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Über die sogenannte Regel von de l’Hospital im Mathematikunterricht
193-208Views:114The aim of this paper is to provide an insight into the problems of the socalled indeterminate expressions, in order to make the students understand them better. The paper deals with the conditions and the proof of the theorem about the limit of a quotient of certain functions of one variable, usually named after l'Hospital. The question is of some interest, since the formulation of the result in several textbooks often appears redundant and the proof is more complex than necessary. First, the historical background is briefly sketched. Second, the theorem is formulated and justified, where three different, simple proof techniques are presented. Finally, possible applications are suggested for teaching, which are usually not treated in this problem area. -
Proof step analysis for proof tutoring - a learning approach to granularity
325-343Views:193We present a proof step diagnosis module based on the mathematical assistant system Ωmega. The task of this module is to evaluate proof steps as typically uttered by students in tutoring sessions on mathematical proofs. In particular, we categorise the step size of proof steps performed by the student, in order to recognise if they are appropriate with respect to the student model. We propose an approach which builds on reconstructions of the proof in question via automated proof search using a cognitively motivated proof calculus. Our approach employs learning techniques and incorporates a student model, and our diagnosis module can be adjusted to different domains and users. We present a first evaluation based on empirical data. -
What does ICT help and does not help?
33-49Views:280Year by year, ICT tools and related teaching methods are evolving a lot. Since 2016, the author of the present lines has been looking for a connection between them that supports the development of mathematical competencies and could be integrated into Transcarpathian minority Hungarian language education too. As a doctoral student at the University of Debrecen, I experienced, for example, how the interactive whiteboard revolutionized illustration in Hungarian mathematics teaching, and how it facilitated students' involvement. During my research of teaching in this regard, in some cases, the digital solution had advantageous effects versus concrete-manipulative representation of
Bruner's too.
At the same time, ICT "canned" learning materials (videos, presentations, ...) allow for a shift towards repetitive learning instead of simultaneous active participation, which can be compensated for by the "retrieval-enhanced" learning method.
I have conducted and intend to conduct several research projects in a Transcarpathian Hungarian primary school. In the research so far, I examined whether, in addition to the financial and infrastructural features of the Transcarpathian Hungarian school, the increased "ICT-supported" and the "retrieval-enhanced" learning method could be integrated into institutional mathematics education. I examined the use of two types of ICT devices: one was the interactive whiteboard, and the other was providing one computer per student.
In this article, I describe my experiences, gained during one semester, in the class taught with the interactive whiteboard on the one hand, and in the class taught according to the "retrieval-enhanced" learning method on the other hand.
I compare the effectiveness of the classes to their previous achievements, to each other, and to a class in Hungary.Subject Classification: 97U70
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Teaching performance testing
17-33Views:244Performance testing plays a vital role in the verification of large scale software systems. It is used for testing the speed, responsiveness, capacity and stability of the investigated system. However, despite the significance of this topic, the effort invested in teaching performance testing in Computer Science is insufficient. The current paper shows, how the fundamentals of performance testing can be demonstrated to students both from a theoretical and a practical viewpoint through step-by-step practical examples that are used in the industry. It is also discussed how a basic toolchain can be set up for performance tests using only free tools. With the presented examples, the reader will be able to take first steps in the performance testing area.
Subject Classification: 68M15
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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 22-24, 2016 Bratislava, Slovakia
115-137Views:167The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Bratislava, Slovakia from the 22th to the 24th of January, 2016 at Comenius University in Bratislava. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen and the Faculty of Education of Comenius University.
The 60 participants – including 47 lecturers and 15 PhD students – came from 5 countries, 23 cities and represented 32 institutions of higher and secondary education. -
Problems of computer-aided assessment of mathematical knowledge
41-52Views:169Although conventional written and oral exams are dominant in assessment nowadays, computer-aided assessment is developing dynamically. There are several assessment systems, but most of them evaluate only multiple choice questions and even the most sophisticated ones cannot follow the process of thinking of students in detail. Why is it? In this article I will analyse the difficulties of the implementation of assessment system focused primarily on mathematics questions and present some of my experience related to the eMax system, developed at Óbuda University. -
Report on the Conference of History of Mathematics & Teaching of Mathematics with Special Subject Ethno-mathematics: Research in History of Mathematics & Teaching of Mathematics : University of Miskolc, 18–21 May, 2006, Miskolc, Hungary
437-449Views:164The 4th Conference on History of Mathematics & Teaching of Mathematics with Special Subject Ethno-mathematics was organized at the University of Miskolc (Hungary). The aim of the conference was to present aspects of the History of Mathematics and Ethno-mathematics, including its impact on the Teaching of Mathematics.
Its motto was: Mathematics – a common language for Europe for thousand years.
There were 21 presentations, a poster lecture (J. Kolumbán, University of Cluj, Romania) and an exhibition made by students of Eötvös University, Budapest (R. Tanács, K. Varga).
After a short historical introduction we present 19 abstracts and the poster lecture. -
The Frobenius exchange problem on competitions and in classroom
203-218Views:62Let a_1, ..., a_n be relatively prime positive integers. The still unsolved Frobenius problem asks for the largest integer which cannot be represented as Σ x_i a_i with non-negative integers xi, and also for the number of non-representable positive integers. These and several related questions have been investigated by many prominent mathematicians, including Paul Erdős, and a wide range of partial results were obtained by various interesting methods differing both in character and difficulty. In this paper we give a self-contained introduction to this field through problems and comments suitable also for treatment in a class of talented students.
