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Development and assessment of non-cognitive skills among engineering students: a comparison across two universities
161-182Views:111Non-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: 97C20
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Mobile devices in Hungarian university statistical education
19-48Views:192The 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
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Mapping students’ motivation in a problem oriented mathematics classroom
111-121Views:225This research focuses on mapping students’ motivation by implementing problem-solving activities, namely how the problem-oriented approach affects the students’ commitment, motivation, and attitude to learning. As a practicing teacher, the author faced difficulties with motivation and sought to improve her practice in the form of action research as described in this paper. Based on the literature, the author describes sources of motivation as task interest, social environment, opportunity to discover, knowing why, using objects, and helping others. The author discusses the effect of problem-oriented teaching on the motivation of 7th-grade students. In this paper, the results of two lessons are presented.
Subject Classification: 97C20, 97D40, 97D50, 97D60
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Young women's barriers to choose IT and methods to overcome them - A case study from Hungary
77-101Views:298Women's scarcity in the STEM, especially in the IT sector is pronouncedly evident. Young women are obstructed from entering and remaining in IT by a broad range of social, educational, and labor market factors. In our paper, we would like to analyze the main barriers girls face in choosing IT, while also proposing potential methods to help them overcome these obstacles. In the second part of the paper, we will present a case study to illustrate in detail how the combination of the above methods can be put into practice to address and tackle the complex set of barriers girls face. We will first introduce a Hungarian annual program, Girls' Day ("Lányok napja"), specifically aimed to promote STEM to girls, then we will present two specific events organized for the 2020 edition of the program and designed with the above principles in mind. The interactive presentation, exposing girls to female role models of the field in a gamified way, and a game development exercise, building Scratch programming skills, have attempted to provide young women both with positive perspectives and experiences in IT, which are instrumental in helping them to surmount entrenched obstacles and raise their interest in the field.
Subject Classification: 97P10, 97U30
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Concept systematization with concept maps in data modelling
149-166Views:149An important goal of concept learning is that students can allocate concepts in the hierarchical system of concepts. In the data modelling course, first, we supported concept systematization with worksheets in which the students had to fill in the blank hierarchical figures of classification of the concepts or blank Venn diagrams describing the relationships between concepts. The hierarchical systems, however, are somewhat restricted to the description of connections. The filling in Venn diagrams did not deliver the expected result, so our attention turned to concept maps. In this paper we introduce the concept maps we drew. Then we evaluate the results of concept mapping survey conducted among students. The survey was done in three courses. We compare the results of our survey with the result of an earlier concept systematising survey. -
Teaching agile operation and leadership through linked university courses
1-32Views:212Agile 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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Our digital education habits in the light of their environmental impact: the role of green computing in education
69-86Views:267With the increasing use of IT tools, the environmental impacts they generate have also increased. Education is increasingly relying on digital tools to become a major emitter of CO2 itself. Therefore, the task of education is to teach future generations how to use IT tools efficiently while being environmentally aware. In addition to some forms of green computing, we show the level and ratio of those teachers who have corresponding IT knowledge in the Hungarian education. In this study, we present the justification of the problem through a case study, which estimates the Internet traffic of a website streaming popular educational resources. In addition, we will examine the extent to which national and international educational organization and guidance documents address the development of digital environmentally aware thinking. Based on the content of this study, we suggest some considerations for content developers to decide if they really need to create the digital content.
Subject Classification: 97P99, 94-06, 94-02
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Teaching correlation and regression in three European countries
161-183Views:249In this article, we compare the presence of correlation and regression analysis in secondary education of Ireland, the Netherlands and Luxembourg, through the analysis of final-exam tasks and curricula based on the Anthropological Theory of Didactics (ATD). It points out that the same topic can appear in different ways and extent in curricula, even if the mathematics teaching goals are similar. This article is a kind of introduction to the research that explores the possibilities for the appearance of these concepts in the Hungarian mathematics education. Therefore, in the second part of the article, Hungarian curricular goals are included, and it is shown which methodology of the three studied countries has the greatest curricular basis in Hungary.
Subject Classification: 97xxx
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Mathematical Laboratory: Semiotic mediation and cultural artefacts in the mathematics classroom
183-195Views:274Aim of this presentation is to summarize the influence of Tamas Varga on the Italian research and practice concerning didactics of mathematics since the 70s of the 20th centuries. While being in Budapest for the Conference I noticed that this influence was not known by most Hungarian mathematics educators. I guess that also in Italy, only the teacher educators of my generation know Varga’s influence on the teaching and learning of mathematics in primary school. Hence I start from a brief summary of development of mathematics curriculum in Italy (mainly in primary school) in the last decades of the 20th century. I focus some elements that may be connected with Varga’s influence and, later, some recent development of them.
Subject Classification: 97G20, 97-U6, 97A40
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Infimum problems derived from the proofs of some generalized Schwarz inequalities
41-57Views:214We define f(a;b)(r) = ar + b/r for all a, b, r Є R with r > 0. And, for some subsets A of R, we determine FA_+ (a; b) = inf (r Є A_+) f(a,b) (r) ; where A_+ ={r Є A : r > 0}. The above in ma are mainly motivated by the proofs of some recent generalized Schwarz inequalities established by the present authors.
Subject Classification: I35
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Conversion between different symbolic representations of rational numbers among 9th-grade students
29-45Views:309Our 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, 97D70
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Pólya’s influence on (my) research
161-171Views:264In this article, I outline the influence of George Pólya's work on research in different areas and especially on mathematics education, namely heuristics and models of the problem-solving process. On a more personal note, I will go into some details regarding Pólya's influence on my own work in mathematical problem solving with a focus on the research project for my PhD thesis.
Subject Classification: 97xxx
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Tamás Varga’s reform movement and the Hungarian Guided Discovery approach
11-28Views:485This paper presents Tamás Varga’s work focusing especially on the Hungarian Complex Mathematics Education reform project led by him between 1963 and 1978 and the underlying conception on mathematics education named “Guided Discovery approach”. In the first part, I describe Varga’s career. In the second part, I situate his reform project in its international and national historical context, including the international “New Math” movement and the “Guided Discovery” teaching tradition, something which is embedded in Hungarian mathematical culture. In the third part, I propose a didactic analysis of Varga’s conception on mathematics education, underlining especially certain of its characteristics which can be related to Inquiry Based Mathematics Education. Finally I briefly discuss Varga’s legacy today.
Subject Classification: 97-03, 97B20, 97D20, 97D40, 97D50
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A retrospective look at discovery learning using the Pósa Method in three Hungarian secondary mathematics classrooms
183-202Views:350While the Pósa Method was originally created for mathematical talent management through extracurricular activities, three "average" public secondary school classrooms in Hungary have taken part in a four-year experiment to implement the Pósa Method, which is based on guided discovery learning of mathematics. In this paper, we examine the students' and teachers' reflections on the Pósa Method, and how student perspectives have changed between their first and last year of high school. Overall, teachers and students had a positive experience with the Pósa Method. Furthermore, our research indicated that this implementation has met several objectives of the Pósa Method, including enjoyment of mathematics and autonomous thinking.
Subject Classification: 97D40
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Many paths lead to statistical inference: Should teaching it focus on elementary approaches or reflect this multiplicity?
259-293Views:241For statistics education, a key question is how to design learning paths to statistical inference that are elementary enough that the learners can understand the concepts and that are rich enough to develop the full complexity of statistical inference later on. There are two ways to approach this problem: One is to restrict the complexity. Informal Inference considers a reduced situation and refers to resampling methods, which may be completely outsourced to computing power. The other is to find informal ways to explore situations of statistical inference, also supported with the graphing and simulating facilities of computers. The latter orientates towards the full complexity of statistical inference though it tries to reduce it for the early learning encoun-ters. We argue for the informal-ways approach as it connects to Bayesian methods of inference and allows for a full concept of probability in comparison to the Informal Inference, which reduces probability to a mere frequentist concept and – based on this – restricts inference to a few special cases. We also develop a didactic framework for our analysis, which includes the approach of Tamás Varga.
Subject Classification: 97K10, 97K70, 97K50, 97D20
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Interdisciplinary Secondary-School Workshop: Physics and Statistics
179-194Views:167The paper describes a teaching unit of four hours with talented students aged 15-18. The workshop was designed as a problem-based sequence of tasks and was intended to deal with judging dice whether they are regular or loaded. We first introduced the students to the physics of free rotations of rigid bodies to develop the physics background of rolling dice. The highlight of this part was to recognise that cubes made from homogeneous material are the optimal form for six-sided objects leading to equal probabilities of the single faces. Experiments with all five regular bodies would lead to similar results; nevertheless, in our experiments we focused on regular cubes. This reinsures that the participants have their own experience with the context. Then, we studied rolling dice from the probabilistic point of view and – step-by-step – by extending tasks and simulations, we introduced the idea of the chi-squared test interactively with the students. The physics and the statistics part of the paper are largely independent and can be also be read separately. The success of the statistics part is best described by the fact that the students recognised that in some cases of loaded dice, it is easier to detect that property and in other cases one would need many data to make a decision with small error probabilities. A physical examination of the dice under inspection can lead to a quick and correct decision. Yet, such a physical check may fail for some reason. However, a statistical test will always lead to reasonable decision, but may require a large database. Furthermore, especially for smaller datasets, balancing the risk of different types of errors remains a key issue, which is a characteristic feature of statistical testing.
Subject Classification: F90, K90, M50, R30
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Self-regulated learning in mathematics lessons at secondary level
139-160Views:99Self-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: 97D10
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Psychology - an inherent part of mathematics education
1-18Views:273On the chronology of individual stations of psychology and their effect on mathematics education designed as working document for use in teacher training.
The article is structured as a literature survey which covers the numerous movements of psychology towards mathematics education. The current role of psychology in mathematics education documented by different statements and models of mathematics education should provide a basis for the subsequent investigations. A longitudinal analysis pausing at essential marks takes centre of the continuative considerations. The observed space of time in the chapter covers a wide range. It starts with the separation of psychology from philosophy as a self-contained discipline in the middle of the 19th and ends with the beginning of the 21st century. Each stop states the names of the originators and the branches of psychology they founded. These stops are accompanied by short descriptions of each single research objective on the one hand, and their contributions to mathematics education on the other hand. For this purpose, context-relevant publications in mathematics education are integrated and analysed. The evaluation of the influence of concepts of psychology on teaching technology in mathematics is addressed repeatedly and of great importance. The layout of this paper is designed for the use as a template for a unit in teacher-training courses. The conclusion of the article where the author refers to experiences when teaching elements of psychology in mathematics education courses at several universities in Austria is intended for a proof on behalf of the requested use.Subject Classification: 01A70, 01-XX, 97-03, 97D80
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A computational thinking problem-thread for grade 7 students and above from the Pósa method
101-110Views:279Lajos 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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Wichtige Momente aus der ungarischen Geschichte des Analysisunterrichts
57-76Views:179Törner et al. (2014) paper gives an outstanding review about teaching analysis at high school level in (Western) Europe. We tried to extend this paper with some results from the Hungarian Math History (Beke and Rátz 1897-1924, after second World War 1949-1960, the current situation-first of all based on schoolbooks, and we also included an experiment from 1984-1989 by E. Deák, which was interrupted and partially forgotten). In summary, this paper deals with the turning points of the brief history of teaching secondary school analysis in the XXth century in Hungary, including some conclusions at the end.
Subject Classification: 97A30, 97C30, 97D30, 97E50, 97I20, 97I40, 97U20
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Rational errors in learning fractions among 5th grade students
347-358Views:195Our paper focuses on empirical research in which we map out the errors in learning fractions. Errors are often logically consistent and rule-based rather than being random. When people face solving an unfamiliar problem, they usually construct rules or strategies in order to solve it (Van Lehn, 1983). These strategies tend to be systematic, often make ‘sense’ to the people who created them but often lead to incorrect solutions (Ben-Zeev, 1996). These mistakes were named rational errors by Ben-Zeev (1996). The research aims to show that when learning fractions, students produce such errors, identified in the literature, and that students who make these kinds of mistakes achieve low results in mathematics tests. The research was done among 5th-grade students.
Subject Classification: 97C10, 97C30, 97C70, 97D60, 97D70, 97F50
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Guided Discovery in Hungarian Education Using Problem Threads: The Pósa Method in Secondary Mathematics Classrooms
51-67Views:272In Hungary, ‘guided discovery’ refers to instruction in which students learn mathematical concepts through task sequences that foster mathematical thinking. A prominent figure of guided discovery is Lajos Pósa, who developed his method to teach gifted students. Rather than teaching mathematics through thematic blocks, the Pósa Method employs webs of interconnected problem threads in which problems are built on each other, and different threads are presented simultaneously, so that students work on problems from multiple threads at the same time. It was found that this method has been successful as extracurricular training for gifted students since the 1980s; however since 2017, as part of an ongoing research, the method has been applied to mainstream curriculum in two public secondary school classrooms. The present paper examines the design and implementation processes of problem threads in this public secondary school context.
Subject Classification: 97D40
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Teaching fractions at elementary level in the light of Hungarian mathematics textbooks in Romania
149-159Views:198According to the new curriculum in Romania, fractions are introduced in the second grade. The present study analyses Hungarian elementary mathematics textbooks on the topic of fractions focusing on the types of tasks in the textbooks, the significance of representations and the proportion of word problems. Additionally, the paper presents a questionnaire-based research on teachers’ opinion regarding the adequacy and sufficiency of the digital materials and exercises related to fractions in the textbooks.
Subject Classification: 97F40, 97F80, 97U20, 97U50
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Group Work at High School According to the Method of Tamás Varga
167-176Views:248The aim of our research is to develop students’ logical thinking. For this reason, Hungarian mathematics teachers need to be encouraged to try new methods which induce greater student involvement. Research all over the world prove that self-instruction or self-verbalizing has high effect on the learning process. This was one of the key elements of Tamás Varga’s experiment in high school. In our classroom experiments we are using a special cooperative method from Kagan among 14-18 years old students, called Sage and Scribe structure. We are looking for the answers to the following question: Does this method make mathematics lessons more enjoyable and more comfortable for students? Furthermore, we assume this structure could open the gate toward other collaborative and cooperative teaching technics.
Subject Classification: 97D40
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"On the way" to the function concept - experiences of a teaching experiment
17-39Views:235Knowing, 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
