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Mathematical gems of Debrecen old mathematical textbooks from the 16-18th centuries
73-110Views:28In 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. -
Expressiveness of programming languages and environments: a comparative study
111-141Views:28In 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. -
Report of Conference XL. National Conference on Teaching Mathematics, Physics and Computer Science August 22-24, 2016 Székesfehérvár, Hungary
259-276Views:7The XL. National Conference on Teaching Mathematics, Physics and Computer Sciences (MAFIOK) was held in Székesfehérvár, Hungary between 22 and 24 August, 2016 at the Alba Regia Technical Faculty of Óbuda University. For the three-day event, more than 80 persons were registered and more than 40 lectures were given. The fortieth anniversary scientific conference was designed for researchers and teachers in mathematics, physics and informatics to promote modern and efficient education in higher education, and through poster presentations and personal meetings to exchange experience. The opening ceremony of the conference followed by the three plenary lectures took place at the ceremonial hall of the Town Hall. ... -
GeoGebra in mathematics teaching
101-110Views:41GeoGebra is a dynamic mathematics software which combines dynamic geometry and computer algebra systems into an easy-to-use package. Its marvel lies in the fact that it offers both the geometrical and algebraic representation of each mathematical object (points, lines etc.). The present article gives a sample of the potential uses of GeoGebra for mathematics teaching in secondary schools. -
Writing a textbook – as we do it
185-201Views:13Recent surveys studying mathematics teaching show that there is a great variety in the level of mathematics teaching in Hungary. To increase efficiency (and decrease differences between schools) it is essential to create textbooks with new attitudes. The experiment we started after the PISA survey of 2000, produced a textbook that is new, in some sense even unusual in its attitude and methods. This paper presents the experiences we gained in the course of this work. -
Cultivating algorithmic thinking: an important issue for both technical and HUMAN sciences
107-116Views:23Algorithmic 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. -
Radio Frequency Identification from the viewpoint of students of computer science
241-250Views:7This 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. -
Linear clause generation by Tableaux and DAGs
109-118Views:24Clause 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. -
"Frontier algorithms"
139-152Views:20In this paper we present a new method to compare algorithm design strategies. As in case of frontier towns the cultures blend, the so called "frontier algorithms" are a mixture of different programming techniques like greedy, backtracking, divide and conquer, dynamic programming. In case of some of them the frontier character is hidden, so it has to be discovered. There are algorithms that combine different techniques purposively. Furthermore, determining the programming technique the algorithm is using can be a matter of point of view. The frontier algorithms represent special opportunities to highlight particular characteristics of the algorithm design strategies. According to our experience the frontier algorithms fit best to the revision classes. -
The influence of computer on examining trigonometric functions
111-123Views:22In this paper the influence of computer on examining trigonometric functions was analyzed throughout the results questionnaire. The students, as usual, had to examine two trigonometric functions, both were given with the appropriate instructions. Three groups were tested. Two of those three groups were prepared with the help of computer and the third one was taught without computer. From the analysis of the questionnaire it follows that the computer has a great influence on understanding of the connections between the graph and very complex calculations. -
Teaching word processing - the theory behind
119-137Views:12It 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. -
Interdisciplinary Secondary-School Workshop: Physics and Statistics
179-194Views:53The 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
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The hyperbola and Geogebra in high-school instruction
277-285Views:30In this article the results of teaching/learning hyperbola and its characteristics in high-school using computers and GeoGebra are shown. Students involved in the research attend Engineering School "Nikola Tesla" in Leposavic, Serbia. The aim of the research was to define ways and volume of computer and GeoGebra usage in mathematics instruction in order to increase significantly students' mathematical knowledge and skills.