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A proposal for an IOI Syllabus
193-216Views:55The 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:40An 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:3In 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:12The 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. -
Teaching XML
317-335Views:31The author has been teaching XML at the Faculty of Informatics, University of Debrecen since the end of the nineties. This paper gives an overview of XML technology from an educators viewpoint that is based on the experience that the author has gained teaching XML over the years. A detailed description of the XML course is provided. Methodological issues are also discussed. -
Teaching model-based testing
1-17Views:1205Different testing methodologies should play an important role in the education of informatics. In the model-based testing (MBT) approach, the specification of the system is described with a formal model. This model can be used to revise the correctness of the specification and as a starting point for automatic test generation. The main problem with MBT is however, that there is a huge gap between theory and practice and that this approach has a high learning curve. To cope with these problems, current paper shows, how the MBT approach can be introduced to students through a small scale example.
Subject Classification: P50
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Metadata and education
325-343Views:36This 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. -
Methods of teaching programming
247-257Views:47Programming methodology is one of the oldest fields of IS education, and thus various methods have evolved for its teaching. While some of them could be used effectively in primary or secondary education, others are more suited for students in higher education. The methods themselves determine the structure and curricula of courses such as Programming methodology, Data types and algorithms, Programming technology. -
Teaching multiparadigm programming based on object-oriented experiences
171-182Views:25Multiparadigm programming is an emerging practice in computer technology. Co-existence of object-oriented, generic and functional techniques can better handle variability of projects. The present paper gives an overview of teaching multiparadigm programming approach through typical language concepts, tools in higher education. Students learning multiparadigm-oriented subjects would gain considerable expertise, which is highly needed by the industrial side in large-scale application development. -
Synthesis of concurrent programs
301-317Views:33Students need a well defined method to be successful in the complex process of writing a concurrent program. In this paper we show a step by step method to create such programs. The method based on UML which has been thought to students during previous courses. UML provides standard and relatively simple tools to describe concurrent systems, and from the description the program can be derived.
First we give a brief introduction to the concurrent systems. This is followed by the description of the method, and finally we demonstrate the method on a small problem. -
Numerical mathematics with GeoGebra in high school
363-378Views:41We have prepared a suite of motivational examples which illustrate numerical methods for equation solving. Fixed point iteration, Newton's method, secant method and regula falsi method are implemented as GeoGebra tools. Our experience in teaching of numerical mathematics in "Jovan Jovanovic Zmaj" high school in Novi Sad is presented. We have tested pupil proficiency in numerical equation solving with and without use of a computer and the results are presented. -
Linear clause generation by Tableaux and DAGs
109-118Views:31Clause 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:55The 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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Writing a textbook – as we do it
185-201Views:17Recent 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. -
Modelling and simulation in education and the NetLogo simulation environment
229-240Views:33Just 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. -
Teachers and the interactive whiteboards
281-298Views:27The spread of IWB (Interactive WhiteBoard) around the world changes, reforms and modernizes the traditional teaching methods. We can find these new ICT devices in more and more schools in Hungary as well and the use of it is getting widespread in everyday teaching. The teachers have the greatest role in the proper use of IWB during the lessons and they are also responsible for providing students with creative and motivating tasks lesson by lesson. In the following research, the advantages of the IWB are highlighted, the difficulties of its usage and the teachers' attitude towards the new ICT devices by asking 205 teachers from different primary and secondary schools. The results are mainly based on questionnaires. -
Equivalence and range of quadratic forms
123-129Views:10If two quadratic forms are equivalent, that is, if there is a linear transformation with integer coefficients and determinant 1 or −1 which takes one form to the other, then their ranges are the same and also their determinants are the same. The result of the paper is that for positive definite binary quadratic forms the converse is also true. Namely, if two positive definite binary quadratic forms of the same determinant have the same range, then they are equivalent. The arguments are guided by geometric considerations. -
Engineering and Economic Mathematics for Engineering Management Students
35-50Views:34In this article we describe the first part of a case study, which was made with 48 Engineering Management students. The participants of the case study were MSc level students at the Szent István University, Gödöllő. We looked for methods by which we can support the most important components of competence motivation and the development of mathematical and other key competences during the mathematics lessons and individual learning. Another goal of our research was to get reliable information about students learning methods and their awareness of self-efficacy, furthermore their achievement in the subject of Engineering and Economic Mathematics. Detailed assistance was provided for the students in the e-learning portal. Knowledge tests, questionnaire and personal interviews with the students were also used. As an example we introduce one of the knowledge tests connected with the first half of the course about linear programming and graph theory. We detail its didactical background and show the results of the students. -
Expressiveness of programming languages and environments: a comparative study
111-141Views:31In 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. -
Gaussian iteration of mean values and the existence of 2^(1/2)
35-42Views:33We propose a method for proving the existence of √2 and finding its approximate value in secondary education. -
The hyperbola and Geogebra in high-school instruction
277-285Views:35In 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. -
Let's learn database programming in an active way
213-228Views:22This paper introduces how I applied the "learning by doing" method in the education of advanced knowledge of database systems in Software Engineering BSc program. The first goal of my method is to enable the students to use the PL/SQL and SQL as a skill, namely they get a practical competence which can be immediately used in business. In the laboratory the students independently practise the material learnt on the lecture. They get feedback for all their activities from the teacher. A software system helps administer the solutions, automatically verifies the syntax of them and helps the teacher to evaluate them. The paper summarises the results of three semesters. In the last year I compared the active learning method with the traditional method. I asked the students in a voluntary survey about the active learning method. -
Analogous programming with a template class library
135-152Views:43In this paper, a template class library and its usage can be read. The classes of the library contain the C++ code of the algorithm of programming theorems. This library supports the implementation of the programs that are planned by analogous programming but the primary aim of its usage is to introduce the object-oriented programming style to show how a reusable code can be written with inheritances, overriding virtual methods, composition of objectcs and template parameters. -
Report of Conference XL. National Conference on Teaching Mathematics, Physics and Computer Science August 22-24, 2016 Székesfehérvár, Hungary
259-276Views:12The 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:43GeoGebra 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.