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Supporting the education of engineering mathematics using the immediate feedback method
49-61Views:157In the literature, several methods are suggested to deal with problems regarding the efficiency of mathematics education including techniques that help integrate new knowledge into long-term memory. We examined how effective the application of the immediate feedback method is in teaching engineering mathematics. The article presents the method used and the results obtained during the study.
Subject Classification: 97D40, 97D60
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Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 20 - January 22, 2012, Levoča, Slovakia
205-230Views:115The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Levoca, Slovakia from the 20th to the 22th of January, 2012. The 66 participants – including 54 lecturers and 25 PhD students – came from 6 countries, 20 cities and represented 33 institutions of higher and secondary education. The abstract of the talks and the posters and also the list of participants are presented in this report. -
Zur Veränderung des Stellenwertesvon Beweisen im Mathematikunterricht - eine Analyse von ungarischen Abiturprüfungenzwischen 1981 und 2020
35-55Views:153Proofs 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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Mathematical Laboratory: Semiotic mediation and cultural artefacts in the mathematics classroom
183-195Views:203Aim 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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Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2014 Eger, Hungary
117-134Views:110The meeting Researches in Didactics of Mathematics and Computer Sciences
was held in Eger, Hungary from the 24th to the 26th of January, 2014 at the
Eszterházy Károly College. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Eszterházy Károly College in Eger.
The 58 participants – including 43 lecturers and 18 PhD students – came from 7 countries, 15 cities and represented 22 institutions of higher education. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 23-25, 2015 Novi Sad, Serbia
141-162Views:121The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Novi Sad, Serbia from the 23th to the 25th of January, 2015 at the University of Novi Sad. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Department of Mathematics and Informatics of the University of Novi Sad.
The 70 participants – including 42 lecturers, and 18 PhD students – came from 9 countries, 28 cities and represented 40 intstitutions of higher education. -
Smartphones and QR-codes in education - a QR-code learning path for Boolean operations
111-120Views:102During the last few years new technologies have become more and more an integrative part of everyday life. The increase of the possession rate of smartphones by young people is especially impressive. This fact asks us educators to think about a didactically and pedagogically well designed integration of smartphones into our lessons and to bring in ideas and concepts. This paper describes a specific learning path where learners can work step by step on the topic Boolean Operations with QR-Code scanners which have been installed on their smartphones. Student teachers for mathematics who completed the learning path took part in a survey where they were asked questions about their willingness to integrate smartphones into their lessons. The results of the survey are presented in the second part of the paper. -
Levels of students' understanding on infinity
317-337Views:164Here we report some results of a two-year study for grades 5-6 and 7-8 (during the academic years 2001-03). The study included a quantitative survey for approximately 150 Finnish mathematics classes out of which 10 classes were selected to a longitudinal part of the study. Additionally, 40 students from these classes participated also a qualitative study. This paper will focus on students' understanding of infinity and the development of that understanding. The results show that most of the students did not have a proper view of infinity but that the share of able students grew, as the students got older. -
What does ICT help and does not help?
33-49Views:224Year 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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A proposal for an IOI Syllabus
193-216Views:171The International Olympiad in Informatics (IOI) is the premier competition in computing science for secondary education. The competition problems are algorithmic in nature, but the IOI Regulations do not clearly define the scope of the competition. The international olympiads in physics, chemistry, and biology do have an official syllabus, whereas the International Mathematical Olympiad has made the deliberate decision not to have an official syllabus. We argue that the benefits of having an official IOI Syllabus outweigh the disadvantages. Guided by a set of general principles we present a proposal for an IOI Syllabus, divided into four main areas: mathematics, computing science, software engineering, and computer literacy. -
Guided Discovery in Hungarian Education Using Problem Threads: The Pósa Method in Secondary Mathematics Classrooms
51-67Views:227In 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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Artworks as illustrations in Hungarian high school Mathematics textbooks
103-117Views:141Three different series of Hungarian Mathematics textbooks used in grade 9-12 education for the past 30 years have been analysed in this research. Our aim is to show and evaluate how the visual arts have been connected to mathematical ideas in these textbooks. We have applied the six dimensions of evaluation, which have recently been introduced in (Diego-Mantec on, Blanco, Búa Ares, & González Sequeiros, 2019) to categorise the illustrations of the three different series. We show examples for each dimension from the textbooks, and we find that even if the number of artistic illustrations in these coursebooks have significantly increased, in most cases these sporadic examples are not closely related to the mathematical context, mainly used for ornamental purposes to decorate the core text. Based on this classification we conclude that the number of artistic illustrations with underlying math concepts making students' participation more active could and should be significantly increased.
Subject Classification: 97U20
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Teaching meaningful mathematics with the Computer Algebra System MAXIMA using the example of inequalities
53-65Views:125The paper was originally motivated by the request to accentuate the meaningful contribution of inequalities in Mathematics Education. Additionally nationwide approved competences such as estimating come to the fore when organizing mathematical contents along some central Big Ideas. Not least the integration of computers enriches the reasonable discussion of inequalities by modern well accepted methodological principles. The freeware MAXIMA is used as Computer Algebra System (CAS) representatively. -
Verification of human-level proof steps in mathematics education
345-362Views:120Automated mathematics tutorial systems need support from a reasoning module which can verify the correctness of students' contributions. However, current systems typically do not reason at a level similar to the student's reasoning level, and do not fully account for underspecified or ambiguous inputs. We present a domain-independent method for automatically verifying correct proof steps and detecting standard reasoning errors. We use a depth limited BFS proof search to determine and maintain multiple possible interpretations consistent with the given proof step, we are able to resolve or otherwise propagate underspecification and ambiguity which occurs due to unrestricted user input. Our approach has been implemented in ΩmegaCoRe. -
Report of Conference XL. National Conference on Teaching Mathematics, Physics and Computer Science August 22-24, 2016 Székesfehérvár, Hungary
259-276Views:100The XL. National Conference on Teaching Mathematics, Physics and Computer Sciences (MAFIOK) was held in Székesfehérvár, Hungary between 22 and 24 August, 2016 at the Alba Regia Technical Faculty of Óbuda University. For the three-day event, more than 80 persons were registered and more than 40 lectures were given. The fortieth anniversary scientific conference was designed for researchers and teachers in mathematics, physics and informatics to promote modern and efficient education in higher education, and through poster presentations and personal meetings to exchange experience. The opening ceremony of the conference followed by the three plenary lectures took place at the ceremonial hall of the Town Hall. ... -
Über einen allgemeinen Übungsbegriff bei verschiedenen Unterrichtsmethoden in der Planung des Mathematikunterrichtes
175-201Views:128Practice is important in the education of mathematics but is neclected in the didactic of mathematics. One of the reasons is that practice is often defined too "narrowly" and the definitions of practice have in most cases an obscure background theory. In the article a general definition of practice is given, which – in contrast to the usual definitions – views practice from the point of the pupils (practice means activity of pupils). By utilising this definition consequences will be drawn. These consequences serve as for the more exact planning of practice in education as for the analysis of the dependency of practice from teachingsmethods.
In the second part an example will be presented for planning together practice and lesson, in two different teachingsmethods (traditionel, problemsolving). The analysis of both worksheets (one for each method, identical teachingsmaterial) was made on the basis of authors practise in lessons i.e. her own concepts and the experience with pupils at a class 5. On the basis of the expectable solutions is specified – using a criteriacatalog – what was practised.
The analysis of practice leads further to the examination of above mentioned dependency from teachingsmethods. -
Learning and teaching combinatorics with Sage
389-398Views:127Learning Mathematics is not an easy task, since this subject works with especially abstract concepts and sophisticated deductions. Many students lose their interest in the subject due to lack of success. Computer algebra systems (CAS) provide new ways of learning and teaching Mathematics. Numerous teachers use them to demonstrate concepts, deductions and algorithms and to make learning process more interesting especially in higher education. It is an even more efficient way to improve the learning process, if students can use the system themselves, which helps them to practice the curriculum.
Sage is a free, open-source math software system that supports research and teaching algebra, analysis, geometry, number theory, cryptography, numerical computation, and related areas. I have been using it for several years to aid the instruction of Discrete Mathematics at Óbuda University. In this article I show some examples how representations provided by this system can help in teaching combinatorics. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 25-27, 2013 Oradea, Romania
123-143Views:103The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Oradea, Romania from the 25th to the 27th of January, 2013 at the Partium Christian University. It was organized by the PhD School of Mathematics and Computer Sciences of the University of Debrecen and the Partium Christian University in Oradea. The meeting was supported by the project: TAMOP-4.2.2/B/10/1-2010-0024.
The 61 participants – including 50 lecturers and 21 PhD students – came from 5 countries, 22 cities and represented 35 intstitutions of higher education. -
Teaching polygons in the secondary school: a four country comparative study
29-65Views:147This study presents the analysis of four sequences of videotaped lessons on polygons in lower secondary schools (grades 7 and 8) taught by four different teachers in four different countries (Belgium, Flanders, England, Hungary and Spain). Our study is a part of the METE project (Mathematics Educational Traditions in Europe). The aims and methodology of the project are described briefly in the introduction. In the next section of this paper we describe various perspectives on teaching and learning polygons which were derived from the literature, concerning the objectives, conceptual aspects and didactic tools of the topic. The next two sections introduce the main outcomes of our study, a quantitative analysis of the collected data and a qualitative description linked to the perspectives on teaching polygons. We conclude by discussing some principal ideas related to the theoretical and educational significance of this research work. -
Sequenced problems for functional equations
179-192Views:82There are many possible methods to solve equations of the form H(f(x + y), f(x − y), f(x), f(y), x, y) = 0 (x, y 2 R), where H is a known function and f is the unknown function to be determined. Here we will create a sequence of problems for equations of type (1) (see on the next page). These sequenced problems are appropriate for the fostering of talented students on different level of mathematical education. -
Mathematics in Good Will Hunting I: the mathematicians in Good Will Hunting
375-388Views:134This 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. -
Comments on the remaining velocity project with reports of school-experiments
117-133Views:145The aim of this article is to introduce different possible solutions to the exercise referring to the calculation of "remaining velocity". We explain the possible approaches to the problem with the help of either using the tools of mathematics or other subjects. During the past few years, we have made Hungarian and Slovakian secondary school students solve the exercise, choosing from both children of average and of high abilities. The experince has shown that very few students were able to solve the problem by themselves, but with the help of their teachers, the exercise and the solution has been an eye-opener experience to all of them. A lot of students were even considering to drive more carefully in the future after getting their driving licenses. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences, April 1-3, 2022 Baja, Hungary
135-155Views:254The 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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Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 28 – January 30, 2011, Satu Mare, Romania
159-179Views:106The meeting Researches in Didactics of Mathematics and Computer Science was held in Satu-Mare, Romania from the 28th to the 30th of January, 2011. The 46 Hungarian participants – including 34 lecturers and 12 PhD students – came from 3 countries, 14 cities and represented 20 institutions of higher education. The abstract of the talks and the posters and also the list of participants are presented in this report. -
Conventions of mathematical problems and their solutions in Hungarian secondary school leaving exams
137-146Views:94Collecting and analyzing the conventions indispensable for interpreting mathematical problems and their solutions correctly assist successful education and objective evaluation. Many professional and didactic questions arose while collecting and analyzing these conventions, which needed clarification, therefore the materials involved concisely in the conventions enrich both the theory and practice of mathematics teaching. In our research we concentrated mainly on the problems and solutions of the Hungarian school leaving examinations at secondary level in mathematics.
