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Integrating elements of data science into high-school teaching: Naïve Bayes-classification algorithm and programming in Python
307-316Views:99Probability theory and mathematical statistics are traditionally one of the most difficult chapters of mathematics to teach. One of the authors, Péter Princz has experience in teaching various topics via computer programming of the problem at hand as a class activity. The proposed method is to involve programming as a didactic tool in hard-to-teach topics. The intended goal in this case is to implement a naïve Bayes-classifier algorithm in Python and demonstrate the machine-learning capabilities of it by applying it to a real-world dataset of edible or poisonous mushrooms. The students would implement the algorithm in a playful and interactive way. The proposed incremental development process aligns well with the spirit of Tamás Varga who considered computers as modern tools of experimental problem solving as early as in the 1960s.
Subject Classification: 97D40, 97D50, 97K50, 97K99, 97M60, 97P40, 97P50, 97U50
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Report of Conference XXXIX. National Conference on Teaching Mathematics, Physics and Computer Science-August 24-26, 2015 Kaposvár, Hungary
309-331Views:9The XXXIX. National Conference on Teaching Mathematics, Physics and Computer Sciences (MAFIOK) was held in Kaposvár, Hungary between 24 and 26 August, 2015 at the Faculty of Economic Sciences of Kaposvár University. It was organized by the Department of Mathematics and Physics. The 67 participants – including 5 invited lecturers and 54 lecturers – came from 5 countries and represented 16 institutions of higher education. -
A proposed application of Monte Carlo method in teaching probability
37-42Views:39Pupils' misconception of probability often results from lack of experience. Combining the concept of probability and statistics, the proposed application is intended for the teachers of mathematics at an elementary school. By reformulating the task in the form of an adventure, pupils examine a mathematical problem, which is too difficult for them to solve by combinatorial method. By recommending the simulation of the problem, we have sought to provide pupils with valuable experience of experimenting, recording and evaluating data. -
Report on the First Central- and Eastern European Conference on Computer Algebra- and Dynamic Geometry Systems in Mathematics Education, 20-23 June, 2007, Pécs, Hungary
409-413Views:26The Department of Mathematics of the University of Pécs, Pollack Mihály Engineering Faculty organized in the year 2007 a conference on the role of CAS and DGS in the Mathematics education. We discuss the conference's activities. -
Categorising question question relationships in the Pósa method
91-100Views:66The 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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Game theory for managers and mechanical manager students
73-91Views:25In this article we describe the second part of a case study, in which 48 Mechanical Management students were involved. The participants of the case study were MSc level students at Szent István University, Gödöllő.
In the case study we looked for methods by which we can support the most important components of competence motivation and the development of mathematical and other key competences during the mathematics lessons and individual learning.
Another goal of our research was to get reliable information about students learning methods and their awareness of self-efficiency, furthermore their achievement in the subject of Engineering and Economic Mathematics.
Detailed assistance was provided for the students in the e-learning portal. Knowledge tests, questionnaire and personal interviews with the students were also used.
During the semester four topics have been discussed: linear programming, graph theory, game theory and differential equations. In this article I will describe the lesson preparations, the help for examinations and the students' achievement on game theory. -
Report of conference XXXVIII. National Conference on Teaching Mathematics, Physics and Computer Sciences: August 25-27, 2014 Pécs, Hungary
281-303Views:9The XXXVIII. National Conference on Teaching Mathematics, Physics and Computer Sciences (MAFIOK) was held in Pécs, Hungary between 25 and 27 August, 2014 at the Pollack Mihály Faculty of Engineering and Information Technology. It was organized by the Engineering Mathematics Department. The 65 participants – including 4 invited lecturers and 53 lecturers – came from 2 countries and represented 14 institutions of higher education. -
CALIBRATE and CAS/DGS resources
267-279Views:28The CALIBRATE project was initiated by the EU with the goal of expanding the use of ICT in education by increasing the amount of available learning resources via resource exchange. Although CAS/DGS can be used to easily create high quality learning resources which are also easily adaptable across national boundaries, such resources are difficult to find at CALIBRATE portals. We believe that this is due to CAS/DGS still being rather exotic to most of the people as well as with the common problem of finding existing appropriate resources. A possible solution is for CALIBRATE portals to properly equip existing and forthcoming CAS/DGS resources with suitable metadata and to provide some integration with CAS/DGS tools, enabling both beginners and power users to create and exchange CAS/DGS resources. -
Teaching undergraduate mathematics - a problem solving course for first year
183-206Views:102In this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers.
Subject Classification: 97B50, 97B70, 97D50, 97D60, 97F60, 97U30
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Some Remarks on History of Mathematical Problem Solving
51-64Views:33In this contribution, it is our goal is to look on history of mathematics as a resource for a long-term study of mathematical problem solving processes and heuristics. In this way we intend to get additional information, e. g., about heuristics which proved to be extremely successful to create new mathematics. "Changing representation" and "false position" are examples of such strategies, which are illustrated by concrete examples to demonstrate the use for classroom teaching and teacher education. Our methods are based on hermeneutic principles. -
Über einen allgemeinen Übungsbegriff bei verschiedenen Unterrichtsmethoden in der Planung des Mathematikunterrichtes
175-201Views:38Practice 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. -
What does ICT help and does not help?
33-49Views:115Year 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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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 22-24, 2016 Bratislava, Slovakia
115-137Views:26The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Bratislava, Slovakia from the 22th to the 24th of January, 2016 at Comenius University in Bratislava. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen and the Faculty of Education of Comenius University.
The 60 participants – including 47 lecturers and 15 PhD students – came from 5 countries, 23 cities and represented 32 institutions of higher and secondary education. -
On a special class of generalized conics with infinitely many focal points
87-99Views:9Let a continuous, piecewise smooth curve in the Euclidean space be given. We are going to investigate the surfaces formed by the vertices of generalized cones with such a curve as the common directrix and the same area. The basic geometric idea in the background is when the curve runs through the sides of a non-void triangle ABC. Then the sum of the areas of some triangles is constant for any point of such a surface. By the help of a growth condition we prove that these are convex compact surfaces in the space provided that the points A, B and C are not collinear. The next step is to introduce the general concept of awnings spanned by a curve. As an important example awnings spanned by a circle will be considered. Estimations for the volume of the convex hull will be also given. -
A proposal for an IOI Syllabus
193-216Views:56The 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:116In 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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Decomposition of triangles into isosceles triangles I: let the students ask bravely
163-184Views:27We report about working up an open geometric problem as a mathematical research with pupils of a mathematics camp. This paper shows the didactic aims and the methods we worked with, the didactic results. The second part of this paper gives a general solution of the problem, using pure mathematics and a computer programme. -
A whole new vigor: About Montel’s book "Les mathématiques et la vie" (1947)
51-60Views:65In this paper, we consider a talk presented by the mathematician Paul Montel in Paris in 1944, dedicated to a general presentation of the importance of mathematics in everyday’s life. The text of this talk, and the context of its elaboration, allows various inceptions in the French mathematical life in the middle of 20th century. In particular Montel’s insistence on applications of mathematics strongly contrasts with the main tendencies of the French mathematical stage after the war under the impulse of the Bourbaki group.
Subject Classification: 97A40, 01A60, 60-03
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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: February 1-3, 2019 Stúrovo, Slovakia
105-129Views:150The 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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Research studies in didactics of mathematics supported by the Operant Motive Test
153-173Views:33The present paper reports a case-study which took place within an EUsupported international program organized for research and development of multi-grade schools (NEMED, [16] [26]). One of the main goals of the research was to develop the connection between disadvantageous social situations and the efficiency (success or failure) in learning mathematics especially from the point of view of average and above-average (talented) students: Why does the talent of children with socially disadvantageous background remain undiscovered? How can we make school mathematics more aware of hidden talents?
The author was looking for a didactical solution that compensated for social disadvantages without restricting the development of "average" students by using sociological, educational, psychological and mathematical (experimental and theoretical) studies in interaction with a series of experimental (hypothesis testing and exploratory) investigations.
We constructed tools and methods for exploration and experimental teaching, adapted to Hungarian conditions (Curriculum Development, teacher training, materials, interviews, Kuhl's motivation test, Malara's "researchers and practicing teachers in cooperation" method, etc., see [18], [20]).
The teaching materials and methodological guidelines are based on Bruner's representation theory (see [5]). The empirical research took place in 16 multi-grade schools located in different parts of the country. The author co-operated with nearly 250 students and 25 teachers for 3 years. In this paper we try to demonstrate how an Operant Motive Test can be involved in this research (see [18]). -
Evaluating admission procedures for teacher education in Finland
231-243Views:35In Finland the number of applicants for elementary teacher education is many times greater than the number of accepted persons. In this article we focus on the significance of the entrance examination procedures at three Finnish universities. Our findings imply that the differing admission procedures at the institutions yielded different student profiles. The test component "mathematics-science" used on the entrance examination in Turku was found to be a significant separating factor, but also the applicants' mathematics achievement in upper secondary school seems to be an applicable criterion for developing admission procedures. -
Prime building blocks in the mathematics classroom
217-228Views:148This theoretical paper is devoted to the presentation of the manifold opportunities in using a little-known but powerful mathematical manipulative, the so-called prime building blocks, originally invented by two close followers of Tamás Varga, to support discovery of various concepts in arithmetic in middle school, including the Fundamental Theorem of Arithmetic or as it is widely taught, prime factorization. The study focuses on a teaching proposal to show how students can learn about greatest common divisor (GCD) and least common multiple (LCM) with understanding, and meanwhile addresses internal connections and levels of abstractness within elementary number theory. The mathematical and methodological background to understanding different aspects of the concept prime property are discussed and the benefits of using prime building blocks to scaffold students’ discovery are highlighted. Although the proposal was designed to be suitable for Hungarian sixth graders, mathematical context and indications for the use of the manipulative in both primary and high school are given.
Subject Classification: F60, C30, E40, U60
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Zoltán Szvetits (1929-2014): legendary teacher, Zoltán Szvetits passed away
287-288Views:12The legendary mathematics teacher of Secondary School Fazekas in Debrecen, Zoltán Szvetits passed away on 5th November 2014, at the age of 84. Beginning in 1954 he had been teaching here almost forty years. His pupils and the society of teachers have lost an outstanding teacher character. This secondary school has been well known for decades about its special mathematics class with 10 math lessons a week. This special class was designed and established by Zoltán Szvetits. -
Process or object? Ways of solving mathematical problems using CAS
117-132Views:26Graphing and symbol manipulating calculators are now a part of mathematics education in many countries. In Norway symbol manipulating calculators have been used at various exams in upper secondary education. An important finding in mathematics education is the duality of mathematical entities – processes and objects. Building on the theoretical development by Anna Sfard and others, the students' solutions on exam problems in upper secondary education are discussed with reference to procedural and structural knowledge. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: 31 March – 2 April, 2023 Oradea, Romania
83-107Views:162The 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.