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Correction to Gofen (2013): "Powers which commute or associate as solutions of ODEs?", Teaching Mathematics and Computer Science 11 (2013), 241-254.
245Views:182In the article "Powers which commute or associate as solutions of ODEs?" by Alexander Gofen (Teaching Mathematics and Computer Science, 2013, 11(2), 241–254. https://doi.org/10.5485/TMCS.2013.0347), there was an error in Conjecture 1 (p. 250), and consequently, in the References (p. 254).
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Why some children fail? Analyzing a test and the possible signs of learning disorders in an answer sheet: dedicated to the memory of Julianna Szendrei
251-268Views:283Teachers and educators in mathematics try to uncover the background of the mistakes their students make for their own and their students' benefit. Doing this they can improve their teaching qualities, and help the cognitive development of their pupils. However, this improvement does not always support their students with learning disorders, since their problem is not caused by wrong attitude or lack of diligence. Therefore, it is the interest of a conscientious teacher to recognize whether the weaker performance of a student is caused by learning disorders, so the helping teacher can give useful advices. Although the teacher is not entirely responsible for the diagnosis, but (s)he should be be familiar with the possible symptoms in order to make suggestions whether or not to take the necessary test of the learning disorders.
In this article, through examining a test and the answer sheet of a single student, I show some signs that might be caused by learning disorders. -
Longest runs in coin tossing. Teaching recursive formulae, asymptotic theorems and computer simulations
261-274Views:248The coin tossing experiment is studied, focusing on higher education. The length of the longest head run can be studied by asymptotic theorems ([3]), by recursive formulae ([10]) or by computer simulations . In this work we make a comparative analysis of recursive formulas, asymptotic results and Monte Carlo simulation for education. We compare the distribution of the longest head run and that of the longest run (i.e. the longest pure heads or pure tails) studying fair coin events. We present a method that helps to understand the concepts and techniques mentioned in the title, which can be a useful didactic tool for colleagues teaching in higher education. -
Examining relation between talent and competence through an experiment among 11th grade students
17-34Views:239The areas of competencies that are formable, that are to be formed and developed by teaching mathematics are well-usable in recognizing talent. We can examine the competencies of a student, we can examine the competencies required to solve a certain exercise, or what competencies an exercise improves.
I studied two exercises of a test taken by students of the IT specialty segment of class 11.d of Jedlik Ányos High School, a class that I teach. These exercises were parts of the thematic unit of Combinatorics and Graph Theory. I analysed what competencies a gifted student has, and what competencies I need to improve while teaching mathematics. I summarized my experience about the solutions of the students, the ways I can take care of the gifted students, and what to do to the less gifted ones. -
Realizing the problem-solving phases of Pólya in classroom practice
219-232Views:474When teaching mathematical problem-solving is mentioned, the name of Pólya György inevitably comes to mind. Many problem-solving lessons are planned using Pólya's steps and helping questions, and teachers often rely on his heuristics even if their application happens unconsciously. In this article, we would like to examine how the two phases, Making a plan and Looking back, can be realized in a secondary school mathematics lesson. A case study was designed to observe and analyse a lesson delivered using cooperative work.
Subject Classification: 97B10, 97C70, 97D40, 97D50
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How to use our own program evaluation system to streamline teaching computer programming
73-80Views:251During computer programming contests the use of automatic evaluation systems is becoming more and more frequent. In said systems the contestants are allowed to submit their source code that will be evaluated with the results reported back to them. According to this report the contestant can realise for what test cases his program works properly and for what cases does it fail. This kind of on-line evaluation system is used for example in the International Olympiad in Informatics (IOI), in the final round of the Nemes Tihamér National Programming Competition, and in the Selection Competition for IOI in Hungary. A contest management system can be used for other purposes apart from this singular example. A well-developed evaluation system can foster not only the teaching of computer programming and the preparation of students for programming contests but the teacher's work as well. -
Teaching Gröbner bases
57-76Views:236In this article we offer a demonstration of how the StudentGroebner package, a didactic oriented Maple package for Gröbner basis theory, could assist the teaching/learning process. Our approach is practical. Instead of expounding on deep didactic theory we simply give examples on how we imagine experimental learning in classroom. The educational goal is to prepare the introduction of two sophisticated algorithms, the division algorithm and Buchberger's algorithm, by gathering preliminary knowledge about them. -
Learning and Knowledge: The results, lessons and consequences of a development experiment on establishing the concept of length and perimeter
119-145Views:186In the paper the four main stages of an experiment are described focusing on the question as to how much measuring the length and perimeter of various objects such as fences, buildings by old Hungarian units of measurements and standards contribute to the establishment of the concept of perimeter.
It has also been examined in what ways and to what extent the various forms of teaching such as frontal, group and pair and individual work contribute to the general knowledge, thinking, creativity and co-operation in this area.
It will also be shown to what extent folk tales, various activities and games have proved to be efficient in the teaching of the particular topic.
Every stage of the experiment was started and closed with a test in order to find out whether the development was successful and children managed to gain lasting knowledge in this particular area. -
Motivating students with projects encompassing the whole duration of their studies
165-180Views:230Based on my ten years of teaching experience at the University of Debrecen, I can say that students majoring Software Information Technology BSc have to face a number of difficulties during their studies. I think these difficulties root from two main problems: students are unmotivated and cannot sense the coherence between the knowledge acquired in the various courses. This paper tries to give some alleviation to both of these problems by the idea of introducing some long-term projects to students, which they can work on throughout their studies, dealing with a particular aspect of the projects in each course. -
Correction to Mneimneh (2019): "Simple variations on the Tower of Hanoi: A study of recurrences and proofs by induction” Teaching Mathematics and Computer Science 17 (2019), 131-158.
109Views:185In the article “Simple variations on the Tower of Hanoi: A study of recurrences and proofs by induction” by Saad Mneimneh (Teaching Mathematics and Computer Science, 2019, 17(2), 131–158. https://doi.org/10.5485/TMCS.2019.0459), there was an error in Table 1 (p. 155), and consequently, the first paragraph of Section 8 (p. 154) also needed correction.
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Teaching puzzle-based learning: development of transferable skills
245-268Views:490While computer science and engineering students are trained to recognise familiar problems with known solutions, they may not be sufficiently prepared to address novel real-world problems. A successful computer science graduate does far more than just program and we must train our students to reach the required levels of analytical and computational thinking, rather than hoping that it will just 'develop'. As a step in this direction, we have created and experimented with a new first-year level course, Puzzle-based Learning (PBL), that is aimed at getting students to think about how to frame and solve unstructured problems. The pedagogical goal is increase students' mathematical awareness and general problem solving skills by employing puzzles, which are educational, engaging, and thought provoking. In this paper we continue sharing our experiences in teaching such a course. Whereas a brief discussion on our pedagogical objectives were covered in the first paper together with the material of the first of two lectures on pattern recognition, this follow-up paper presents the material of the second of two lectures, in which additional exercises are discussed to reinforce the lesson. Along the way we provide a glimpse of some foundational ideas of computer science such as incomputability and general system development strategies such as incremental and iterative reasoning. This paper discusses the outcomes of PBL courses, which include expected improvement in the overall results achieved by students who have undertaken PBL courses, compared to those students who have not. -
Comparative geometry on plane and sphere: didactical impressions
81-101Views:93Description of experiences in teaching comparative geometry for prospective teachers of primary schools. We focus on examples that refer to changes in our students' thinking, in their mathematical knowledge and their learning and teaching attitudes. At the beginning, we expected from our students familiarity with the basics of the geographic coordinate system, such as North and South Poles, Equator, latitudes and longitudes. Spherical trigonometry was not dealt with in the whole project. -
Teaching agile operation and leadership through linked university courses
1-32Views:273Agile software development methods, especially Scrum, are commonly used in software development companies. For this reason, our goal was that our undergraduate students gain experience as Scrum development team members and our master's students as agile leaders. To this end, we had redesigned and linked an undergraduate and a master's course, and launched the new course in the spring of 2021. The success of our approach was confirmed by a questionnaire survey of 86 undergraduate and 27 master's students. A/B testing was also performed. Our approach is a novelty compared to solutions where the Scrum Master is a course member, an instructor, or a university employee. In addition to being resource-efficient, it also offers master's students an unparalleled opportunity to develop agile leadership skills.
Subject Classification: 97U50
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Strategies used in solving proportion problems among seventh-grade students
101-127Views:176In 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
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Mathematical gems of Debrecen old mathematical textbooks from the 16-18th centuries
73-110Views:130In the Great Library of the Debrecen Reformed College (Hungary) we find a lot of old mathematical textbooks. We present: Arithmetic of Debrecen (1577), Maróthi's Arithmetic (1743), Hatvani's introductio (1757), Karacs's Figurae Geometricae (1788), Segner's Anfangsgründe (1764) and Mayer's Mathematischer Atlas (1745). These old mathematical textbooks let us know facts about real life of the 16-18th centuries, the contemporary level of sciences, learning and teaching methods. They are rich sources of motivation in the teaching of mathematics. -
Assimilation of mathematical knowledge using Maple
321-331Views:175For 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. -
Our duties in talent management in the light of the results of the International Hungarian Mathematics Competition of 2017
55-71Views:236The 4th International Hungarian Mathematics Competition held in Transcarpathia, Beregszász between April 28 and May 1, 2017, was organized by the Hungarian Carpathian Hungarian Teachers' Association (KMPSZ) and the Ferenc Rákóczi II. Transcarpathian Hungarian Institute (II. RFKMF).
The venue for the competition was the building of the Ferenc Rákóczi II. Transcarpathian Hungarian Institute. 175 students participated in the competition from Hungary, Romania, Serbia, Slovakia and Transcarpathia.
In this article, we are going to deal with the problems given in the two rounds to students in grades 5 and 6, and, in the light of expectations and performance, we make some suggestions for a more effective preparation of talented students on after-school lessons. -
Erratum to the paper "The theory of functional equations in high school education" Teaching Mathematics and Computer Science 10/2 (2012), 345-360
145Views:208A correction is necessary in subsection 2.5. although this does not affect the truth of the main formula. -
Research on IT language use at a company
203-219Views:236The aim of the research of the IT language, used in the written documents of a company, is to contribute to the creation of a (mono- or bilingual) dictionary or encyclopaedia available for the public on the Internet, serving, among others, as a reference tool for the unified, controlled and unambiguous use of IT terms for students at various educational levels. To this ongoing work, the participation and cooperation of a panel of experts of different competences, linguists as well as IT experts, is indispensable.
The methods of corpus linguistics were used to carry out the research. The IT terms were separated from the texts and then a concordance software was used to see the environment of the IT words and phrases in which they occur. So their morphological analysis became possible.
The results of the research showed that a great number of Hungarian morphological language use problems stem from the way the IT terms are used in the documents. This paper lists, groups, analyses these phenomena.
The conclusions of the author are: (1) If such an Internet dictionary is used generally and consulted when e.g. somebody wants to write a composition or essay, translate an article, write a newspaper article, a scientific publication or a textbook to be taught at schools of different types and levels, etc. most of the communication noises could be filtered out. (2) At the same time it could promote the use of adequate (both in linguistic and technical meaning) Hungarian terms eliminating the "Hunglish" usage. (3) It could also contribute to the prevailing use of the relevant Hungarian terminology. Such a dictionary would be indispensable, not only in educational and industrial environments but in the electronic and traditional media as well. Last but not least, it could raise the level of different teaching materials (textbooks, e-materials, etc.) used in public and higher education. -
An examination of descriptive statistical knowledge of 12th-grade secondary school students - comparing and analysing their answers to closed and open questions
63-81Views:274In 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
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Zoltán Szvetits (1929-2014): legendary teacher, Zoltán Szvetits passed away
287-288Views:140The legendary mathematics teacher of Secondary School Fazekas in Debrecen, Zoltán Szvetits passed away on 5th November 2014, at the age of 84. Beginning in 1954 he had been teaching here almost forty years. His pupils and the society of teachers have lost an outstanding teacher character. This secondary school has been well known for decades about its special mathematics class with 10 math lessons a week. This special class was designed and established by Zoltán Szvetits. -
Examples of analogies and generalizations in synthetic geometry
19-39Views:183Teaching 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. -
Solving mathematical problems by using Maple factorization algorithms
293-297Views:222Computer algebra gives methods for manipulating mathematical expression. In this paper we use the Maple software to solve some elementary problems. Computeraided approach in the instruction of mathematics helps to impart problem solving skills to students. -
Visualisation in geometry education as a tool for teaching with better understanding
337-346Views:485In primary and secondary geometry education, some problems exist with pupils’ space thinking and understanding of geometric notions. Visualisation plays an important role in geometry education, and the development of pupils’ visualisation skills can support their spatial imagination. The authors present their own thoughts on the potential of including visualisation in geometry education, based on the analysis of the Hungarian National Core Curriculum and Slovak National Curriculum. Tasks for visualisation are also found in international studies, for example the Programme for International Student Assessment (PISA). Augmented reality (AR) and other information and communication technology (ICT) tools bring new possibilities to develop geometric thinking and space imagination, and they also support mathematics education with better understanding.
Subject Classification: 97U10, 97G10
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Metacognition – necessities and possibilities in teaching and learning mathematics
69-87Views:314This article focuses on the design of mathematics lessons as well as on the research in mathematics didactics from the perspective that metacognition is necessary and possible.
Humans are able to self-reflect on their thoughts and actions. They are able to make themselves the subject of their thoughts and reflections. In particular, it is possible to become aware of one’s own cognition, which means the way in which one thinks about something, and thus regulate and control it. This is what the term metacognition, thinking about one’s own thinking, stands for.
Human thinking tends to biases and faults. Both are often caused by fast thinking. Certain biases occur in mathematical thinking. Overall, this makes it necessary to think slow and to reflect on one’s own thinking in a targeted manner.
The cognitive processes of thinking, learning and understanding in mathematics become more effective and successful when they are supplemented and extended by metacognitive processes. However, it depends on a specific design of the mathematics lessons and the corresponding tasks in mathematics.Subject Classification: 97C30, 97C70, 97D40, 97D50, 97D70
