Articles

• CAS-aided visualization in LATEX documents for mathematical education

  1-18

  Masataka Kaneko

  Takayuki Abe

  Kenji Fukazawa

  Masayoshi Sekiguchi

  Yuuki Tadokoro

  Satoshi Yamashita

  Setsuo Takato

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  24

  We have been developing KETpic as a macro package of a CAS for drawing fine LATEX-pictures, and we use it efficiently in mathematical education. Printed materials for mathematics classes are prepared under several constraints, such as "without animation", "mass printings", "monochrome", and "without halftone shadings". Because of these constraints, visualization in mathematical education tends to be unsatisfactory. Taking full advantages of LATEX and CAS, KETpic enables us to provide teaching materials with figures which are effective for mathematical education. The effects are summarized as follows:
  (1) The plottings of KETpic are accurate due to CAS, and enable students to deduce mathematical laws.
  (2) KETpic can provide adequate pictures for students' various interest. For example, when some students who understand a matter try to modify it, KETpic can give them appropriate and experimental figures.
  (3) Even though CAS can draw 3D-figures beautifully and automatically, it is expensive for mass printings and the figures are sometimes not easy to understand. Oppositely, 3D-graphics by KETpic are monochrome, but are richly expressive.
  In this paper, we give various examples of LATEX-pictures which we drew by using KETpic. For instance, the picture which is used in order to explain the convergence theorem of Fourier series makes it easier for students to understand the idea that function series converge to another function. Also the picture of skeleton is endowed with clear perspective. KETpic gives us great potential for the teaching of combinatorial mathematics. Through these examples, we claim that KETpic should have great possibilities of rich mathematical expressions under the constraints above mentioned.

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• Examples of analogies and generalizations in synthetic geometry

  19-39

  Ioana E. Agut

  Calin M. Agut

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  25

  Teaching tools and different methods of generalizations and analogies are often used at different levels of education. Starting with primary grades, the students can be guided through simple aspects of collateral development of their studies. In middle school, high school and especially in entry-level courses in higher education, the extension of logical tools are possible and indicated.
  In this article, the authors present an example of generalization and then of building the analogy in 3-D space for a given synthetic geometric problem in 2-D.
  The idea can be followed, extended and developed further by teachers and students as well.

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• Some thoughts on a student survey

  41-59

  István Molnár

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  26

  The paper analyzes a survey of college students and describes its major findings. The object of the survey, involving 154 students, was to discover and highlight the problems that arise in taking the course Economic Mathematics I. The paper, as the summary of the first phase of a research project, wishes to present these problems, ways that may lead out of them, and possible means of help that can be offered to those taking the course.

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• An idea which yields a lot of elementary inequalities

  61-72

  István Szalay

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  6

  The aim of the article is to show how studies in higher mathematics can be applied in everyday teaching practice to construct new problems for their pupils. In higher mathematics it is known that the set of real numbers with the addition and multiplication (shortly: (R,+,x)) is an ordered field. Considering a strictly monotonic increasing and continuous function σ with domain ...
  By this idea, using different kinds of functions σ we show a lot of different elementary inequalities.

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• Difference lists in Prolog

  73-87

  Attila Csenki

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  23

  Prolog is taught at Bradford University within the two-semester module Symbolic and Declarative Computing/Artificial Intelligence. Second year undergraduate students are taught here the basics of the functional and the logic programming paradigms, the latter by using the Linux implementation of SWI Prolog [6]. The topic 'Difference lists' is mentioned in traditional textbooks such as [2] and [5] but it was felt that the available texts do not quite serve our purposes. We present here a lecture handout and a laboratory sheet for the teaching sessions on Difference lists. It is believed that the lectures and lab sessions together with the handouts shown here are a gentle, self-contained and reasoned introduction into the topic. The figures here shown to illustrate the concepts are considered a special feature of the handouts which in this form do not seem to be well known.

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• Programming theorems on enumerator

  89-108

  Tibor Gregorics

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  30

  This paper deals with the examination of the programming patterns best known by programmers: the programming theorems. It is a significant issue that in what way these patterns can be formulated in order to solve a relatively broad spectrum of problems using a small number of patterns. In this paper, the well known programming theorems are applied to the processing of enumerators. To this end, the robustness of patterns gained this way will be presented, and it will be also pointed out how the programs thus constructed can be implemented in the modern object-oriented programming environments: in language C++, Java and C#.

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• Hungarian mathematicians in the twentieth century: Ottó Varga (1909–1969)

  109-120

  Tünde Kántor

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  23

  In this article we want to present life and work of Ottó Varga on occasion of the centenary of his birth. He was an outstanding geometer, the head of the Mathematical Seminar / Department (1942-1959) and the first dean of the Faculty of Sciences of the University of Debrecen (Hungary).
  His area of research was differential geometry. The Debrecen school of differential geometry emerged due his activity. He wrote 57 papers.

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• Normalization based on dependency diagram

  121-132

  Márta Czenky

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  19

  Normalization is an important database planning method, although the understanding and application of this method brings up the utmost problem during data modelling. That is why we were looking for alternative normalization methods, from which the normalization with dependency diagram proved to be the most efficient. This was also confirmed by the statistical estimation of the carried out survey.

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• Software engineering education in cooperation with industrial partners

  133-148

  Zoltán Horváth

  Tamás Kozsik

  László Lövei

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  21

  This paper presents our experiences on teaching software engineering in teams which are organized around different R+D projects. These long-running, innovative projects are carried out in cooperation with industrial partners, and are supported by student exchange. While MSc and PhD students work together with faculty staff members on the projects in an industrial-like environment, the students develop skills that would be otherwise very hard for them to obtain. The methodological contributions of the paper are illustrated by, and substantiated with, the description of a concrete software engineering project.

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• MRP tasks, critical thinking and intrinsic motivation to proving

  149-168

  Zdenko Takáč

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  23

  The lack of students' need for proof is often discussed. This is an important topic, on which quite a few others have written ([26], [27], [28], [17], [8]). Nevertheless, there is limited research knowledge about how teacher can participate in process of raising of students' intrinsic motivation to proving. In this article, we discuss relationships between intrinsic motivation to proving, critical thinking and special activity – engaging with so-called MRP tasks. We present here results of a research carried out by author in two elementary schools (21 classes, grade 5-9) in Ruzomberok, Slovakia. We identified the interesting relationship between students' dealing with MRP tasks and increasing of their intrinsic motivation to proving.

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• Report on the "English Language Section of Varga Tamás Days 2009"

  169-175

  Krisztina Barczi

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  28

  The 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.

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• Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 21 – January 23, 2010, Debrecen, Hungary

  177-195

  Károly Lajkó

  Gyula Maksa

  Zsolt Páles

  Views:

  10

  The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Debrecen, Hungary from January 21 to January 23, 2010. The 42 Hungarian participants – including 16 PhD students – came from 5 countries, 14 cities and represented 25 institutions of higher education. The abstracts of the talks and the posters and also the list of participants are presented in this report.

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