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Experimentieren um einen Satz zu finden - vollständig separierbare Mosaike auf der Kugel und ihre Anwendungen
297-319Views:94This paper reports a case-study which took place within the project named "Inner differentiation and individualization by creating prototypes and analogies under consideration of motivational constraints (taking into account computer-based teaching and learning)" as a part of a pre-service teacher training at the University of Salzburg (Herber, H.-J. & Vásárhelyi, É.).
The goal of the experiment was to help students to learn the fundamental concepts and basic constructions of spherical geometry using the Lénárt Sphere (a transparent plastic ball with construction-tools) and some self-made interactive worksheets with the Windows version of the dynamical geometry software Cabri. -
MRP tasks, critical thinking and intrinsic motivation to proving
149-168Views:130The 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. -
A mathematical and didactical analysis of the concept of orientation
111-130Views:264The 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. -
Forming the concept of congruence I.
181-192Views:112Teaching isometries of the plane plays a major role in the formation of the congruence-concept in the Hungarian curricula.
In the present paper I investigate the way the isometries of the plane are traditionally introduced in most of the textbooks, especially the influence of the representations on the congruence concept, created in the teaching process.
I am going to publish a second part on this topic about a non-traditional approach (Forming the concept of congruence II). The main idea is to introduce the isometries of the two dimensional plane with the help of concrete, enactive experiences in the three dimensional space, using transparent paper as a legitimate enactive tool for building the concept of geometric motion. I will show that this is both in strict analogy with the axioms of 3-dimensional motion and at the same time close to the children's intuitive concept of congruence. -
Connections between discovery learning through the Pósa Method and the secondary school leaving examination in three Hungarian mathematics classrooms
67-85Views:405The Pósa Method is a guided discovery learning method that has been used in Hungarian education in the form of extracurricular activities for "gifted" mathematics students. A four-year experiment implemented the method in three more "average" classrooms. This article reports on the relationship between the Pósa Method and the standardized secondary school leaving mathematics exam (Matura Exam in short) in Hungary. Data consists of students' survey responses, teacher interviews, and exam results from the three Hungarian classrooms who took part in the four-year experiment. We identify aspects of the Pósa Method that can benefit and hinder exam performance. In addition, we find that learning through the Pósa Method for the four years of high school has adequately prepared students for the exam.
Subject Classification: 97D44, 97D54, 97D64
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Comparing various functions of the divisors of an integer in different residue classes
247-258Views:140The main goal of this paper is to investigate some problems related to the distribution of the divisors of a number in different residue classes. We study these questions modulo 3, and use mostly just elementary number theory. In some special cases, we demonstrate how this problem is related to other fields of maths, especially to combinatorics. Since the author is also a secondary school teacher, we use elementary methods that can be discussed in secondary school, mainly within the framework of group study sessions or in special maths classes. We do think that the investigation of these types of questions can motivate children to find their own way to create their own questions, and to get a deeper insight into problem solving by these experimentations. -
Teaching probability using graph representations
103-122Views:145The main objective of this paper is to present an elementary approach to classical probability theory, based on a Van Hiele type framework, using graph representation and counting techniques, highly suitable for teaching in lower and upper secondary schools. The main advantage of this approach is that it is not based on set theoretical, or combinatorial knowledge, hence it is more suitable for beginners and facilitates the transitions from level 0 to level 3. We also mention a few teaching experiences on different levels (lower secondary school, upper secondary school, teacher training, professional development, university students) based on this approach. -
Forming the concept of parameter with examples of problem solving
201-215Views:122Pupils are encountering difficulties with learning algebra. In order for them to understand algebraic concepts, particularly the concept of parameter it was decided by the teacher of mathematics and Information Technology to integrate the teaching of these two subjects. The aim of this study is to investigate whether, and to what degree, software can be useful in process of forming the concept of parameter. This longitudinal study was conducted in a junior high school (13-16 year old children) using different computer programs. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 28 – January 30, 2011, Satu Mare, Romania
159-179Views:116The meeting Researches in Didactics of Mathematics and Computer Science was held in Satu-Mare, Romania from the 28th to the 30th of January, 2011. The 46 Hungarian participants – including 34 lecturers and 12 PhD students – came from 3 countries, 14 cities and represented 20 institutions of higher education. The abstract of the talks and the posters and also the list of participants are presented in this report. -
Manipulatives and semiotic tools of Game of Go as playful and creative activity to learn mathematics in early grades in France
197-206Views:167This research develops resources to teach mathematics in French primary school by using the game of Go. A group of searchers, teachers and go players meet at university to produce teaching resources. These resources are implemented in the classroom. Then the group evaluate this implementation and improve the resources. The aim of this classroom research is to study the opportunities of the game of Go to learn mathematics and to propose a teacher training course to implement the game of Go in French primary schools in accordance with the French syllabus. Game of Go appears as a manipulative and semiotic tool to learn mathematics at primary school.
Subject Classification: 97D50, 97U60
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The Mathematics Education Traditions of Europe (METE) Project
353-364Views:106This study is based on the work of the METE (Mathematics Education Traditions of Europe Project) team. Following a short introduction of the project, its theoretical background, methods and research design are presented in the next three sections. In the 4th section the tools developed by the METE team for qualitative and quantitative analysis of the collected data are discussed in details. The 5th section contains some personal remarks about using these tools. The 6th section presents the main results of the project, followed by a summary of the project's educational and theoretical significance. -
The theory of functional equations in high school education
345-360Views:157In 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. -
The use of e-tests in education as a tool for retrieval practice and motivation
59-76Views:238In 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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Teaching word processing - the theory behind
119-137Views:135It 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.
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