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Group Work at High School According to the Method of Tamás Varga
167-176Views:224The aim of our research is to develop students’ logical thinking. For this reason, Hungarian mathematics teachers need to be encouraged to try new methods which induce greater student involvement. Research all over the world prove that self-instruction or self-verbalizing has high effect on the learning process. This was one of the key elements of Tamás Varga’s experiment in high school. In our classroom experiments we are using a special cooperative method from Kagan among 14-18 years old students, called Sage and Scribe structure. We are looking for the answers to the following question: Does this method make mathematics lessons more enjoyable and more comfortable for students? Furthermore, we assume this structure could open the gate toward other collaborative and cooperative teaching technics.
Subject Classification: 97D40
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A didactic analysis of merge sort
195-210Views:146Due to technical difficulties, educators teaching merge sort often avoid the analysis of the cost in the general and average cases. Using basic discrete mathematics, elementary real analysis and mathematical induction, we propose a self-contained derivation of bounds αn log_2 n + βn + γ in all cases. Independent of any programming language or pseudo-code, supported by intuitive figures, it is suitable for informatics students interested in the analysis of algorithms. It is also a good exercise in showing that induction allows us to actually discover constants, instead of simply checking them a posteriori. -
Combinatorics – competition – Excel
427-435Views:143In 2001 the Informatics Points Competition of the Mathematics Journal for Secondary School Students (KÖMAL) was restarted [1]. The editors set themselves an aim to make the formerly mere programming competition a bit more varied. Therefore, every month there has been published a spreadsheet problem, a part of which was related to combinatorics. This article is intended to discuss the above mentioned problems and the solutions given to them at competitions. We will prove that traditional mathematical and programming tasks can be solved with a system developed for application purposes when applying a different way of thinking. -
Young women's barriers to choose IT and methods to overcome them - A case study from Hungary
77-101Views:280Women's scarcity in the STEM, especially in the IT sector is pronouncedly evident. Young women are obstructed from entering and remaining in IT by a broad range of social, educational, and labor market factors. In our paper, we would like to analyze the main barriers girls face in choosing IT, while also proposing potential methods to help them overcome these obstacles. In the second part of the paper, we will present a case study to illustrate in detail how the combination of the above methods can be put into practice to address and tackle the complex set of barriers girls face. We will first introduce a Hungarian annual program, Girls' Day ("Lányok napja"), specifically aimed to promote STEM to girls, then we will present two specific events organized for the 2020 edition of the program and designed with the above principles in mind. The interactive presentation, exposing girls to female role models of the field in a gamified way, and a game development exercise, building Scratch programming skills, have attempted to provide young women both with positive perspectives and experiences in IT, which are instrumental in helping them to surmount entrenched obstacles and raise their interest in the field.
Subject Classification: 97P10, 97U30
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Task variations for backtrack
107-120Views:172This 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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Increasing the popularity and efficiency of distance education by old-new methods
211-228Views:161In our essay we aim to provide suggestions to develop distance education and we decisively focus on programmed education that is supported by e-learning environment. We both think that the shortage of programmed educational methods is causeless in Hungary's distance education. The widespread usage of info-communication devices and of the Internet makes the programmed educational methods (not as an exclusive method) possible to use in distance education together with e-learning environment. In our work we summarize the possible solutions and at the same time we also provide a case study, as an insight into our e-learning project (called Logical Programming) by Moodle. -
Applications of methods of descriptive geometry in solving ordinary geometric problems
103-115Views:91The importance of descriptive geometry is well-known in two fields. Spatial objects can be mapped bijectively onto a plane and then we can make constructions concerning the spatial objects. The other significance of descriptive geometry is that mathematical visual perception of objects in three-dimensional space can be improved by the aid of it. The topic of this paper is an unusual application of descriptive geometry. We may come across many geometric problems in mathematical competitions, in entrance examinations and in exercise books whose solution is expected in a classical way, however, the solution can be found more easily and many times more general than it is by the standard manner. We demonstrate some of these problems to encourage to use this geometric method. Understanding the solution requires very little knowledge of descriptive geometry, however, finding a solution needs to have some idea of descriptive geometry. -
A proposal for an IOI Syllabus
193-216Views:209The International Olympiad in Informatics (IOI) is the premier competition in computing science for secondary education. The competition problems are algorithmic in nature, but the IOI Regulations do not clearly define the scope of the competition. The international olympiads in physics, chemistry, and biology do have an official syllabus, whereas the International Mathematical Olympiad has made the deliberate decision not to have an official syllabus. We argue that the benefits of having an official IOI Syllabus outweigh the disadvantages. Guided by a set of general principles we present a proposal for an IOI Syllabus, divided into four main areas: mathematics, computing science, software engineering, and computer literacy. -
Concept systematization with concept maps in data modelling
149-166Views:136An important goal of concept learning is that students can allocate concepts in the hierarchical system of concepts. In the data modelling course, first, we supported concept systematization with worksheets in which the students had to fill in the blank hierarchical figures of classification of the concepts or blank Venn diagrams describing the relationships between concepts. The hierarchical systems, however, are somewhat restricted to the description of connections. The filling in Venn diagrams did not deliver the expected result, so our attention turned to concept maps. In this paper we introduce the concept maps we drew. Then we evaluate the results of concept mapping survey conducted among students. The survey was done in three courses. We compare the results of our survey with the result of an earlier concept systematising survey. -
The "Teaching Mathematics and Computer Science" Journal logo's mathematical background
55-65Views:63In the present contribution we give an elementary technology for drawing the geodesics, paracycles and hypercycles on the pseudosphere. -
Notes on the representational possibilities of projective quadrics in four dimensions
167-177Views:104The paper deals with hyper-quadrics in the real projective 4-space. According to [1] there exist 11 types of hypersurfaces of 2nd order, which can be represented by 'projective normal forms' with respect to a polar simplex as coordinate frame. By interpreting this frame as a Cartesian frame in the (projectively extended) Euclidean 4-space one will receive sort of Euclidean standard types of hyper-quadrics resp., hypersurfaces of 2nd order: the sphere as representative of hyper-ellipsoids, equilateral hyper-hyperboloids, and hyper-cones of revolution. It seems to be worthwhile to visualize the "typical" projective hyper-quadrics by means of descriptive geometry in the (projectively extended) Euclidean 4-space using Maurin's method [4] or the classical (skew) axonometric mapping of that 4-space into an image plane. -
Cultivating algorithmic thinking: an important issue for both technical and HUMAN sciences
107-116Views:141Algorithmic thinking is a valuable skill that all people should master. In this paper we propose a one-semester, algorithm-oriented computer science course for human science students. According to our experience such an initiative could succeed only if the next recipe is followed: interesting and practical content + exciting didactical methods + minimal programming. More explicitly, we suggest: (1) A special, simple, minimal, pseudo-code like imperative programming language that integrates a graphic library. (2) Interesting, practical and problem-oriented content with philosophical implications. (3) Exciting, human science related didactical methods including art-based, inter-cultural elements. -
E-learning management systems in Hungarian higher education
357-383Views:82Computers, informatics, and information technology have an ever-increasing role in the establishment and spread of new educational forms and methods. The role of e-learning as a new educational model is increasing in the world of computer networks, because of a widespread access to the net and a growing demand for learning beside work.
Technological elements of e-learning can be separated as Learning Management System, authoring system, course material and a browser. Learning Management System is the software package that creates the structure of the whole educational process: course organisation, course material presentation, tracking student work, recording results, and the completion of the program.
This publication shows examples of Learning Management Systems used in Hungarian higher education. Summarizing and systematizing expectations and demands expressed in connection with learning management systems, the present work tries to help the reader orientate on an ever-expanding market. -
How to use our own program evaluation system to streamline teaching computer programming
73-80Views:148During computer programming contests the use of automatic evaluation systems is becoming more and more frequent. In said systems the contestants are allowed to submit their source code that will be evaluated with the results reported back to them. According to this report the contestant can realise for what test cases his program works properly and for what cases does it fail. This kind of on-line evaluation system is used for example in the International Olympiad in Informatics (IOI), in the final round of the Nemes Tihamér National Programming Competition, and in the Selection Competition for IOI in Hungary. A contest management system can be used for other purposes apart from this singular example. A well-developed evaluation system can foster not only the teaching of computer programming and the preparation of students for programming contests but the teacher's work as well. -
Teaching agile operation and leadership through linked university courses
1-32Views:204Agile software development methods, especially Scrum, are commonly used in software development companies. For this reason, our goal was that our undergraduate students gain experience as Scrum development team members and our master's students as agile leaders. To this end, we had redesigned and linked an undergraduate and a master's course, and launched the new course in the spring of 2021. The success of our approach was confirmed by a questionnaire survey of 86 undergraduate and 27 master's students. A/B testing was also performed. Our approach is a novelty compared to solutions where the Scrum Master is a course member, an instructor, or a university employee. In addition to being resource-efficient, it also offers master's students an unparalleled opportunity to develop agile leadership skills.
Subject Classification: 97U50
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Frequency-based dynamic models for the analysis of English and Hungarian literary works and coursebooks for English as a second language
53-70Views:130We examined the characteristics of how word types are introduced in English and Hungarian literary works as well as in English coursebooks written for second language learners. By subdividing the texts into small segments of equal length, we were able to pinpoint subtle changes in the narrative. Based on the frequency of the word types in the original text a model was generated, and applying the model artificial texts were created. By comparing the original and the artificial texts, the places where these changes within the narrative occurred, could be located. Studying coursebooks we found that their vocabulary and how they introduce word types resembled those of randomly collected and concatenated short stories. According to our observations writers of the coursebooks forget that not only should the number of word types be carefully planned, but their repetition, in sufficient number, should also be cared for. -
Teaching word processing - the theory behind
119-137Views:157It is widely thought and believed that word processors – especially MS Word – are software, which everyone can use. However, if we take a closer look at the documents we find that the picture is not at all that clear. In most of these documents even the basic rules of word processing are broken. The question is how it is possible that most of the users are satisfied with their performance, and do not realize that they only use a less noisy typewriter, and not able to take advantage of the opportunities offered by these software. In the search of clearing this misunderstanding I found that there are no publicly available sources, which would clearly set the rules to determine when the documents are properly formatted. Here I set three maxims which, together, are able to control the tools applied in word processing in order to create properly formatted texts. In summary, they state that the layout of a properly formatted text should be invariant to modification, that is, any modification of the body of text should not initiate its re-formatting. To prove that these maxims work and to show that we desperately need them I give examples of works of professionals from the administration, of those who passed ecdl exams, of teachers of various subjects, and finally of teachers of Informatics. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2014 Eger, Hungary
117-134Views:142The meeting Researches in Didactics of Mathematics and Computer Sciences
was held in Eger, Hungary from the 24th to the 26th of January, 2014 at the
Eszterházy Károly College. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Eszterházy Károly College in Eger.
The 58 participants – including 43 lecturers and 18 PhD students – came from 7 countries, 15 cities and represented 22 institutions of higher education. -
Teaching reliability theory with the Computer Algebra System Maxima
45-75Views:145The use of the Computer Algebra System Maxima as a teaching aid in an MSc module in Reliability Theory is described here. Extracts from student handouts are used to show how the ideas in Reliability Theory are developed and how they are intertwined with their applications implemented in Maxima. Three themes from the lectures are used to illustrate this: (1) Normal Approximations, (2) Markov Modelling, (3) Laplace Transform Techniques.
It is argued that Maxima is a good tool for the task, since: it is fairly easy to learn & use; it is well documented; it has extensive facilities; it is available for any operating system; and, finally, it can be freely downloaded from the Web. Maxima proves to be a useful tool even for Reliability research for certain tasks. This latter feature provides a seamless link from teaching to research – an important feature in postgraduate education. -
Radio Frequency Identification from the viewpoint of students of computer science
241-250Views:119This paper aims at creating the right pedagogical attitudes in term of teaching a new technology, Radio Frequency Identification (RFID) by evaluating the social acceptance of this new method. Survey of future teachers, students of teacher master studies and students from informatics oriented secondary schools were surveyed comparing their attitudes in terms of RFID to other recent technologies. Consequences of this survey are incorporated into the curriculum of the new RFID course at our institution. -
Virtual worlds in education – best practice, design and research considerations
309-323Views:123The article briefly describes and characterizes the virtual worlds, different kinds of virtual worlds and possibilities of their use in education. The virtual worlds beyond the passive learning opportunities offer active, constructive and collaborative learning possibilities as well. In the middle section of this article we present the most common ways of different kinds of learning methods, which are illustrated by practical examples as well. In the final sections of the article we deal with the design research approach of 3D virtual worlds. -
CS unplugged in higher education
1-23Views:167Nowadays, there is a significant lack of workforce in the IT industry, even though it is one of the most lucrative professions. According to researchers' forecasts, the existing shortage is growing, so the wages offered will be higher, yet it seems that young people are not attracted to the profession. This problem draws attention to the need to change the curriculum so that it can attract students more. One possible solution is to supplement the curriculum with CS Unplugged activities, which makes it easier to understand and deepen difficult concepts and make IT lessons more colorful. In my article, besides presenting the already known CS Unplugged activities, I will deal with how this can be applied in Hungarian higher education as well. -
Mathematical gems of Debrecen old mathematical textbooks from the 16-18th centuries
73-110Views:91In the Great Library of the Debrecen Reformed College (Hungary) we find a lot of old mathematical textbooks. We present: Arithmetic of Debrecen (1577), Maróthi's Arithmetic (1743), Hatvani's introductio (1757), Karacs's Figurae Geometricae (1788), Segner's Anfangsgründe (1764) and Mayer's Mathematischer Atlas (1745). These old mathematical textbooks let us know facts about real life of the 16-18th centuries, the contemporary level of sciences, learning and teaching methods. They are rich sources of motivation in the teaching of mathematics. -
Linear clause generation by Tableaux and DAGs
109-118Views:136Clause generation is a preliminary step in theorem proving since most of the state-of-the-art theorem proving methods act on clause sets. Several clause generating algorithms are known. Most of them rewrite a formula according to well-known logical equivalences, thus they are quite complicated and produce not very understandable information on their functioning for humans. There are other methods that can be considered as ones based on tableaux, but only in propositional logic. In this paper, we propose a new method for clause generation in first-order logic. Since it inherits rules from analytic tableaux, analytic dual tableaux, and free-variable tableaux, this method is called clause generating tableaux (CGT). All of the known clause generating algorithms are exponential, so is CGT. However, by switching to directed acyclic graphs (DAGs) from trees, we propose a linear CGT method. Another advantageous feature is the detection of valid clauses only by the closing of CGT branches. Last but not least, CGT generates a graph as output, which is visual and easy-to-understand. Thus, CGT can also be used in teaching logic and theorem proving. -
Interdisciplinary Secondary-School Workshop: Physics and Statistics
179-194Views:152The paper describes a teaching unit of four hours with talented students aged 15-18. The workshop was designed as a problem-based sequence of tasks and was intended to deal with judging dice whether they are regular or loaded. We first introduced the students to the physics of free rotations of rigid bodies to develop the physics background of rolling dice. The highlight of this part was to recognise that cubes made from homogeneous material are the optimal form for six-sided objects leading to equal probabilities of the single faces. Experiments with all five regular bodies would lead to similar results; nevertheless, in our experiments we focused on regular cubes. This reinsures that the participants have their own experience with the context. Then, we studied rolling dice from the probabilistic point of view and – step-by-step – by extending tasks and simulations, we introduced the idea of the chi-squared test interactively with the students. The physics and the statistics part of the paper are largely independent and can be also be read separately. The success of the statistics part is best described by the fact that the students recognised that in some cases of loaded dice, it is easier to detect that property and in other cases one would need many data to make a decision with small error probabilities. A physical examination of the dice under inspection can lead to a quick and correct decision. Yet, such a physical check may fail for some reason. However, a statistical test will always lead to reasonable decision, but may require a large database. Furthermore, especially for smaller datasets, balancing the risk of different types of errors remains a key issue, which is a characteristic feature of statistical testing.
Subject Classification: F90, K90, M50, R30
