Search
Search Results
-
Katalin Juhász (1952-2012)
1-2Views:137Katalin 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. -
Les mathématiques dans le grand public et dans l'enseignement: quelques éléments d'une analyse didactique
195-216Views:156The paper looks for reaction of the public at large that is people out of educational system, concerning the mathematical exercises. We can see some results about:
• impact of terms on the motivation
• the effects of the traditional didactic on the method to resolve a problem.
Résumé. Cet article cherche la réactions du grand public c.a.d. de personnes hors systéme scolaire, de nombreuses années aprés avoir terminé leurs études vis á vis des exercises mathématiques.
Nous présentons quelques résultats concernant les points suivants:
– l'impact de l'« habillage » d'un énoncé sur la motivation
– les effets de l'absence d'un contrat didactique traditionnel sur la maniére de résoudre un probléme. -
On four-dimensional crystallographic groups
391-404Views:175In his paper [12] S. S. Ryshkov gave the group of integral automorphisms of some quadratic forms (according to Dade [6]). These groups can be considered as maximal point groups of some four-dimensional translation lattices in E^4. The maximal reflection group of each point group, its fundamental domain, then the reflection group in the whole symmetry group of the lattice and its fundamental domain will be discussed. This program will be carried out first on group T. G. Maxwell [9] raised the question whether group T was a reflection group. He conjectured that it was not. We proved that he had been right. We shall answer this question for other groups as well. Finally we shall give the location of the considered groups in the tables of monograph [4]. We hope that our elementary method will be useful in studying linear algebra and analytic geometry. Futhermore, 4-dimensional geometry with some visualisation helps in better understanding important concepts in higher-dimensional mathematics, in general. -
Exploring the basic concepts of Calculus through a case study on motion in gravitational space
111-132Views:325In universities, the Calculus course presents significant challenges year after year. In this article, we will demonstrate how to use methods of Realistic Mathematics Education (RME) to introduce the concepts of limits, differentiation, and integration based on high school kinematics and dynamics knowledge. All mathematical concepts are coherently built upon experiences, experiments, and fundamental dynamics knowledge related to motion in a gravitational field. With the help of worksheets created using GeoGebra or Microsoft Excel, students can conduct digital experiments and later independently visualize and relate abstract concepts to practical applications, thereby facilitating their understanding.
Subject Classification: 97D40, 97I40, 97M50
-
Pupils' meta-discursive reflection on their cooperation in mathematics: a case study
147-169Views:186This article addresses the issue of how 10–11 year old pupils in pairs can actively get involved in reforming their behavior as they reflect on their interaction in order to solve mathematical problems. We studied the opportunities offered for the development of meta-discursive reflection in a pair of pupils in two alternative environments: (1) pupils' observations and discussions on their video-recorded cooperation and (2) pupils' participation in playing and acting in a drama. The results of the research revealed three levels of the pupils' meta-discursive reflection on their interaction: (1) focusing on the achievement of personal goals, (2) focusing on partners' responsibility and (3) focusing on mutual responsibility. Both environments helped the pupils to improve their socio-mathematical interaction. -
Looking back on Pólya’s teaching of problem solving
207-217Views:596This article is a personal reflection on Pólya's work on problem solving, supported by a re-reading of some of his books and viewing his film Let Us Teach Guessing. Pólya's work has had lasting impact on the goals of school mathematics, especially in establishing solving problems (including non-routine problems) as a major goal and in establishing the elements of how to teach for problem solving. His work demonstrated the importance of choosing rich problems for students to explore, equipping them with some heuristic strategies and metacognitive awareness of the problem solving process, and promoting 'looking back' as a way of learning from the problem solving experience. The ideas are all still influential. What has changed most is the nature of classrooms, with the subsequent appreciation of a supporting yet challenging classroom where students work collaboratively and play an active role in classroom discussion.
Subject Classification: 97D50, 97A30
-
Erratum to the paper "The theory of functional equations in high school education" Teaching Mathematics and Computer Science 10/2 (2012), 345-360
145Views:173A correction is necessary in subsection 2.5. although this does not affect the truth of the main formula. -
Eine geometrische Interpretation der Ausgleichsrechnung
159-173Views:154Using real examples of applied mathematics in upper secondary school one has do deal with inaccurate measures. This will lead to over constrained systems of linear equations. This paper shows an instructive approach which uses methods of descriptive and computer aided geometry to get a deeper insight into the area of calculus of observations. Using a qualified interpretation one can solve problems of calculus of observations with elementary construction techniques of descriptive geometry, independent of the norm one uses. -
Probabilistic thinking, characteristic features
13-36Views:147This paper is the first step in a series of a general research project on possible development in probability approach. Our goal is to check with quantitative methods how correct our presumptions formulated during our teaching experience were. In order to get an answer to this question, we conducted a survey among third-year students at our college about their general and scientific concepts as well as about the way they typically think. -
Decomposition of triangles into isosceles triangles II: complete solution of the problem by using a computer
275-300Views:213We solve an open decomposition problem in elementary geometry using pure mathematics and a computer programme, utilizing a computer algebra system. -
Strategies used in solving proportion problems among seventh-grade students
101-127Views:146In the 2023/2024 school year, 146 seventh-grade Hungarian students (aged 12-13) participated in our classroom experiment on solving proportion problems. At the beginning and the end of the teaching phase, both the experimental and the control groups solved a test. Regarding the answers of the students, in the pre- and post-test mostly consisting of word problems, we examined the success of solving the problems, as well as the solution strategies. For this, we used the strategies of proportional thinking that already exist in the literature of mathematical didactics. We intended to answer the following questions: To what extent and in which ways do the different types of problems and texts influence the solution strategies chosen by the students? How successfully do seventh-grade students solve proportion problems?
Subject Classification: 97D50, 97F80
-
Teaching integral transforms in secondary schools
241-260Views:181Today, Hungarian students in the secondary schools do not know the idea of complex numbers, and they can not integrate except those ones who learn mathematics in advance level. Without this knowledge we can teach Fourier transform for students. Why should we teach Fourier transform (FT) or Wavelet transform (WT) for them? To teach image file formats like JPEG, (JPEG2000) we need to talk about integral transforms. For students who are good in computer programming, writing the program of 1D FT or 2D FT is a nice task. In this article we demonstrate how we can teach Fourier and Wavelet transform for students in secondary school. -
Das Konzept des Analysisunterrichts von Professor Igor Kluvánek – einige Ergebnisse der qualitativen Forschung
349-361Views:163A renowned Slovak mathematician Professor Igor Kluvanek (1931-1993) during his affiliation with the University of Adelaide in Australia (1968-1990) has worked out a unique course of mathematical analysis for future high school teachers of mathematics. The course has been tested in its conceptual form but, as a whole, it still awaits its publication in the form of a monograph. Along these lines, our aim is to present the way he has introduced some key notions of differential calculus and to discuss its advantages. Central is the continuity of a function via which the limit and the derivative of a function at a point is defined. -
An examination of descriptive statistical knowledge of 12th-grade secondary school students - comparing and analysing their answers to closed and open questions
63-81Views:249In this article, we examine the conceptual knowledge of 12th-grade students in the field of descriptive statistics (hereafter statistics), how their knowledge is aligned with the output requirements, and how they can apply their conceptual knowledge in terms of means, graphs, and dispersion indicators. What is the proportion and the result of their answers to (semi-)open questions for which they have the necessary conceptual knowledge, but which they encounter less frequently (or not at all) in the classroom and during questioning? In spring 2020, before the outbreak of the pandemic in Hungary, a traditional-classroom, “paper-based” survey was conducted with 159 graduating students and their teachers from 3 secondary schools. According to the results of the survey, the majority of students have no difficulties in solving the type of tasks included in the final exam. Solving more complex, open-ended tasks with longer texts is more challenging, despite having all the tools to solve them, based on their conceptual knowledge and comprehension skills. A valuable supplement to the analysis and interpretation of the results is the student attitudes test, also included in the questionnaire.
Subject Classification: 97K40, 97-11, 97D60
-
On the past of a famous theorem: the predecessors of a theorem of Pythagoras
255-267Views:197The well-known Theorem of Pythagoras asserts a relation among the sides of any right-angled triangle. It can be found any secondary school textbook. An interesting question whether this result due to the Pythagoreans from the VIth century BC, or it was known in earlier civilizations. The first answer is a vague yes. According to the legends the Egyptian rope-stretchers used a triangle with sides 3,4,5 units to create right angle. But are there real evidences that this result was known earlier? We will argue that in almost all river-valley civilizations it was known and used. -
A mathematical and didactical analysis of the concept of orientation
111-130Views:355The development of spatial ability, in particular the development of spatial orientation is one of the aims of mathematics education.
In my work, I examine the concept of orientation, especially concepts of between, left, right, below, above, front, back, clockwise and anticlockwise. I analyze answers given for a simple orientation task prepared for elementary school pupils. I would like to call attention to the difficulties pupils have even in case of solving simple orientation problems.
We have different ways to know more about the crucial points of a concept, especially of the concept of orientation. In this study I bring out one of them. I analyze and make some didactical conclusions about the origin and the axiomatic structure of orientation. -
Report on the "English Language Section of Varga Tamás Days 2009"
169-175Views:170The 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. -
Mobile devices in Hungarian university statistical education
19-48Views:211The methodological renewal of university statistics education has been continuous for the last 30 years. During this time, the involvement of technology tools in learning statistics played an important role. In the Introduction, we emphasize the importance of using technological tools in learning statistics, also referring to international research. After that, we firstly examine the methodological development of university statistical education over the past three decades. To do this, we analyze the writings of statistics teachers teaching at various universities in the country. To assess the use of innovative tools, in the second half of the study, we briefly present an online questionnaire survey of students in tertiary economics and an interview survey conducted with statistics teachers.
Subject Classification: 97-01, 97U70, 87K80
-
The study of sequences defined by a first order recursion by means of a pocket calculator
231-240Views:169This paper will present the way we can use a simple pocket calculator to teach mathematics. Namely, a pocket calculator can be very useful to study the properties of sequences defined by first order recursion (e.g. monotonicity, boundedness and convergence) and to gain a deeper understanding.
