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Concept systematization with concept maps in data modelling
149-166Views:182An 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. -
Report on the "English Language Section of Varga Tamás Days 2009"
169-175Views:171The 9th English Language Section as a part of the Varga Tamás Days was organised by the Department of Mathematics Education at the Teacher Training Institute of the Eötvös Loránd University. We report on the talks and the following discussions in this section. -
Teaching word processing – the practice
247-262Views:206I compared two surveys, which were aimed to check the word processing ability of students in high schools and universities. The surveys were carried out ten years apart from one another, in 1997 and 2006. The results clearly show that most of the students are not able to use word processors properly. In the survey of 1997 I found explanation for this underperformance in the lack of computers and teachers. However, the results of the second survey did not prove any better than the results of the first, and in 2006 neither the number of computers nor the number of teachers can be blamed. What else then? I suggest that the reason for this general ignorance, for this `modern illiteracy' is the ignorance of the teachers. Until the teachers are not prepared and the senior students of the universities leave the education system without a proper knowledge of the required subjects, there is little chance that they would be able to teach word processing at a satisfactory level. -
Report on INFODIDACT 2008 - the First National Conference on Didactics of Informatics: 11-12 April, 2008, Szombathely, Hungary
1-2Views:127Acquiring a PhD in any subject has been possible only in the last twentish years in Hungary. To take degree in didactics, especially didactics of informatics is still very difficult. There are not enough forums for the PhD students where they could report of their research work and results. -
The investigation of students' skills in the process of function concept creation
249-266Views:218Function is a basic concept of mathematics, in particular, mathematical analysis. After an analysis of the function concept development process, I propose a model of rule following and rule recognition skills development that combines features of the van Hiele levels and the levels of language about function [11]. Using this model I investigate students' rule following and rule recognition skills from the viewpoint of the preparation for the function concept of sixth grade students (12-13 years old) in the Ukrainian and Hungarian education system. -
Katalin Juhász (1952-2012)
1-2Views:138Katalin Juhász was born in 1952, in Tarnaméra (Hungary), where she also completed her primary school studies. She finished Erzsébet Szilágyi Highschool, Eger, in 1971 and she graduated in mathematics from Lajos Kossuth University (KLTE), Debrecen, in 1976. That year she married a physicist and together they brought up their son. -
Problem-solving in mathematics with the help of computers
405-422Views:112One 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. -
Let's learn database programming in an active way
213-228Views:215This 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. -
Teaching word processing - the theory behind
119-137Views:214It 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. -
Gaussian iteration of mean values and the existence of 2^(1/2)
35-42Views:116We propose a method for proving the existence of √2 and finding its approximate value in secondary education. -
Teaching of old historical mathematics problems with ICT tools
13-24Views:274The aim of this study is to examine how teachers can use ICT (information and communications technology) tools and the method of blended learning to teach mathematical problem solving. The new Hungarian mathematics curriculum (NAT) emphasizes the role of history of science, therefore we chose a topic from the history of mathematics, from the geometry of triangles: Viviani's Theorem and its problem field. We carried out our teaching experiments at a secondary school with 14-year-old students. Students investigated open geometrical problems with the help of a dynamic geometric software (GeoGebra). Their research work was similar to the historical way. -
Teachers and the interactive whiteboards
281-298Views:156The 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. -
Mapping students’ motivation in a problem oriented mathematics classroom
111-121Views:271This research focuses on mapping students’ motivation by implementing problem-solving activities, namely how the problem-oriented approach affects the students’ commitment, motivation, and attitude to learning. As a practicing teacher, the author faced difficulties with motivation and sought to improve her practice in the form of action research as described in this paper. Based on the literature, the author describes sources of motivation as task interest, social environment, opportunity to discover, knowing why, using objects, and helping others. The author discusses the effect of problem-oriented teaching on the motivation of 7th-grade students. In this paper, the results of two lessons are presented.
Subject Classification: 97C20, 97D40, 97D50, 97D60
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Information System’s experiences of EGERFOOD project making use of it in the education of the database management
197-210Views:158We 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. -
Solving mathematical problems by using Maple factorization algorithms
293-297Views:186Computer algebra gives methods for manipulating mathematical expression. In this paper we use the Maple software to solve some elementary problems. Computeraided approach in the instruction of mathematics helps to impart problem solving skills to students. -
"On the way" to the function concept - experiences of a teaching experiment
17-39Views:285Knowing, comprehending and applying the function concept is essential not only from the aspect of dealing with mathematics but with several scientific fields such as engineering. Since most mathematical notions cannot be acquired in one step (Vinner, 1983) the development of the function concept is a long process, either. One of the goals of the process is evolving an "ideal" concept image (the image is interrelated with the definition of the concept). Such concept image plays an important role in solving problems of engineering. This study reports on the beginning of a research aiming the scholastic forming of the students' function concept image i.e. on the experiences of a "pilot" study. By the experiment, we are looking for the answer of the following question: how can the analysis of such function relations be built into the studied period (8th grade) of the evolving process of the function concept that students meet in everyday life and also in engineering life?
Subject Classification: D43, U73
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Some problems of solving linear equation with fractions
339-351Views:210The aim of this paper is to offer some possible ways of solving linear equations, using manipulative tools, in which the "−" sign is found in front of an algebraic fraction which has a binomial as a numerator. It is used at 8th grade. -
Frequency-based dynamic models for the analysis of English and Hungarian literary works and coursebooks for English as a second language
53-70Views:168We 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. -
Some thoughts concerning power sums
303-308Views:151In this note we present an elementary way to derive directly closed-form expressions for power sums. Applying this method, we deduce some general results on power sums with arbitrary exponents. Finally, we give an outlook on higher mathematical connections between power sums, Stirling and Bernoulli numbers. -
Dynamic geometry systems in teaching geometry
67-80Views:135Computer drawing programs opened up new opportunities in the teaching of geometry: they make it possible to create a multitude of drawings quickly, accurately and with flexibly changing the input data, and thus make the discovery of geometry an easier process. The objective of this paper is to demonstrate the application possibilities of dynamic geometric systems in primary and secondary schools, as well as in distance education. A general characteristic feature of these systems is that they store the steps of the construction, and can also execute those steps after a change is made to the input data. For the demonstration of the applications, we chose the Cinderella program. We had an opportunity to test some parts of the present paper in an eighth grade primary school. -
What can we learn from Tamás Varga’s work regarding the arithmetic-algebra transition?
39-50Views:270Tamás Varga’s Complex Mathematics Education program plays an important role in Hungarian mathematics education. In this program, attention is given to the continuous “movement” between concrete and abstract levels. In the process of transition from arithmetic to algebra, the learner moves from a concrete level to a more abstract level. In our research, we aim to track the transition process from arithmetic to algebra by studying the 5-8-grader textbooks and teacher manuals edited under Tamás Varga's supervision. For this, we use the appearance of “working backward” and “use an equation” heuristic strategies in the examined textbooks and manuals, which play a central role in the mentioned process.
Subject Classification: 97-01, 97-03, 97D50
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The theory of functional equations in high school education
345-360Views:235In this paper, we are going to discuss some possible applications of the theory of functional equations in high school education. We would like to line up some problems, the solution of which by functional equations are mostly not new results – they have also been treated in [1] and [2] –, although their demonstrations in high school can show a new way in teaching of talented students. The area of the rectangle, the calculating method of compound interest, binomial coefficients, Euler's formula, the scalar product and the vector product of vectors – we are looking for the reasons behind the well-known formulas. Finally, we are going to give a functional equation in connection with mean values. It can be understood easily, but its solution is beyond the high school curriculum, so we advise this part only to the most talented students. -
Linear clause generation by Tableaux and DAGs
109-118Views:184Clause 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. -
The use of e-tests in education as a tool for retrieval practice and motivation
59-76Views:306In 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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Using the computer to visualise graph-oriented problems
15-32Views:168The 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.
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