Teaching Mathematics and Computer Science (DE-journals)
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Tétel Szabadon hozzáférhető Development and assessment of non-cognitive skills among engineering students: a comparison across two universities(2025-12-01) Vámosiné Varga, Adrienn; Burján-Mosoni, Boglárka; Rozgonyi, Erika; Homolya, SzilviaNon-cognitive skills, such as logical thinking and problem solving, are crucial for success in engineering fields. To assess these skills in undergraduate engineering students, we designed a targeted test comprising four different types of tasks. The study was conducted among students at the Faculty of Engineering at the University of Debrecen, and the Faculty of Mechanical Engineering and Informatics at the University of Miskolc. The aim of this paper is to analyze the test results, gather students’ feedback, and examine the strength of the relationships between deductive reasoning, diagrammatic reasoning, and algebraic thinking. Subject Classification: 97C20Tétel Szabadon hozzáférhető Solving word problems - a crucial step in lower secondary school education(2025-06-03) Fülöp, ZsoltAlgebra is considered one of the most important parts of Mathematics teaching and learning, because it lays the foundations of abstract thinking as well as reasoning abilities among the lower secondary school pupils who have just transited from the world of numbers and computations to the area of equalities, signs, symbols and letters. The present article focuses on the fact that how the transition from arithmetic to algebra can be made more smooth. We have concentrated our experiments towards the approach of algebraic reasoning and its utilities in filling the gap between arithmetic and beginning algebra in lower secondary school education.We also underline the importance of another approach in overcoming the challenges in the transition from arithmetic to algebra, to enhance and make algebraic learning more effective, with special considerations to word problem-solving processes. In our opinion, we have to go through three phases in the introducing of algebra in Grade 7 Mathematics education: Regula Falsi method (based only on numerical calculations); functional approach to algebra (which combines the numerical computation with letter-symbolic manipulation); and writing equations to word problems. The conclusions of the present article would be helpful to Mathematics teachers for applying themselves to develop the pupils’ interest in word problem-solving processes during algebra teaching classroom activities. Subject Classification: 97B10, 97C30, 97C50, 97D10, 97D40Tétel Szabadon hozzáférhető Self-regulated learning in mathematics lessons at secondary level(2025-12-01) Rusznak, Sophie; Götz, StefanSelf-regulation is a prerequisite to be able to set goals and to find suitable ways to reach them. Furthermore, it is an important ability which affects different areas of every day’s life. In educational context, self-regulation is often linked to self-regulated learning. The concept of self-regulated learning as well as key terms related to this topic such as problem-solving and modelling tasks will be discussed, while an emphasis lays on the role of the teacher. In this paper, a study on the attitudes of mathematics teachers towards self-regulated learning is presented. It focuses on teachers’ assessment of the possibility and limitations of self-regulated learning in mathematics lessons. It can be observed that most of the surveyed teachers try to incorporate self-regulatory processes in their teaching, but encounter difficulties related to various factors, such as their students, framework conditions, and the time required for such learning processes. Subject Classification: 97D10Tétel Szabadon hozzáférhető Metacognition – necessities and possibilities in teaching and learning mathematics(2025-06-03) Sjuts, JohannThis 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, 97D70Tétel Szabadon hozzáférhető Challenges that a teacher-researcher faces during an action research – a case study(2025-06-03) Báró, EmőkeThis paper explores the dual role of the teacher-researcher in a four-year action research project focused on problem-based learning in mathematics. It highlights the challenges faced during the phases of planning, implementation, analysis, and reflection. Drawing on insights from the author’s experiences and observations based on both qualitative and quantitative data collection methods, the study identifies distinct challenges linked to the dual role, like differing design goals or subjective-objective voices. The author also proposes solutions to the identified challenges, such as collaboration with university experts and using reflective practices. Furthermore, the research underscores the beneficial impact of action research on enhancing teachers’ awareness and bridging the theory-practice gap, calling for further studies in this area. Subject Classification: 97D99Tétel Szabadon hozzáférhető Professional Competence in science education(2025-12-01) Fuchs, Karl JosefThe article begins with a brief introduction aimed at sensitizing the reader to the perception of a trend in Mathematics and Computer Science Education publications towards empirical studies. Contrary to the stated trend, the characterization of Professional Competence is intended to serve as the guiding concept for the paper. The role of Professional Competence is discussed in various areas incorporating context-relevant publications in consecutive chapters. The discussion starts with the area of material development, covering Educational Standards and ends with Didactic Principles. Subject Classification: 97xxx, 94xxxTétel Szabadon hozzáférhető On the nine-point conic of hyperbolic triangles(2025-12-01) Szilasi, ZoltánIn the Cayley–Klein model, we review some basic results concerning the geometry of hyperbolic triangles. We introduce a new definition of the circumcircle of a hyperbolic triangle, guaranteed to exist in every case, and describe its main properties. Our central theorem establishes, by means of purely elementary projective geometric arguments, that a hyperbolic triangle has a nine-point conic if and only if it is a right triangle. Subject Classification: 51M09Tétel Szabadon hozzáférhető Apollonea.com project: integrating geometry and collaboration in education(2025-12-01) Fabián, TomášThis article presents the Apollonea.com project, which aims to make the solutions to Apollonius’ problems accessible to students and teachers through modern technology. The web platform contains more than 150 interactive constructions created by students using GeoGebra, allowing for dynamic manipulation and visualization of solutions to various variants of Apollonius’ problems. The project combines classical geometric problems with an interdisciplinary approach, teamwork, and the use of modern technology. The article describes the process of developing the Apollonea.com website, the use of GeoGebra in the project, the structure and functions of the website, and its educational benefits in enhancing students’ geometric skills. The project demonstrates how traditional mathematics education can be connected with modern ICT tools. Subject Classification: 97U50, 97G40, 51M04, 68U05Tétel Szabadon hozzáférhető Conversion between different symbolic representations of rational numbers among 9th-grade students(2025-06-03) Torma, Gábor; Kosztolányi, JózsefOur research involved nearly 800 ninth-grade secondary school students (aged 14-15) during the first weeks of the 2023/2024 school year. Less than 40% of students solved the text problems related to common fractions and percentages correctly. In terms of student solutions, pupils showed a higher success rate when the text of the problem contained common fractions, and the solution had to be given as a percentage. In this case, the success rate of switching between different symbolic representations of rational numbers (common fraction, percentage) was also higher. Observation of the methods used to solve also suggests that the majority of students are not flexible enough when it comes to switching between different representations. Subject Classification: 97F80, 97D70Tétel Szabadon hozzáférhető Impact of teacher communication skills on students’ classroom engagement in mathematics learning(2025-06-03) Chianson-Akaa, Martha Mimi; Achor, Emmanuel Edoja; Rott, BenjaminThe study investigated teachers’ communication skills in relation to students’ classroom engagement in mathematics learning. The study area is Makurdi Local Government Area in Benue State, Nigeria. This study adopted a cross-sectional research design. A sample of 34 teachers and 204 students were drawn from twenty schools. Two researcher-structured instruments were used for data collection: Mathematics Teacher’s Communication Skills Questionnaire (MTCSQ) and Students’ Engagement in Mathematics Questionnaire (SEMQ). Descriptive statistics, analysis of variance, and independent t-tests were used to address the research questions and test the hypotheses. It was found that there is significant difference among the mean ratings on behavioural, and emotional engagements of students in mathematics classes taught by teachers with poor, fair, and good communication skills. There is no significant difference among the mean ratings on combined and cognitive engagements of students in mathematics classes taught by teachers with poor, fair, and good communication skills. Equally found was that the differences between male and female students’ mean engagement in mathematics for poor, fair, and good communication skill classes were not statistically significant. It was then recommended that teacher communication skills should be fashioned in ways to accommodate and strengthen each component of students’ engagement. Subject Classification: 97C70Tétel Szabadon hozzáférhető Sage and scribe – asymmetrical pair work that can easily fit into any mathematics lesson, yet still have cooperative benefits(2024-12-20) Kovács-Kószó, Eszter; Czakó, Viktória; Kosztolányi, JózsefThis article uses a case study experiment to learn the characteristics of a pair work, called the sage and scribe method (Kagan, 2008). We also wished to explore the positive and negative effects of the systematic application of this single cooperative element without any other structural changes during the lessons. In the case study experiment, we asked two teachers, accustomed to traditional frontal teaching methods, to substitute individual work tasks in their standard lesson plans with the sage and scribe method. Our experiments indicate that this method wastes insignificant time, requires little extra effort on the part of the teacher, yet has many of the positive effects of cooperative methods: in our experiments, students received immediate feedback, corrected each other’s mistakes, learned from each other in meaningful discussions and engaged in collaborative reasoning to address emerging problems. Subject Classification: 97D40Tétel Szabadon hozzáférhető Exploring the basic concepts of Calculus through a case study on motion in gravitational space(2024-12-20) Tekeli, Miklós; Karsai, János; Kopasz, KatalinIn 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, 97M50Tétel Szabadon hozzáférhető Didactical remarks on the changes in the requirements of the matriculation exam in Mathematics in Hungary(2024-12-20) Geszler, Evelin AnnaStudents 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, 97U40Tétel Szabadon hozzáférhető Strategies used in solving proportion problems among seventh-grade students(2025-12-01) Torma, Gábor; Kosztolányi, JózsefIn 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, 97F80Tétel Szabadon hozzáférhető survey on how students seek information on the internet(2006-06-01) Krausz-Princz, MáriaNavigating among the information available on the Internet has become an expectation for the members of the information society we are living in. This especially applies to students of higher education, the intellectuals of the future. It is a general experience that most users make one or two word searches and they don't know about the possibilities offered by various search engines, which can make searches more effective. Given results from abroad we have set up a study among the students of the University of Debrecen (UD) about their use of the Internet, their knowledge of searching strategies and techniques, their perceptions of the effectiveness and efficiency of search engines. This paper reports the results of this study. The results imply that it is imperative that area should be included in the curriculum.Tétel Szabadon hozzáférhető Mathematics in Good Will Hunting I(2012-12-01) Korándi, József; Pluhár, GabriellaThis is the first part of a three paper long series exploring the role of mathematicians and of the mathematical content occurring in popular media. In particular, we analyze the movie Good Will Hunting. In the present paper we investigate stereotypes about mathematicians living in the society and appearing in Good Will Hunting.Tétel Szabadon hozzáférhető ungewöhnlicher Weg zu Jakob Steiners Umellipse eines Dreiecks und zur Steiner–Hypozykloide(2004-06-01) , OswaldIn real projective geometry of triangles two problems of collinear points are discussed. The problems differ only from the running through the vertices of a given triangle ABC. Resolving the problems we find two cubic curves kS and kT . Affine specialization leads to the circumscribed Steiner ellipse about the triangle ABC and shows us this ellipse in more general surroundings. Euclidean specialization leads to Steiners three-cusped hypocycloid.Tétel Szabadon hozzáférhető Key concepts in informatics(2014-06-01) Gudenus, László; Helfenbein, Henrik; Zsakó, László"The system of key concepts contains the most important key concepts related to the development tasks of knowledge areas and their vertical hierarchy as well as the links of basic key concepts of different knowledge areas. When you try to identify the key concepts of a field of knowledge, you should ask the following questions: Which are the concepts that are the nodes of the concept net and can be related to many other concepts? Which are the concepts that necessarily keep re-appearing in different contexts when interpreting what you have learnt before? Which are the concepts that arrange specific facts in structures, which contribute to interpreting and apprehending new information and experience? Which are the concepts that – if you are unfamiliar with and unaware of – inhibits you in systematizing various items of knowledge or sensibly utilizing them?" [8] One of the most important of these concepts is the document.Tétel Szabadon hozzáférhető Solving mathematical problems by using Maple factorization algorithms(2007-12-01) Princz, MáriaComputer 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.Tétel Szabadon hozzáférhető Dynamic geometry systems in teaching geometry(2004-06-01) Nagy-Kondor, RitaComputer drawing programs opened up new opportunities in the teaching of geometry: they make it possible to create a multitude of drawings quickly, accurately and with flexibly changing the input data, and thus make the discovery of geometry an easier process. The objective of this paper is to demonstrate the application possibilities of dynamic geometric systems in primary and secondary schools, as well as in distance education. A general characteristic feature of these systems is that they store the steps of the construction, and can also execute those steps after a change is made to the input data. For the demonstration of the applications, we chose the Cinderella program. We had an opportunity to test some parts of the present paper in an eighth grade primary school.