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Fostering engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks
1-14Views:270We designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics.
Subject Classification: 97U70, 97H60
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Synthesis of concurrent programs
301-317Views:94Students need a well defined method to be successful in the complex process of writing a concurrent program. In this paper we show a step by step method to create such programs. The method based on UML which has been thought to students during previous courses. UML provides standard and relatively simple tools to describe concurrent systems, and from the description the program can be derived.
First we give a brief introduction to the concurrent systems. This is followed by the description of the method, and finally we demonstrate the method on a small problem. -
Software engineering education in cooperation with industrial partners
133-148Views:171This 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. -
A computational thinking problem-thread for grade 7 students and above from the Pósa method
101-110Views:292Lajos Pósa has been developing his “learning through discovery” (Győri & Juhász, 2018) method since 1988. His weekend math camps are focused on fostering problem-solving skills and high-level mathematical-thinking skills in gifted students from grades 7 to 11. One of the core aspects of the method is the structure of the problems, all problems are part of a complex, intertwined, and rich network. In this article we analyze a computational thinking problem-thread and its role in the camps’s network of problems (Gosztonyi, 2019), and show some aspects of the method. The insights gained using this method can be useful in other contexts. The possible adaptation of the method to secondary and high schools is briefly discussed as well.
Subject Classification: 97D40
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Typical mistakes in Mental Cutting Test and their consequences in gender differences
385-392Views:204Spatial ability of first year university students is measured and evaluated in this paper. We used standard Mental Cutting Test (MCT), where a body is given by perspective view and correct cross section has to be chosen. While gender differences in MCT are reported by several papers including our earlier results, much less known are the reasons of these differences. Here we show that typical mistakes (answers to problems which are close to be correct) can be one of the possible reasons, since female students made typical mistakes in some cases more frequently than males. -
Examining continuity/discontinuity of a function by using GeoGebra
241-257Views:200The possibility to visualize the things with the help of today's dynamic software (GeoGebra being one of them), enables the students to see and explore mathematical relations and concepts that were difficult to be presented in the past, prior to the state-of-the-art technologies. In methodological sense, the contribution of this paper lies in the presentation of a set of visualizations designed to help students better understand and explore the basic calculus concepts such as continuity at a point, to examine discontinuity at a point, to display discontinuities and the relations between continuity and differentiability of single variable functions. In technical sense, this paper presents creative GeoGebra applets which offer new possibilities that could be of a vital importance for the future development of e-learning of College mathematics. -
Didactical remarks on the changes in the requirements of the matriculation exam in Mathematics in Hungary
95-110Views:202Students within the Hungarian education system typically take a matriculation exam to obtain a secondary education certificate, which also serves as a prerequisite for university admission. Public education is regulated at different levels. One of its most fundamental elements is the National Core Curriculum, the current version of which came into force in September 2020. It is crucial to adapt the requirements of the matriculation exam in mathematics to this and ensure transparent communication about the changes. Regarding this, there exists a sample paper that contains tasks that one can reasonably expect in the actual exam in the spring. Since I have been working as a private math tutor for almost a decade and have been preparing students for the matriculation exam since then, I intend to highlight the most outstanding features from a didactic point of view based on the analysis of this sample paper.
Subject Classification: 97A30, 97B10, 97B70, 97D60, 97U40
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"Upperview" algorithm design in teaching computer science in high schools
221-240Views:157In this paper we are going to present a teaching/learning method and suggest a syllabus that help the high school students look at the algorithm design strategies from a so called "upperview": greedy, backtracking, divide and conquer, dynamic programming. The goal of the suggested syllabus is, beyond the presentation of the techniques, to offer the students a view that reveals them the basic and even the slight principal differences and similarities between the strategies. In consensus with the Comenius principle this is essential, if we want to master this field of programming ("To teach means scarcely anything more than to show how things differ from one another in their different purposes, forms, and origins. ... Therefore, he who differentiates well teaches well."). -
"On the way" to the function concept - experiences of a teaching experiment
17-39Views:244Knowing, 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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Practice based course of Information Technology Service Management for BSc students
229-246Views:118Currently IT systems are primarily observed as sets of services, for example finance services can be accessed via the Internet. The IT background of an enterprise has strategic importance in its activity, but it is also important, that IT helps the enterprise supporting course of business really from the background. To implement this kind of conception, IT Infrastructure Library (ITIL) provides practical advices.
The paper describes the topic of an optional course which introduces BSc students to the subject of IT Service Management the way that it can be used as a practice supplement beside theory courses of IT Service Management. -
Prime building blocks in the mathematics classroom
217-228Views:358This theoretical paper is devoted to the presentation of the manifold opportunities in using a little-known but powerful mathematical manipulative, the so-called prime building blocks, originally invented by two close followers of Tamás Varga, to support discovery of various concepts in arithmetic in middle school, including the Fundamental Theorem of Arithmetic or as it is widely taught, prime factorization. The study focuses on a teaching proposal to show how students can learn about greatest common divisor (GCD) and least common multiple (LCM) with understanding, and meanwhile addresses internal connections and levels of abstractness within elementary number theory. The mathematical and methodological background to understanding different aspects of the concept prime property are discussed and the benefits of using prime building blocks to scaffold students’ discovery are highlighted. Although the proposal was designed to be suitable for Hungarian sixth graders, mathematical context and indications for the use of the manipulative in both primary and high school are given.
Subject Classification: F60, C30, E40, U60
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Teaching of old historical mathematics problems with ICT tools
13-24Views:224The 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. -
The single-source shortest paths algorithms and the dynamic programming
25-35Views:172In this paper we are going to present a teaching—learning method that help students look at three single-source shortest paths graph-algorithms from a so called "upperview": the algorithm based on the topological order of the nodes, the Dijkstra algorithm, the Bellman-Ford algorithm. The goal of the suggested method is, beyond the presentation of the algorithms, to offer the students a view that reveals them the basic and even the slight principal differences and similarities between the strategies. In order to succeed in this object, teachers should present the mentioned algorithms as cousin dynamic programming strategies. -
The transition problem in Hungary: curricular approach
1-16Views:298The curricular background of the transition problem from highschool to universty is analysed in Hungary. While students finish their mathematical studies successfully at highschool, pass their final exams, this knowledge seems to disappear at their first year at university. We investigate the mathematical knowledge expected by the Hungarian universities and compare it to expectations of the National Core Curriculum. Based on the levelling tests of four universities we created a seven problem test for highschool students containing very basic problems required both by the universities and the National Core Curriculum. We analyse the results of the test.
Subject Classification: D34, D35
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Assimilation of mathematical knowledge using Maple
321-331Views:127For more than four years we have been teaching a Maple course at University of Debrecen for prospective mathematics teachers. The aim of the course is that students get some experience on mathematical visualization with Maple. At the last part of the course the student is provided with a problem of geometrical flavor. Within three or four weeks he/she must obtain a solution. In this paper we present and analyze two of student projects: rotation of the hypercube and drawing of complex functions. The concluding remark is that most of the students will profit from using Maple for such type of problems: it helps to assimilate mathematical knowledge. -
The tools for developing a spatial geometric approach
207-216Views:193Tamás Varga writes about the use of tools: "The rational use of tools - the colored bars, the Dienes set, the logical set, the geoboard, and some other tools - is an element of our experiment that is important for all students, but especially for disadvantaged learners." (Varga T. 1977) The range of tools that can be used well in teaching has grown significantly over the years. This paper compares spatial geometric modeling kits. Tamás Varga uses the possibilities of the Babylon building set available in Hungary in the 1970s, collects space and flat geometry problems for this (Varga T. 1973). Similarly, structured kits with significantly more options have been developed later, e.g. ZomeTool and 4D Frame. These tools are regularly used in the programs of the International Experience Workshop (http://www.elmenymuhely.-hu/?lang=en). Teachers, schools that have become familiar with the versatile possibilities of these sets, use them often in the optional and regular classes. We recorded a lesson on video where secondary students worked with the 4D Frame kit. We make some comments and offer some thoughts on this lesson.
Subject Classification: 97G40, 97D40
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Comment les enseignants en formation initiale utilisent les technologies informatiques dans leurs classes
187-208Views:160The research presented here deals with the way French pre-service teachers assimilate the working of technology tools and the effects on professional practice of integrating these tools into classes. We focused on the professional writings of pre-service teachers regarding the use of technology in their teaching. The results show that, besides official instructions, the motivations put forward by pre-service teachers who integrated technology in their classes are mainly their students' interest in computers and how powerful this tool is. They also show that in such an environment teachers tend to keep in the background and to leave the students to interact chiefly with the computer. We also noticed that the specificities of managing a classroom in computer environment are not taken into account unless they generate problems.
Résumé. La recherche présentée ici porte sur l'appropriation des outils informatiques par les enseignants français en formation initiale et les effets de leur intégration dans les classes sur les pratiques professionnelles. Nous avons pris comme objet d'étude des écrits professionnels, élaborés par ces professeurs stagiaires, portant sur l'utilisation des TIC dans leur enseignement. Les résultats obtenus font apparaître qu'outre les injonctions institutionnelles, les motivations invoquées par les stagiaires pour recourir à l'informatique concernent surtout l'attrait de leurs élèves pour l'ordinateur et la puissance de cet outil. Dans le cadre des usages en classe, nos résultats montrent que l'enseignant a tendance à s'effacer devant l'ordinateur, considéré comme l'interlocuteur privilégié de l'élève. Nous avons aussi pu constater que les spécificités de la gestion de la classe en environnement informatique ne sont prises en compte que lorsqu'elles se révèlent sources de problèmes. -
Learning and teaching combinatorics with Sage
389-398Views:178Learning Mathematics is not an easy task, since this subject works with especially abstract concepts and sophisticated deductions. Many students lose their interest in the subject due to lack of success. Computer algebra systems (CAS) provide new ways of learning and teaching Mathematics. Numerous teachers use them to demonstrate concepts, deductions and algorithms and to make learning process more interesting especially in higher education. It is an even more efficient way to improve the learning process, if students can use the system themselves, which helps them to practice the curriculum.
Sage is a free, open-source math software system that supports research and teaching algebra, analysis, geometry, number theory, cryptography, numerical computation, and related areas. I have been using it for several years to aid the instruction of Discrete Mathematics at Óbuda University. In this article I show some examples how representations provided by this system can help in teaching combinatorics. -
Examples of analogies and generalizations in synthetic geometry
19-39Views:130Teaching 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. -
Why do we complicate the solution of the problem? reflection of Finnish students and teachers on a mathematical summer camp
405-415Views:208This paper deals with reactions and reflections of Finnish secondary school students and teachers on Hungarian mathematics teaching culture. The experiences were collected at a mathematics summer camp in Hungary. -
Demonstrating the feature of energy saving of transforms in secondary schools
43-55Views:138When we are teaching the digital image formats and we are explaining the JPEG format we may get into difficulties how to explain the point and the usefulness of the discrete cosine transform (DCT) to our students. Why do we need this transform before compressing? Students probably do not know that the feature of energy saving of this transform makes the chance of good compression. In this article we show how we can demonstrate that feature of these transforms which make the chance of good compression while saving the most energy of images. -
Lehre der Trigonometrie anhand realistischer Aufgaben im Online-Unterricht
87-105Views:215The aim of our study was to explore the effects of the active use of realistic exercises in the field of trigonometry. We taught a group of 14 pupils, who were in grade 11. The most of them told us they did not plan mathematics-related studies in the future. We included realistic exercises into our teaching plan, which covered the fields of scalar product, as well as the sine and cosine theorems. Our teaching experiment was done within the framework of online teaching. Effects on the motivation, performance and results of the students were taken into consideration. We also attempted to examine the effects of online teaching on motivation and whether the use of realistic exercises is worthwhile in an online classroom environment. Performance of the students showed a tendency of improvement when they were dealing with the material through realistic exercises even despite the teaching happened online.
Subject Classification: 97C70, 97D40, 97G60
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Teaching sorting in ICT
101-117Views:190This article is aimed at considering how an algorithmic problem – more precisely a sorting problem – can be used in an informatics class in primary and secondary education to make students mobilize the largest possible amount of their intellectual skills in the problem solving process. We will be outlining a method which essentially forces students to utilize their mathematical knowledge besides algorithmization in order to provide an efficient solution. What is more, they are expected to use efficiently a tool that has so far not been associated with creative thinking. Sorting is meant to be just an example, through which our thoughts can easily be demonstrated, but – of course the method of education outlined can be linked to several other algorithmic problems, as well. -
Recalling calculus knowledge
55-70Views:123The main purpose of educational system is not only that the students perform well at the exam, but to remember the learnt material to some degree some time after the learning. This paper investigates students' retained knowledge, focusing mainly on topics concerning derivatives and differentiation, and examines the effect of re-learning in a short period of time. Results indicate that retained knowledge should be taken into consideration in instructional design and curriculum planning for the sequencing courses. -
How to teach computer programming if our goal is the International Olympiad in Informatics
13-25Views:182Nowadays if a student in Hungary (age between 17-20 years old) wants to be the member of the Hungarian selected team (has four members) to participate in the International Olympiad in Informatics (IOI), first, he has to qualify himself in the first fifteen of the National Secondary School Competition (OKTV) in the programming category after the III. round. Then he should be in the first four place after the sixth round of the Selection Competition. Being successful is necessary that the student wants to start studying computer programming at least in the 9th school year and he needs a teacher who prepares him. In the last nine years three students of the author have participated in five Olympics and two of them won gold and bronze medals. This article wants to demonstrate the methods that a teacher needs to use to teach students in 9th school year for computer programming, to be the member of the Hungarian National Team after three or four years.
