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The Project Method and investigation in school mathematics
241-255Views:147The Project Method (PM) is becoming more common in the teaching of mathematics. Most of the time, Project Method means solving open and relatively wide formulated problems for the application of particular mathematical topics and the solving of everyday life problems.
At present many experts in the theory of teaching mathematics advocate teaching activities as the characteristic for most mathematical work in the classroom. Thus, there is a question: whether it is possible or eventual desirable to use the PM for solving genuine mathematical problems. This paper deals with this question and discusses the connection between the PM and investigation of new mathematical knowledge for students. Our experience has shown that the PM in connection with investigations can be a useful and effective approach to teaching mathematics. -
Über die sogenannte Regel von de l’Hospital im Mathematikunterricht
193-208Views:99The aim of this paper is to provide an insight into the problems of the socalled indeterminate expressions, in order to make the students understand them better. The paper deals with the conditions and the proof of the theorem about the limit of a quotient of certain functions of one variable, usually named after l'Hospital. The question is of some interest, since the formulation of the result in several textbooks often appears redundant and the proof is more complex than necessary. First, the historical background is briefly sketched. Second, the theorem is formulated and justified, where three different, simple proof techniques are presented. Finally, possible applications are suggested for teaching, which are usually not treated in this problem area. -
Many paths lead to statistical inference: Should teaching it focus on elementary approaches or reflect this multiplicity?
259-293Views:213For 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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Bemerkungen zur Prototypentheorie – Begriffs - und Konzeptbildung
365-389Views:106Psychological theories of prototypes are put forward by mathematical modelling. Some didactical consequences are discussed on the background of this analysis. By the help of an example (classification of convex quadrangles) hints are given for didactical interpretations of actual models of cognitive psychology dealing with problems of constructing prototypes. -
Analysis of a problem in plane geometry discussed in an 11th grade group study session
181-193Views:113The main aim of this paper is to show those strategies and proof methods we try to teach in secondary maths education through an interesting geometric problem: Find a relation for the sides of a triangle where an angle is the double of another angle. Is the converse also true? Is it possible to generalize the problem? We try to answer these questions while discussing the upcoming difficulties in detail and presenting more possible solutions. Hopefully the paper can be successfully used in study group sessions and problem solving seminars in secondary schools. -
Research on IT language use at a company
203-219Views:150The 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. -
Categorising question question relationships in the Pósa method
91-100Views:213The 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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Mathematical Doctoral School of the Mathematical Seminar of the University of Debrecen at the beginning of the 20th century (Debrecen, 1927-1940)
195-214Views:178In this article, we present the life and carrier of Professor Lajos Dávid, and those 16 mathematical dissertations, along with their authors, which were written under the supervision of Professor Dávid between 1927 and 1940. At the time mentioned, Lajos Dávid was the leader of the Mathematical Seminar of the University of Debrecen. The themes of the dissertations were connected with his scientific work, such as the history of mathematics (the two Bolyais), or his research work in mathematical analysis (arithmetic-geometric mean). -
The Mathematics Education Traditions of Europe (METE) Project
353-364Views:115This study is based on the work of the METE (Mathematics Education Traditions of Europe Project) team. Following a short introduction of the project, its theoretical background, methods and research design are presented in the next three sections. In the 4th section the tools developed by the METE team for qualitative and quantitative analysis of the collected data are discussed in details. The 5th section contains some personal remarks about using these tools. The 6th section presents the main results of the project, followed by a summary of the project's educational and theoretical significance. -
Development of classification module for automated question generation framework
89-102Views:150Automatic question generation is in the focus of recent researches which includes bordering disciplines like education, text mining, knowledge-engineering. The elaborated system generates multi-choice questions from textbooks without using an external semantic database. One of the base modules of the system is the classification module defining the extracted word. This paper describes modules of the framework including a detailed analysis of the classification part. We show the operability of the elaborated system through a practical test. -
An examination of descriptive statistical knowledge of 12th-grade secondary school students - comparing and analysing their answers to closed and open questions
63-81Views:192In 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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Transition from arithmetic to algebra in primary school education
225-248Views:188The main aim of this paper is to report a study that explores the thinking strategies and the most frequent errors of Hungarian grade 5-8 students in solving some problems involving arithmetical first-degree equations. The present study also aims at identifying the main arithmetical strategies attempted to solve a problem that can be solved algebraically. The analysis focuses on the shifts from arithmetic computations to algebraic thinking and procedures. Our second aim was to identify the main difficulties which students face when they have to deal with mathematical word problems. The errors made by students were categorized by stages in the problem solving process. The students' written works were analyzed seeking for patterns and regularities concerning both of the methods used by the students and the errors which occured in the problem solving process. In this paper, three prominent error types and their causes are discussed. -
Willy Servais and Tamás Varga A Belgian Hungarian perspective on teaching school mathematics
29-38Views:175Willy Servais and Tamás Varga had a major influence on the development of mathematics education during the 1960s and 1970s, both in their home countries and internationally. In 1971 they jointly published Teaching School Mathematics–A Unesco Source Book, a review of curriculum reforms that were under way in different parts of the world. The book, presenting several modern syllabuses as well as examples of classroom techniques and segments of teacher-student dialogues, provided an often consulted guide to the field of mathematics education. We re-read this book and in this way acquire a unique insight into the modernization efforts of school mathematics during the 1960s and early 1970s. We take this opportunity to discuss the sometimes partly divergent views of Servais and Varga on modern mathematics education as reflected in this book.
Subject Classification: 97-03
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Challenges that a teacher-researcher faces during an action research – a case study
89-99Views:194This 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: 97D99
