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Engineering and Economic Mathematics for Engineering Management Students
35-50Views:35In this article we describe the first part of a case study, which was made with 48 Engineering Management students. The participants of the case study were MSc level students at the Szent István University, Gödöllő. 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-efficacy, 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. As an example we introduce one of the knowledge tests connected with the first half of the course about linear programming and graph theory. We detail its didactical background and show the results of the students. -
Supporting the education of engineering mathematics using the immediate feedback method
49-61Views:74In 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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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 on "The Computer Algebra and Dynamical Geometry Systems, as the catalysts of the Mathematics education": Conference, 6-7 June, 2003, Pécs, Hungary
259-269Views:10The Department of Mathematics of the University of Pécs, Pollack Mihály Engineering Faculty organized in the year 2003 a conference on the role of CAS and DGS in the Mathematics education. We discuss – based on the authors' abstracts – the conference's activities. -
"On the way" to the function concept - experiences of a teaching experiment
17-39Views:80Knowing, comprehending and applying the function concept is essential not only from the aspect of dealing with mathematics but with several scientific fields such as engineering. Since most mathematical notions cannot be acquired in one step (Vinner, 1983) the development of the function concept is a long process, either. One of the goals of the process is evolving an "ideal" concept image (the image is interrelated with the definition of the concept). Such concept image plays an important role in solving problems of engineering. This study reports on the beginning of a research aiming the scholastic forming of the students' function concept image i.e. on the experiences of a "pilot" study. By the experiment, we are looking for the answer of the following question: how can the analysis of such function relations be built into the studied period (8th grade) of the evolving process of the function concept that students meet in everyday life and also in engineering life?
Subject Classification: D43, U73
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Mathematician Judita Cofman (1936–2001)
91-115Views:21Judita Cofman was the first generation student of mathematics and physics at Faculty of Philosophy in Novi Sad, Serbia, and the first holder of doctoral degree in mathematical sciences at University of Novi Sad. Her Ph.D. thesis as well as her scientific works till the end of 70's belong to the field of finite projective and affine planes and the papers within this topic were published in prestigious international mathematical journals. She dedicated the second part of her life and scientific work to didactic and teaching of mathematics and to work with young mathematicians. -
Zbigniew Michalewicz - Matthew Michalewicz: Puzzle Based Learning: An introduction to critical thinking, mathematics, and problem solving. Hybrid Publishers Melbourne 2008 (Book review)
415-420Views:42Based on their experiences with engineering, mathematics, computer science, business students concerning the puzzle based learning in different countries the authors summarize their main problem solving teaching ideas. With help of interesting, motivating, nice problems they analyze the main mathematical principles and problem types. The review gives an overview about the main ideas, results of an interesting book. -
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. -
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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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. -
The hyperbola and Geogebra in high-school instruction
277-285Views:35In this article the results of teaching/learning hyperbola and its characteristics in high-school using computers and GeoGebra are shown. Students involved in the research attend Engineering School "Nikola Tesla" in Leposavic, Serbia. The aim of the research was to define ways and volume of computer and GeoGebra usage in mathematics instruction in order to increase significantly students' mathematical knowledge and skills. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 24-26, 2020 Sárospatak, Hungary
243-271Views:105The 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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Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 26-28, 2018 Hajdúszoboszló, Hungary
131-153Views:10The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Hajdúszoboszló, Hungary from the 26th to the 28th of January, 2018. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen.
The 61 participants – including 47 lectures and 17 PhD students – came from 8 countries, 21 cities and represented 37 institutions of higher and secondary education. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: February 1-3, 2019 Stúrovo, Slovakia
105-129Views:147The 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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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. -
Comparing the IT skills and the programming knowledge of Hungarian students specialized in informatics with Romanian students attending a science course or a mathematics-informatics course
21-40Views:33The goal of this research is an analysis of the IT skills and programming knowledge of Hungarian and Romanian students attending a Science course or a Mathematics-Informatics course. Analysed was how effectively can students from different grades answer questions dealing with different subjects. After having evaluated the test results correctness of the original presumption emerged. Significance level was 5% through the analysis. Significant divergency in knowledge of Hungarian students and Romanian students of Humanities (Profil Uman) was found in 11th and 12th grades too. Romanian students attending a science course (Profil Real) and a Mathematics-Informatics course scored higher in programming than their Hungarian counterparts specialized in Informatics in the 11th grade. After the evaluation a final conclusion can be made: Romanian students of the Real Profile have the same or more practice in programming than Hungarian students specialized in Informatics, though the latters have the same or better IT skills. Unfortunately, Hungarian teachers concentrate on word processing and spreadsheet calculation and teach programming just for the students specialized in Informatics, although algorithm thinking would be important for every student before finishing secondary school. -
Teaching Fourier series, partial differential equations and their applications with help of computer algebra system
51-68Views:27In this paper, some examples of Fourier series and partial difference equations will be shown to demonstrate opportunities for CAS use in various circumstances. The well-known white-box – black-box teaching-learning techniques and the modularization will be used to allow the use of the same worksheet in different ways. -
Fostering engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks
1-14Views:105We designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics.
Subject Classification: 97U70, 97H60
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Solving mathematical problems by using Maple factorization algorithms
293-297Views:32Computer algebra gives methods for manipulating mathematical expression. In this paper we use the Maple software to solve some elementary problems. Computeraided approach in the instruction of mathematics helps to impart problem solving skills to students. -
What can we learn from Tamás Varga’s work regarding the arithmetic-algebra transition?
39-50Views:82Tamás Varga’s Complex Mathematics Education program plays an important role in Hungarian mathematics education. In this program, attention is given to the continuous “movement” between concrete and abstract levels. In the process of transition from arithmetic to algebra, the learner moves from a concrete level to a more abstract level. In our research, we aim to track the transition process from arithmetic to algebra by studying the 5-8-grader textbooks and teacher manuals edited under Tamás Varga's supervision. For this, we use the appearance of “working backward” and “use an equation” heuristic strategies in the examined textbooks and manuals, which play a central role in the mentioned process.
Subject Classification: 97-01, 97-03, 97D50
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Experiences using CAS and multimedia int teaching vectorcalculus
363-382Views:31The development of informatics brings new opportunities that need reevaluating of the teaching concepts. For this reason we have performed a comprehensive educational development for engineering students. Our main goals were to work out a new educational strategy, to develop the needed package of the subject material, to introduce the strategy in the practice, to analyze and evaluate the experiences. In the developed and adapted teaching-learning strategy the teacher is the organizer, designer and the manager of the process. In this paper we summarize the concepts, the results and experiences of the 3-years-long development. -
A constructive and metacognitive teaching path at university level on the Principle of Mathematical Induction: focus on the students' behaviours, productions and awareness
133-161Views:124We present the main results about a teaching/learning path for engineering university students devoted to the Principle of Mathematical Induction (PMI). The path, of constructive and metacognitive type, is aimed at fostering an aware and meaningful learning of PMI and it is based on providing students with a range of explorations and conjecturing activities, after which the formulation of the statement of the PMI is devolved to the students themselves, organized in working groups. A specific focus is put on the quantification in the statement of PMI to bring students to a deep understanding and a mature view of PMI as a convincing method of proof. The results show the effectiveness of the metacognitive reflections on each phase of the path for what concerns a) students' handling of structural complexity of the PMI, b) students' conceptualization of quantification as a key element for the reification of the proving process by PMI; c) students' perception of the PMI as a convincing method of proof.
Subject Classification: 97B40, 97C70
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Concept systematization with concept maps in data modelling
149-166Views:41An important goal of concept learning is that students can allocate concepts in the hierarchical system of concepts. In the data modelling course, first, we supported concept systematization with worksheets in which the students had to fill in the blank hierarchical figures of classification of the concepts or blank Venn diagrams describing the relationships between concepts. The hierarchical systems, however, are somewhat restricted to the description of connections. The filling in Venn diagrams did not deliver the expected result, so our attention turned to concept maps. In this paper we introduce the concept maps we drew. Then we evaluate the results of concept mapping survey conducted among students. The survey was done in three courses. We compare the results of our survey with the result of an earlier concept systematising survey. -
Online tests in Comprehensive Exams – during and after the pandemic
77-93Views:82The Covid-19 pandemic accelerated the development of electronic (e-learning) assessment methods and forced their use worldwide. Many instructors and students had to familiarize themselves with the form of distance education. During and since Covid-19 in Hungary, at the Faculty of Engineering of the University of Debrecen, the written part of the Comprehensive Exam in Mathematics is organized in a computer lab of the university using an online test. Our goal is that the results of the tests may be as reliable as possible in terms of measuring the students’ knowledge, and thus the grades given based on the test results would be realistic. In this paper, we show the analysis of a sample written exam and compare the real exam results of students who were prepared for the comprehensive exam during Covid-19 and who have participated in face-to-face education since then. The tools provided by the Moodle system necessary for comparison are also presented.
Subject Classification: 97D40, 97D70, 97U50
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Teaching Gröbner bases
57-76Views:23In this article we offer a demonstration of how the StudentGroebner package, a didactic oriented Maple package for Gröbner basis theory, could assist the teaching/learning process. Our approach is practical. Instead of expounding on deep didactic theory we simply give examples on how we imagine experimental learning in classroom. The educational goal is to prepare the introduction of two sophisticated algorithms, the division algorithm and Buchberger's algorithm, by gathering preliminary knowledge about them.