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Teaching agile operation and leadership through linked university courses
1-32Views:100Agile 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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Differentiated instruction not only for Mathematics teachers
163-182Views:168The aim of differentiated development in a heterogeneous group of learners (DDHG) is to reduce school leaving without education, using an adaptive and innovative teaching-learning environment and using the most effective strategies, methods and techniques. Furthermore, this strategy helps in developing skills for learners and building cooperation between learners in heterogeneous classes through the use of the special, status-management educational procedure, and finally its strength is to sort the status ranking among learners, and to change the social structure of the class. Our goal is to figure out how to share best practices with teachers. One of the effective ways to renew teaching practice is through further training for teachers. As a trainer of the Logic-based subprogram of the Complex Basic Program (CBP) the author of the paper has experienced how well logic-based and decision-making strategies work in other subjects as well as in mathematics.
Subject Classification: 97D40
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Mathematical gems of Debrecen old mathematical textbooks from the 16-18th centuries
73-110Views:29In the Great Library of the Debrecen Reformed College (Hungary) we find a lot of old mathematical textbooks. We present: Arithmetic of Debrecen (1577), Maróthi's Arithmetic (1743), Hatvani's introductio (1757), Karacs's Figurae Geometricae (1788), Segner's Anfangsgründe (1764) and Mayer's Mathematischer Atlas (1745). These old mathematical textbooks let us know facts about real life of the 16-18th centuries, the contemporary level of sciences, learning and teaching methods. They are rich sources of motivation in the teaching of mathematics. -
Assimilation of mathematical knowledge using Maple
321-331Views:41For more than four years we have been teaching a Maple course at University of Debrecen for prospective mathematics teachers. The aim of the course is that students get some experience on mathematical visualization with Maple. At the last part of the course the student is provided with a problem of geometrical flavor. Within three or four weeks he/she must obtain a solution. In this paper we present and analyze two of student projects: rotation of the hypercube and drawing of complex functions. The concluding remark is that most of the students will profit from using Maple for such type of problems: it helps to assimilate mathematical knowledge. -
Dynamic geometry systems in teaching geometry
67-80Views:29Computer drawing programs opened up new opportunities in the teaching of geometry: they make it possible to create a multitude of drawings quickly, accurately and with flexibly changing the input data, and thus make the discovery of geometry an easier process. The objective of this paper is to demonstrate the application possibilities of dynamic geometric systems in primary and secondary schools, as well as in distance education. A general characteristic feature of these systems is that they store the steps of the construction, and can also execute those steps after a change is made to the input data. For the demonstration of the applications, we chose the Cinderella program. We had an opportunity to test some parts of the present paper in an eighth grade primary school. -
Expressiveness of programming languages and environments: a comparative study
111-141Views:31In written and oral communication tools, the support of the understanding of our message have an important role: we can increase the expressiveness and the level of understanding of our topic by approaching it in several ways, i.e. in written methods by highlighting the important parts; in oral by changing tone and other elements of non-verbal communication. In this paper programming languages and developing environments are compared with each other in terms of their methods and their level of support to the solution of programming tasks.
There is a need to have these tools in programming and, of course, in teaching programming. What are the factors that define the distinctness and the legibility of a program? What are the basic principles which give an instrument in programmers' and students' hands in order to create a properly working program from already existing algorithms in the most efficient way? We search for the answers to these questions in this paper. -
Report of Conference XL. National Conference on Teaching Mathematics, Physics and Computer Science August 22-24, 2016 Székesfehérvár, Hungary
259-276Views:12The 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. ... -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 21 – January 23, 2010, Debrecen, Hungary
177-195Views:11The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Debrecen, Hungary from January 21 to January 23, 2010. The 42 Hungarian participants – including 16 PhD students – came from 5 countries, 14 cities and represented 25 institutions of higher education. The abstracts of the talks and the posters and also the list of participants are presented in this report. -
Report of meeting Researches in Didactics of Mathematics and Computer Sciences: January 30 - February 1, 2009, Debrecen, Hungary
165-186Views:17The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Debrecen, Hungary from January 30 to February 1, 2009. The 49 Hungarian participants – including 15 PhD students – came from 18 cities and represented 29 institutions of higher education. The abstracts of the talks and the posters and also the list of participants are presented in this report. -
Combinatorics teaching experiment
27-44Views:36Teaching combinatorics has got its conventional method. One has to see: the combinatorical formations won't be follow each other by a heuristic way. The formulas kept by pupils seem to come from "deus ex machina". We try to offer now an alternative way to approach combinatorical concepts from a nontraditional direction and point of view. -
Teaching model-based testing
1-17Views:1205Different 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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CAS-aided visualization in LATEX documents for mathematical education
1-18Views:26We have been developing KETpic as a macro package of a CAS for drawing fine LATEX-pictures, and we use it efficiently in mathematical education. Printed materials for mathematics classes are prepared under several constraints, such as "without animation", "mass printings", "monochrome", and "without halftone shadings". Because of these constraints, visualization in mathematical education tends to be unsatisfactory. Taking full advantages of LATEX and CAS, KETpic enables us to provide teaching materials with figures which are effective for mathematical education. The effects are summarized as follows:
(1) The plottings of KETpic are accurate due to CAS, and enable students to deduce mathematical laws.
(2) KETpic can provide adequate pictures for students' various interest. For example, when some students who understand a matter try to modify it, KETpic can give them appropriate and experimental figures.
(3) Even though CAS can draw 3D-figures beautifully and automatically, it is expensive for mass printings and the figures are sometimes not easy to understand. Oppositely, 3D-graphics by KETpic are monochrome, but are richly expressive.
In this paper, we give various examples of LATEX-pictures which we drew by using KETpic. For instance, the picture which is used in order to explain the convergence theorem of Fourier series makes it easier for students to understand the idea that function series converge to another function. Also the picture of skeleton is endowed with clear perspective. KETpic gives us great potential for the teaching of combinatorial mathematics. Through these examples, we claim that KETpic should have great possibilities of rich mathematical expressions under the constraints above mentioned. -
Straight line or line segment? Students’ concepts and their thought processes
327-336Views:100The article focuses on students’ understanding of the concept of a straight line. Attention is paid to whether students of various ages work with only part of a straight line shown or if they are aware that it can be extended. The presented results were obtained by a qualitative analysis of tests given to nearly 1,500 Czech students. The paper introduces the statistics of students’ solutions, and discusses the students’ thought processes. The results show that most of the tested students, even after completing upper secondary school, are not aware that a straight line can be extended. Finally, we present some recommendations for fostering the appropriate concept of a straight line in mathematics teaching.
Subject Classification: 97C30, 97D70, 97G40
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GeoGebra in mathematics teaching
101-110Views:43GeoGebra is a dynamic mathematics software which combines dynamic geometry and computer algebra systems into an easy-to-use package. Its marvel lies in the fact that it offers both the geometrical and algebraic representation of each mathematical object (points, lines etc.). The present article gives a sample of the potential uses of GeoGebra for mathematics teaching in secondary schools. -
Computer cooking vs. problem solving
35-58Views:66Computer cooking is a task-related phenomenon where students (end-users) must blindly follow a long list of orders without any connection to the content of the problem, if there is any. Despite its low efficacy, this method is widely used and accepted in informatics both in the learning-teaching process and testing. The National Base Curriculum 2020 in Hungary is in complete accordance with the ‘Informatics Reference Framework for Schools’, but the course books hardly use the latest results of computer education research. The present paper provides examples of how the results of computer education research can be integrated into teaching-learning materials and classroom practices and discusses the effectiveness and consequences of the different solutions, where tool-centred approaches are compared to problem-focused solutions.
Subject Classification: 94-01
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Willy Servais and Tamás Varga A Belgian Hungarian perspective on teaching school mathematics
29-38Views:74Willy 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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Ist eine schnelle tiefgehende (und nachhaltige) Änderung in der Vorstellung von Mathematiklehrern möglich? - Reflexion der Erfahrungen eines Fortbildungskurses im Bereich der mathematischen Modellierung
1-20Views:13Based on the material which was worked out within the project LEMA (2006-2009) pilot-teacher training courses were organized in the six partner countries, so in Hungary as well in the subject: Practice of Modelling tasks in the classroom. According to the tests which were filled out by the participants the conclusion was formulated that they achieved some changes in their pedagogical knowledge and in their estimation concerning their self-efficacy, but they didn't have shown any changes in their beliefs of mathematics and mathematics education. However according to their experience as project partners and leaders of the Hungarian course the authors have the idea that despite of the international results there are changes in this subject in the case of the Hungarian participants. This way can formulated the question:
Which changes can be observed in the case of the participants concerning belief towards mathematics and mathematics education after the course and how long-lasting these changes are?
The question is examined on the example of two teachers who were participants of the course. -
Teaching puzzle-based learning: development of basic concepts
183-204Views:17While computer science and engineering students are trained to recognise familiar problems with known solutions, they may not be sufficiently prepared to address novel real-world problems. A successful computer science graduate does far more than just program and we must train our students to reach the required levels of analytical and computational thinking, rather than hoping that it will just 'develop'. As a step in this direction, we have created and experimented with a new first-year level course, Puzzle-based Learning (PBL), that is aimed at getting students to think about how to frame and solve unstructured problems. The pedagogical goal is increase students' mathematical awareness and general problem solving skills by employing puzzles, which are educational, engaging, and thought provoking. We share our experiences in teaching such a course – apart from a brief discussion on our pedagogical objectives, we concentrate on discussing the presented material which covers (in two lectures) just one selected topic (pattern recognition). In this paper we present the ideas behind foundations for PBL and the material of the first of two lectures on pattern recognition, in which we address core concepts and provide students with sufficient exemplars to illustrate the main points. -
Comparison of teaching exponential and logarithmic functions based on mathematics textbook analysis
297-318Views:28Exponential and logarithmic functions are key mathematical concepts that play central roles in advanced mathematics. Unfortunately these are also concepts that give students serious difficulties. In this paper I would like to give an overview – based on textbook analysis – about the Hungarian, Austrian and Dutch situation of teaching exponential and logarithmic functions. This comparison could also provide some ideas for Hungarian teachers on how to embed this topic in their practice in another more "realistic" way. -
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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Algorithmics of the knapsack type tasks
37-71Views:27We propose a new kind of approach of the teaching of knapsack type problems in the classroom. We will remind you the context of the general knapsack-task and we will classify it, including the two most popular task variants: the discrete and the continuous one. Once we briefly present the solving algorithm of the continuous variant, we will focus on the solving of the discrete task, and we will determine the complexity of the algorithms, looking for different optimizing possibilities. All these issues are presented in a useful way for highschool teachers, who are preparing students in order to participate in different programming contests. -
Tamás Varga’s reform movement and the Hungarian Guided Discovery approach
11-28Views:155This 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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Heads or Tails gambling — what can be learned about probability?
15-41Views:23During the teaching of probability theory, a problem may appear whose solution requires the use of methods that are unfamiliar to secondary school students. In this paper, examples of methods that can resolve this difficulties are demonstrated, which could in future allow school students to tackle and solve a wide variety of problems involving probability. -
Writing a textbook – as we do it
185-201Views:17Recent surveys studying mathematics teaching show that there is a great variety in the level of mathematics teaching in Hungary. To increase efficiency (and decrease differences between schools) it is essential to create textbooks with new attitudes. The experiment we started after the PISA survey of 2000, produced a textbook that is new, in some sense even unusual in its attitude and methods. This paper presents the experiences we gained in the course of this work. -
Report of conference XXXVIII. National Conference on Teaching Mathematics, Physics and Computer Sciences: August 25-27, 2014 Pécs, Hungary
281-303Views:8The 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.