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The tradition of problem-posing in Hungarian mathematics teaching
233-254Views:124Based on the literature, Pólya was influential in problem-posing research. The present paper draws attention to a book written with Pólya's collaboration, which has not yet received sufficient emphasis in the problem-posing literature. On the other hand, Pólya's impact on mathematics education in Hungary has been significant, including the problem-posing paradigm. Two works, published only in Hungarian, that rely heavily on problem-posing are highlighted. Furthermore, it is presented how problem-posing appeared in the Hungarian Complex Mathematics Teaching Experiment (1962-78) led by Tamás Varga.
Subject Classification: 97D50
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Teaching correlation and regression in three European countries
161-183Views:31In 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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What does ICT help and does not help?
33-49Views:77Year by year, ICT tools and related teaching methods are evolving a lot. Since 2016, the author of the present lines has been looking for a connection between them that supports the development of mathematical competencies and could be integrated into Transcarpathian minority Hungarian language education too. As a doctoral student at the University of Debrecen, I experienced, for example, how the interactive whiteboard revolutionized illustration in Hungarian mathematics teaching, and how it facilitated students' involvement. During my research of teaching in this regard, in some cases, the digital solution had advantageous effects versus concrete-manipulative representation of
Bruner's too.
At the same time, ICT "canned" learning materials (videos, presentations, ...) allow for a shift towards repetitive learning instead of simultaneous active participation, which can be compensated for by the "retrieval-enhanced" learning method.
I have conducted and intend to conduct several research projects in a Transcarpathian Hungarian primary school. In the research so far, I examined whether, in addition to the financial and infrastructural features of the Transcarpathian Hungarian school, the increased "ICT-supported" and the "retrieval-enhanced" learning method could be integrated into institutional mathematics education. I examined the use of two types of ICT devices: one was the interactive whiteboard, and the other was providing one computer per student.
In this article, I describe my experiences, gained during one semester, in the class taught with the interactive whiteboard on the one hand, and in the class taught according to the "retrieval-enhanced" learning method on the other hand.
I compare the effectiveness of the classes to their previous achievements, to each other, and to a class in Hungary.Subject Classification: 97U70
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Regula falsi in lower secondary school education II
121-142Views:65The aim of this paper is to investigate the pupils' word problem solving strategies in lower secondary school education. Students prior experiences with solving word problems by arithmetic methods can create serious difficulties in the transition from arithmetic to algebra. The arithmetical methods are mainly based on manipulation with numbers. When pupils are faced with the methods of algebra they often have difficulty in formulating algebraic equations to represent the information given in word problems. Their troubles are manifested in the meaning they give to the unknown, their interpretation what an equation is, and the methods they choose to set up and solve equations. Therefore they mainly use arithmetical and numerical checking methods to solve word problems. In this situation it is necessary to introduce alternative methods which make the transition from arithmetic to algebra more smooth. In the following we will give a detailed presentation of the false position method. In our opinion this method is useful in the lower secondary school educational processes, especially to reduce the great number of random trial-and-error problem solving attempts among the lower secondary school pupils. We will also show the results of some problem solving activities among grade 6-8 pupils. We analysed their problem solving strategies and we compared our findings with the results of other research works.
Subject Classification: 97-03, 97-11, 97B10, 97B50, 97D40, 97F10, 97H10, 97H20, 97H30, 97N10, 97N20
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Task variations for backtrack
107-120Views:41This article has been written for informatics teachers who want to issue back-track based tasks on their lessons or as homework or on competitions. We present a few methods to generate a more complicated problem from a simpler task, which will be more complex, and its solution needs a good idea or trick. Starting from an example, we lead the reader through increasingly di cult task variations.
Subject Classification: 97P50
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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences, April 1-3, 2022 Baja, Hungary
135-155Views:134The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Baja, Hungary, at Eötvös József College, from the 1st to the 3th of April, 2022. It was organized by the Doctoral School of Mathematical and Computational Sciences of the University of Debrecen and by Eötvös József College. The 62 participants - including 18 PhD students - came from 8 countries and represented 26 institutions of higher and secondary education. There were 3 plenary and 40 session talks in the program.
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Promoting a meaningful learning of double integrals through routes of digital tasks
107-134Views:112Within a wider project aimed at innovating the teaching of mathematics for freshmen, in this study we describe the design and the implementation of two routes of digital tasks aimed at fostering students' approach to double integrals. The tasks are built on a formative assessment frame and classical works on problem solving. They provide facilitative and response-specific feedback and the possibility to request different hints. In this way, students may be guided to the development of well-connected knowledge, operative and decision-making skills. We investigated the effects of the interaction with the digital tasks on the learning of engineering freshmen, by comparing the behaviours of students who worked with the digital tasks (experimental group, N=19) and students who did not (control group, N=19). We detected that students in the experimental group showed more exibility of thinking and obtained better results in the final exam than students in the control group. The results confirmed the effectiveness of the experimental educational path and offered us interesting indications for further studies.
Subject Classification: 97D40, 97U70, 44A45
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The shift of contents in prototypical tasks used in education reforms
203-219Views:68The paper discusses the shift of contents in prototypical tasks provoked by the current educational reform in Austria. The paper starts with the educational backboard of the process of changes in particular with the out tting of the students' abilities in different taxonomies and its implementation in the competence models of Mathematics. A methodological didactical point of view on the process is given additionally. Examples out of a specific collection of math problems which arise from the educational reform are integrated and analysed in the context of educational principles and methods. The discussion ends with a short evaluation of the role of traditional approaches to tasks in the ongoing reform. A bundle of tasks as proof that they are still alive is presented finally.
Subject Classification: 97B50, 97D40, 97D50
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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: February 1-3, 2019 Stúrovo, Slovakia
105-129Views:107The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Sturovo, Slovakia from the 1st to the 3th of February, 2019. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen. The 63 participants – including 17 PhD students – came from 7 countries, 22 cities and represented 36 institutions of higher and secondary education. There were 4 plenary, 42 session talks and 7 poster presentations in the program.
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Many paths lead to statistical inference: Should teaching it focus on elementary approaches or reflect this multiplicity?
259-293Views:50For 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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A retrospective look at discovery learning using the Pósa Method in three Hungarian secondary mathematics classrooms
183-202Views:152While 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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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: 31 March – 2 April, 2023 Oradea, Romania
83-107Views:132The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Oradea, Romania, at Partium Christian University, from 31 March to 2 April, 2023. It was organized by the Doctoral School of Mathematical and Computational Sciences of the University of Debrecen and Partium Christian University. The 85 participants – including 18 PhD students – came from 9 countries and represented 30 institutions of higher and secondary education. There were 4 plenary and 53 session talks in the program.
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Young women's barriers to choose IT and methods to overcome them - A case study from Hungary
77-101Views:119Women'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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Mathematical Laboratory: Semiotic mediation and cultural artefacts in the mathematics classroom
183-195Views:55Aim 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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Teaching model-based testing
1-17Views:938Different testing methodologies should play an important role in the education of informatics. In the model-based testing (MBT) approach, the specification of the system is described with a formal model. This model can be used to revise the correctness of the specification and as a starting point for automatic test generation. The main problem with MBT is however, that there is a huge gap between theory and practice and that this approach has a high learning curve. To cope with these problems, current paper shows, how the MBT approach can be introduced to students through a small scale example.
Subject Classification: P50
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Solution of an open reality based word-problem in two secondary schools
143-156Views:80This survey through an open reality based word problem is intended to assess - in two secondary schools in Komárom (Hungary) and in Komarno (Slovakia, Hungarian name: Révkomárom) in grade 10 - the ability of students to realize openness of a task. The comparison is justified by the fact that the language of teaching is Hungarian in both secondary schools, but with different curricula. This survey is related to the Content Pedagogy Research Program by the Hungarian Academy of Sciences. It is preceded by several surveys with a word problem (Pocket Money) of the third author and led by her between 2012 and 2015, and within that project in 2017 within a large sample test, among about 1500 students and university students in Hungary (?, ?) (?, ?). In our research we wanted first to assess how openly work students in two schools of the two cities mentioned in solving the same task. The answer to this question was similar to the large sample test results, so most of the students worked in a closed way, when solving this word problem. So we went on and tried to explore how students thought about their own solution given to this task, through mixed-type interviews.
Subject Classification: 97D70, 97F90, 97D50, 97M10
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Zur Veränderung des Stellenwertesvon Beweisen im Mathematikunterricht - eine Analyse von ungarischen Abiturprüfungenzwischen 1981 und 2020
35-55Views:43Proofs are not just an essential, crucial part of mathematics as a science, they also have a long tradition in Hungarian mathematics classrooms. However, the school in general and, mathematics education in particular, have been changed in the last few decades enormously, including the final secondary school examinations in mathematics. The current paper's main goal is to answer the question, how has been changed the weight and the content of reasoning and especially proving tasks in the relevant examinations.
Subject Classification: 97E54, 97D64, 97U44
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Categorising question question relationships in the Pósa method
91-100Views:42The doctoral research of the author – with a reverse didactic engineering (RDE) methodology – aims at reconstructing the theoretical background of the ‘intuitively developed’ Pósa method for inquiry-based learning mathematics (IBME) in Hungarian talent education. Preliminary results of the second step of this theorization is presented, which applies tools of the Anthropological Theory of the Didactic (ATD). A model is proposed for categorizing question-question relationship with 3 categories: helping question, follow-up question and question of a kernel. The first two of them are claimed to represent two types (relevant or not) of generating-derived questions relationship. The model is also a prospective tool for connected task- and curriculum design and analysis within IBME development.
Subject Classification: 97D20, 97D40, 97D50, 97E50, 97K30
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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2020 Sárospatak, Hungary
243-271Views:74The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Sárospatak, Hungary, on the Comenius Campus of the Eszterházy Károly University, from the 24th to the 26th of February, 2020. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen and the Eszterházy Károly University. The 76 participants – including 15 PhD students – came from 9 countries, 23 cities and represented 33 institutions of higher and secondary education. There were 4 plenary, 48 session talks and 4 poster presentations in the program.
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Pólya’s influence on (my) research
161-171Views:78In 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