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The effect of augmented reality assisted geometry instruction on students' achiveement and attitudes
177-193Views:311In this study, geometry instruction's academic success for the students and their attitudes towards mathematics which is supported by education materials of Augmented Reality (AR) and its effect on the acceptance of AR and its usage by teachers and students have been researched. Under this research, ARGE3D software has been developed by using augmented reality technology as for the issue of geometric objects that is contained in the mathematics curriculum of 6th class of primary education. It has been provided with this software that three-dimensional static drawings can be displayed in a dynamic and interactive way. The research was conducted in two different schools by an experiment and control group. In the process of data collection, Geometry Achievement Test (GAT), Geometric Reasoning Test (GRT), Attitudes Scale for Mathematics (ASM), students' math lecture notes, semi-structured interviews with teachers and students and observation and video recordings were used. Results showed that geometry instruction with ARGE3D increased students' academic success. In addition, it was found that geometry instruction with ARGE3D became more effective on students' attitudes that had negative attitudes towards mathematics and it also provided support to reduce fear and anxiety. -
Didactical remarks on the changes in the requirements of the matriculation exam in Mathematics in Hungary
95-110Views:202Students within the Hungarian education system typically take a matriculation exam to obtain a secondary education certificate, which also serves as a prerequisite for university admission. Public education is regulated at different levels. One of its most fundamental elements is the National Core Curriculum, the current version of which came into force in September 2020. It is crucial to adapt the requirements of the matriculation exam in mathematics to this and ensure transparent communication about the changes. Regarding this, there exists a sample paper that contains tasks that one can reasonably expect in the actual exam in the spring. Since I have been working as a private math tutor for almost a decade and have been preparing students for the matriculation exam since then, I intend to highlight the most outstanding features from a didactic point of view based on the analysis of this sample paper.
Subject Classification: 97A30, 97B10, 97B70, 97D60, 97U40
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CAS-aided visualization in LATEX documents for mathematical education
1-18Views:181We 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. -
Shall we use one more representation? Suggestions about establishing the notion of recursion in teaching informatics in primary schools
209-229Views:120Among the most prominent developmental tasks of primary school education one finds increasing pupils' cognitive capacity with especial regard to observing, interpreting, coding and proving skills, which form an integral part of information and communication culture.
Info-technology (problem solving with the tools and methods of informatics), a subject matter within informatics, provides outstanding opportunities to reach the aims outlined above.
This study presents methodological ideas related to the subfield Algorithmization and data modelling of Info-technology. More specifically, it presents teaching methods to be applied while establishing the notion of recursion in grades 3–8 of primary education, and at the same time it also focuses on various realization possibilities of the prominent developmental tasks mentioned above. -
Better understanding mathematics by algorithmic thinking and computer programming
295-305Views:304Tamás Varga’s mathematics education experiment covered not just mathematics, but also other related topics. In many of his works he clearly stated that computer science can support the understanding of mathematics as much as mathematics supports informatics. On the other hand, not much later than the introduction of the new curriculum in 1978, personal computers started to spread, making it possible to teach informatics in classes and in extracurricular activities. Varga’s guided discovery approach has a didactic value for other age groups as well, not only in primary school. Its long-lasting effect can be observed even in present times. Having reviewed several educational results in the spirit of Tamás Varga, we have decided to present an extracurricular course. It is an open study group for age 12-18. Students solve problems by developing Python programs and, according to our experiences, this results in a deeper understanding of mathematical concepts.
Subject Classification: 97B10, 97B20, 97D50, 97N80, 97P20, 97P30, 97P40, 97P50, 97U70
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Levels of students' understanding on infinity
317-337Views:249Here 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. -
Smartphones and QR-codes in education - a QR-code learning path for Boolean operations
111-120Views:135During 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. -
Longest runs in coin tossing. Teaching recursive formulae, asymptotic theorems and computer simulations
261-274Views:167The coin tossing experiment is studied, focusing on higher education. The length of the longest head run can be studied by asymptotic theorems ([3]), by recursive formulae ([10]) or by computer simulations . In this work we make a comparative analysis of recursive formulas, asymptotic results and Monte Carlo simulation for education. We compare the distribution of the longest head run and that of the longest run (i.e. the longest pure heads or pure tails) studying fair coin events. We present a method that helps to understand the concepts and techniques mentioned in the title, which can be a useful didactic tool for colleagues teaching in higher education. -
E-learning management systems in Hungarian higher education
357-383Views:93Computers, informatics, and information technology have an ever-increasing role in the establishment and spread of new educational forms and methods. The role of e-learning as a new educational model is increasing in the world of computer networks, because of a widespread access to the net and a growing demand for learning beside work.
Technological elements of e-learning can be separated as Learning Management System, authoring system, course material and a browser. Learning Management System is the software package that creates the structure of the whole educational process: course organisation, course material presentation, tracking student work, recording results, and the completion of the program.
This publication shows examples of Learning Management Systems used in Hungarian higher education. Summarizing and systematizing expectations and demands expressed in connection with learning management systems, the present work tries to help the reader orientate on an ever-expanding market. -
Methodological questions of digital teaching material development made in the subject of mathematics
25-41Views:169In the methodology of mathematics teaching, the selection and the manner of using applicable digital teaching materials appeared as a new element. As the number of digital teaching materials applicable in education is constantly increasing, their purposeful use is rarely discussed. In what areas digital teaching materials can be used in mathematics? What are the problems for which they could provide a solution? Shall we use them besides traditional solutions, or instead?
The authors of this article have had the opportunity to participate in projects aiming to develop digital learning materials on various occasions. During the implementation of the projects, they needed to make methodological compromises at various points.
In our article, we are seeking a more emphatic use of methodology belonging to digital teaching materials, drawing on the experiences of three implemented projects. Our aim is to draw the attention to the anomalies we found in the implementation of the projects, which must be taken into consideration in new developments already at the planning stage. -
The requirements in statistics education – comparison of PISA mathematical tasks and tasks from the mathematical textbooks in the field of statistics
263-275Views:159This work presents the results of the analysis of both PISA items and Croatian mathematical textbooks in the field of statistics.
The analysis shows that PISA's released statistics problems have in many ways different mathematical requirements from the requirements of textbook problems in the statistics chapters, with respect to the mathematical activities, complexity and in the forms of questions. The textbook analysis shows that mathematical examples and problems often require operation and interpretation skills on a reproductive or connections level. Statistics textbook problems are given in the closed-answer form. The results also show that while PISA puts strong emphasis on the statistics field, in the current Croatian curriculum this field is barely present. These discrepancies in requirements and portion of statistics activities surely affect the results of Croatian pupils on PISA assessment in the field of mathematical literacy. -
Methods of teaching programming
247-257Views:127Programming methodology is one of the oldest fields of IS education, and thus various methods have evolved for its teaching. While some of them could be used effectively in primary or secondary education, others are more suited for students in higher education. The methods themselves determine the structure and curricula of courses such as Programming methodology, Data types and algorithms, Programming technology. -
CS unplugged in higher education
1-23Views:199Nowadays, there is a significant lack of workforce in the IT industry, even though it is one of the most lucrative professions. According to researchers' forecasts, the existing shortage is growing, so the wages offered will be higher, yet it seems that young people are not attracted to the profession. This problem draws attention to the need to change the curriculum so that it can attract students more. One possible solution is to supplement the curriculum with CS Unplugged activities, which makes it easier to understand and deepen difficult concepts and make IT lessons more colorful. In my article, besides presenting the already known CS Unplugged activities, I will deal with how this can be applied in Hungarian higher education as well. -
A case study of the integration of Algorithm Visualizations in Hungarian programming education
51-66Views:286In this study, I will introduce how Algorithm Visualizations (AV) can help programming education or, in this case, the acquisition of basic programming theorems. I used two di erent methods to test this: in the first round, I examined in a larger group how much the students' ability to solve specific tasks changes after being introduced to a visualization tool, and then, what was their motivation and experience during this process. In the second round, I looked for the components that could be important when choosing a tool with the help of an in-depth interview with a smaller number of individuals. In both cases, I describe the research, experience, and results of the study, and then summarize them at the end.
Subject Classification: 97P10
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Regula falsi in lower secondary school education
169-194Views:188The aim of this paper is to offer some possible ways of solving word problems in lower secondary school education. Many studies have shown that pupils in lower secondary school education (age 13-14) encounter difficulties with learning algebra. Therefore they mainly use arithmetical and numerical checking methods to solve word problems. By numerical checking methods we mean guess-and-check and trial-anderror. We will give a detailed presentation of the false position method. In our opinion this method is useful in the loweer secondary school educational processes, especially to reduce the great number of random trial-and-error problem solving attempts among the primary school pupils. We will also show the results of some problem solving activities among 19 grade 8 pupils at our school. We analysed their problem solving strategies and compared our findings with the results of other research works. -
Solving word problems - a crucial step in lower secondary school education
47-68Views:314Algebra is considered one of the most important parts of Mathematics teaching and learning, because it lays the foundations of abstract thinking as well as reasoning abilities among the lower secondary school pupils who have just transited from the world of numbers and computations to the area of equalities, signs, symbols and letters. The present article focuses on the fact that how the transition from arithmetic to algebra can be made more smooth. We have concentrated our experiments towards the approach of algebraic reasoning and its utilities in filling the gap between arithmetic and beginning algebra in lower secondary school education.We also underline the importance of another approach in overcoming the challenges in the transition from arithmetic to algebra, to enhance and make algebraic learning more effective, with special considerations to word problem-solving processes. In our opinion, we have to go through three phases in the introducing of algebra in Grade 7 Mathematics education: Regula Falsi method (based only on numerical calculations); functional approach to algebra (which combines the numerical computation with letter-symbolic manipulation); and writing equations to word problems. The conclusions of the present article would be helpful to Mathematics teachers for applying themselves to develop the pupils’ interest in word problem-solving processes during algebra teaching classroom activities.
Subject Classification: 97B10, 97C30, 97C50, 97D10, 97D40
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Herschel's heritage and today's technology integration: a postulated parallel
419-430Views:172During the early 20th century, advocacy of a range of mathematical technologies played a central part in movements for the reform of mathematical education which emphasised ‘practical mathematics' and the ‘mathematical laboratory'. However, as these movements faltered, few of the associated technologies were able to gain and maintain a place in school mathematics. One conspicuous exception was a technology, originally championed by the mathematician Herschel, which successfully permeated the school mathematics curriculum because of its:
• Disciplinary congruence with influential contemporary trends in mathematics.
• External currency in wider mathematical practice beyond the school.
• Adoptive facility of incorporation in classroom practice and curricular activity.
• Educational advantage of perceived benefits outweighing costs and concerns.
An analogous perspective is applied to the situation of new technologies in school mathematics in the early 21st century. At a general level, the cases of calculators and computers are contrasted. At a more specific level, the educational prospects of CAS and DGS are assessed. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: January 22-24, 2016 Bratislava, Slovakia
115-137Views:167The 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. -
The theory of functional equations in high school education
345-360Views:204In this paper, we are going to discuss some possible applications of the theory of functional equations in high school education. We would like to line up some problems, the solution of which by functional equations are mostly not new results – they have also been treated in [1] and [2] –, although their demonstrations in high school can show a new way in teaching of talented students. The area of the rectangle, the calculating method of compound interest, binomial coefficients, Euler's formula, the scalar product and the vector product of vectors – we are looking for the reasons behind the well-known formulas. Finally, we are going to give a functional equation in connection with mean values. It can be understood easily, but its solution is beyond the high school curriculum, so we advise this part only to the most talented students. -
Integrating Didactic Games in Higher Education: Benefits and Challenges
1-15Views:875In our paper, we study the reasons for the introduction of didactic games and the way of their application in higher education, especially in teaching mathematics. After describing the main characteristics and needs of Generation Z students, we outline the advantages and drawbacks of gamification and game-based learning, followed by some new aspects to their classification. The idea of device-based grouping arose because the most commonly used methods require IC tools. Gen Zs naturally accept gamified learning materials available on digital and mobile platforms, but we must not forget about traditional games either. In higher education, especially in the case of small-group teaching there should also be room for traditional, specialized didactic games, of which we focus on the benefits of card games.
Subject Classification: 97C70, 97D20, 97D40, 97U70
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Capturing how students' abilities and teaching experiences affect teachers' beliefs about mathematics teaching and learning
195-212Views:254We developed an instrument to investigate the effect of students' abilities and teaching experiences on teachers' beliefs about teaching and learning of mathematics. In this pilot study, we used the instrument to measure the beliefs of 43 Indonesian math teachers and five additional teachers. Then, for further investigation, we interviewed those five additional teachers. Results from the 43 teachers' responses to the instrument show that in contrast to teachers with less than five years of teaching, teachers with more than five years elicit significantly different beliefs about mathematics teaching and learning in different contexts related to students' abilities. Teachers' reports in the further investigation indicate that teaching experiences with high and low ability students in teaching mathematics could be a possible explanation of this contrast.
Subject Classification: C20
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Evaluating admission procedures for teacher education in Finland
231-243Views:207In 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. -
The Mathematics Education Traditions of Europe (METE) Project
353-364Views:150This 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. -
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:160The 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. -
Teaching reliability theory with the Computer Algebra System Maxima
45-75Views:168The use of the Computer Algebra System Maxima as a teaching aid in an MSc module in Reliability Theory is described here. Extracts from student handouts are used to show how the ideas in Reliability Theory are developed and how they are intertwined with their applications implemented in Maxima. Three themes from the lectures are used to illustrate this: (1) Normal Approximations, (2) Markov Modelling, (3) Laplace Transform Techniques.
It is argued that Maxima is a good tool for the task, since: it is fairly easy to learn & use; it is well documented; it has extensive facilities; it is available for any operating system; and, finally, it can be freely downloaded from the Web. Maxima proves to be a useful tool even for Reliability research for certain tasks. This latter feature provides a seamless link from teaching to research – an important feature in postgraduate education.
