometry. Since the concept of central axonometry is not widely known in engineering practice it is necessary to introduce it during the education phase. When teaching axonometries dynamic geometry software can also be used in an interactive way. We shall provide a method to demonstrate the basic constructions of various axonometries and use these computer applications to highlight their similarities. Our paper sheds light on the advantages of a unified approach in such areas of engineering practice as making hand drawn plans and using CAD-systems. -
Information System’s experiences of EGERFOOD project making use of it in the education of the database management
197-210Views:138We present in this article the background of a developed food safety tracking system searched and formed in the Regional Knowledge Centre of Eszterházy Károly College, the requirements following from this, and by way of the requirements towards the information system appearing expectations. The development of the consumer centre system is a complex task which provides fast and cost-effective information for consumers, food producers and concerned authorities. It accomplishes severe expectations of the tracking system in connection with data security and encryption beside all this. We demonstrate in this article that forming of database model why we chose the general model. We also demonstrate what kind of SQL server we chose for buffer servers and central data warehouse. We wish to support our choosing with the result of done efficiency examinations. It is important viewpoint what kind of database planning principles we base these examinations on and how we match them to the requirements of the system. As software engineers took part in the development effectively from the first minute of the planning of the system, we can examine with what this project work was able to raise students' qualification and knowledge in addition to the general curricular substance. -
The use of e-tests in education as a tool for retrieval practice and motivation
59-76Views:275In many studies we can read about what techniques are used in the educational process to deepen knowledge, and what can motivate students to learn. We aimed to give our students (who will be a teacher) a practical demonstration of learning techniques. We carried it within the framework of a course, at the end of which we also examined how much it motivates students if they write an e-test as a retrospective in order to deepen the material of the lesson. In the paper, we will present the results of the research as well as students’ opinions regarding the motivating effect of the tests.
Subject Classification: 97-01, 97D40, 97I10
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Task variations for backtrack
107-120Views:198This article has been written for informatics teachers who want to issue back-track based tasks on their lessons or as homework or on competitions. We present a few methods to generate a more complicated problem from a simpler task, which will be more complex, and its solution needs a good idea or trick. Starting from an example, we lead the reader through increasingly di cult task variations.
Subject Classification: 97P50
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Fehleranalyse beim Lösen von offenen Aufgaben Ergebnisse einer empirischen Studie in der Grundschule
83-113Views:206Open problems play a key role in mathematics education, also in primary school. However, children in primary school work in many relations in a different way from learner in secondary school. Therefore, the (possibly) first confrontation with an open task could be problematical. Within the framework of an international paper and pencil test it was examined how far children of primary school notice the openness of a task and which mistakes they do during working on that task. In particularly are meant by openness different interpretations of the task, which all lead to a set of numbers with more than one element as a result. For evaluation, a common classification system was adapted by slightly modification of the original system. -
Metadata and education
325-343Views:157This article is a (possible) conceptual educational model, which introduces data representation, information storage and retrieval possibilities on the Web in a way analogous to the levels of organization of metadata.
The model uses the traditional library and information systems as a starting point, referring to the levels and types of information organization, and describes directions of its development. General acquaintance with the dominant organizational levels and types helps to understand the information organization on the internet, the coexistence of both structured and unstructured elements, the closedness and deficiencies of the content of information, and also helps to find possible ways of correcting these deficiencies. One of the main advantages of model-driven approaches is that they, by using the well-known classical systems, make tangible the development of physical and content data organization types and levels of organization of information for medical students that usually do not possess informatics knowledge.
The conceptual model presented in details in the article can provide a basis for a general introduction to metadata and to develop curricula equally appropriate for traditional face to face classes, trainings and online courses. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences, April 1-3, 2022 Baja, Hungary
135-155Views:295The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Baja, Hungary, at Eötvös József College, from the 1st to the 3th of April, 2022. It was organized by the Doctoral School of Mathematical and Computational Sciences of the University of Debrecen and by Eötvös József College. The 62 participants - including 18 PhD students - came from 8 countries and represented 26 institutions of higher and secondary education. There were 3 plenary and 40 session talks in the program.
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Modelling and simulation in education and the NetLogo simulation environment
229-240Views:178Just like real experimentation, computer simulation is a method for understanding the world. In the present paper I will demonstrate its possible didactic advantages and application potentials. The displayed simulations, which will be analyzed in a separate section, were all made in the NetLogo environment, one of them by the author himself.
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