Search
Search Results
-
Development and assessment of non-cognitive skills among engineering students: a comparison across two universities
161-182Views:159Non-cognitive skills, such as logical thinking and problem solving, are crucial for success in engineering fields. To assess these skills in undergraduate engineering students, we designed a targeted test comprising four different types of tasks. The study was conducted among students at the Faculty of Engineering at the University of Debrecen, and the Faculty of Mechanical Engineering and Informatics at the University of Miskolc. The aim of this paper is to analyze the test results, gather students’ feedback, and examine the strength of the relationships between deductive reasoning, diagrammatic reasoning, and algebraic thinking.
Subject Classification: 97C20
-
The application of modelling tasks in the classroom – why and how? with reflections on an EU teacher training course
231-244Views:266The aim of the article is to present the concept of mathematical modelling in the classroom. LEMA (Learning and Education in and through Modelling and Applications) was an EU Comenius funded project in which mathematics educators from six countries worked to produce materials to support teachers' professional development. A group of voluntary Hungarian mathematics teachers were taught modelling for a year and we were and still are given feedback continously. The article leads us from the general concept of mathematical modelling to its practice in the classroom. It presents difficulties that teachers have to face when doing modelling lessons and their students' reactions are also mentioned. We present sample tasks from the material of the teacher training course as well as tasks that were created by the participants. -
Freudenthal fantasy on the bus, an American adaptation
133-142Views:200In the 1960’s two mathematicians, Hans Freudenthal in the Netherlands and Tamás Varga in Hungary, had argued that people learn mathematics by being actively involved and investigating realistic mathematical problems. Their method lives on in today’s teaching and learning through the various components of cooperative and active learning, by taking ownership in learning, and learning through student dialogue. The goal is to create a welcoming classroom atmosphere in which play takes the front seat. One such scenario is visiting various (animal) stations at the zoo by bus (illustrated by pictures). Passengers are getting on and off the bus at each station (illustrated by arrows), which is modeled on the open number line. This adapted and modified action research was carried out with 5-yearl-old children in public schools of Staten Island, NY in 2019.
Subject Classification: 97D40, 97F20, 97F30
-
Combinatorics – competition – Excel
427-435Views:194In 2001 the Informatics Points Competition of the Mathematics Journal for Secondary School Students (KÖMAL) was restarted [1]. The editors set themselves an aim to make the formerly mere programming competition a bit more varied. Therefore, every month there has been published a spreadsheet problem, a part of which was related to combinatorics. This article is intended to discuss the above mentioned problems and the solutions given to them at competitions. We will prove that traditional mathematical and programming tasks can be solved with a system developed for application purposes when applying a different way of thinking. -
Rational errors in learning fractions among 5th grade students
347-358Views:208Our paper focuses on empirical research in which we map out the errors in learning fractions. Errors are often logically consistent and rule-based rather than being random. When people face solving an unfamiliar problem, they usually construct rules or strategies in order to solve it (Van Lehn, 1983). These strategies tend to be systematic, often make ‘sense’ to the people who created them but often lead to incorrect solutions (Ben-Zeev, 1996). These mistakes were named rational errors by Ben-Zeev (1996). The research aims to show that when learning fractions, students produce such errors, identified in the literature, and that students who make these kinds of mistakes achieve low results in mathematics tests. The research was done among 5th-grade students.
Subject Classification: 97C10, 97C30, 97C70, 97D60, 97D70, 97F50
-
CS unplugged in higher education
1-23Views:221Nowadays, 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. -
Cultivating algorithmic thinking: an important issue for both technical and HUMAN sciences
107-116Views:183Algorithmic thinking is a valuable skill that all people should master. In this paper we propose a one-semester, algorithm-oriented computer science course for human science students. According to our experience such an initiative could succeed only if the next recipe is followed: interesting and practical content + exciting didactical methods + minimal programming. More explicitly, we suggest: (1) A special, simple, minimal, pseudo-code like imperative programming language that integrates a graphic library. (2) Interesting, practical and problem-oriented content with philosophical implications. (3) Exciting, human science related didactical methods including art-based, inter-cultural elements. -
Task variations for backtrack
107-120Views:222This article has been written for informatics teachers who want to issue back-track based tasks on their lessons or as homework or on competitions. We present a few methods to generate a more complicated problem from a simpler task, which will be more complex, and its solution needs a good idea or trick. Starting from an example, we lead the reader through increasingly di cult task variations.
Subject Classification: 97P50
-
Live & Learn: When a wrong program works
195-208Views:159In this paper an interesting and surprising case study of my programming education practice is presented. This case underlines the importance of methods, standards and rules of thumb of the programming process. These elements of the programming technology can be taught well in education and they can guarantee the quality of the implemented programs. However the case described in this paper brings an anomaly when a programming standard is violated during the programming process and, although it should imply that the implemented program code works badly, the program works perfectly. This anomaly is caused by a typical implementation problem: the boundary and rules of the machine representation of numbers. This anomaly is going to be analyzed and the appropriate conclusions of our case study will be deducted. -
Blind versus wise use of CAS
407-417Views:214During my courses for mathematics major students I often use technology linked to the arising problems. In such cases I noted that some students were used to learn just some procedures, which made them able to solve (partially) some problems and when they got the result, they accepted it passively and did not relate it to the initial problem.
In this paper I outline a strategy and investigate some simple exercises about how to develop a critical attitude towards the results obtained by technology in an introductory course to CAS.
I believe that wise use of technology offers an effective method in teaching mathematics, without reducing the students' mental contribution. -
Self-regulated learning in mathematics lessons at secondary level
139-160Views:141Self-regulation is a prerequisite to be able to set goals and to find suitable ways to reach them. Furthermore, it is an important ability which affects different areas of every day’s life. In educational context, self-regulation is often linked to self-regulated learning. The concept of self-regulated learning as well as key terms related to this topic such as problem-solving and modelling tasks will be discussed, while an emphasis lays on the role of the teacher. In this paper, a study on the attitudes of mathematics teachers towards self-regulated learning is presented. It focuses on teachers’ assessment of the possibility and limitations of self-regulated learning in mathematics lessons. It can be observed that most of the surveyed teachers try to incorporate self-regulatory processes in their teaching, but encounter difficulties related to various factors, such as their students, framework conditions, and the time required for such learning processes.
Subject Classification: 97D10
-
The Project Method and investigation in school mathematics
241-255Views:210The Project Method (PM) is becoming more common in the teaching of mathematics. Most of the time, Project Method means solving open and relatively wide formulated problems for the application of particular mathematical topics and the solving of everyday life problems.
At present many experts in the theory of teaching mathematics advocate teaching activities as the characteristic for most mathematical work in the classroom. Thus, there is a question: whether it is possible or eventual desirable to use the PM for solving genuine mathematical problems. This paper deals with this question and discusses the connection between the PM and investigation of new mathematical knowledge for students. Our experience has shown that the PM in connection with investigations can be a useful and effective approach to teaching mathematics. -
A geometric application to the third-order recurrence relations for sequences
287-302Views:181Using a third-order linear homogeneous recurrence relation with constant coefficients, it is found a limit-point of a sequence of affixes in plane. Starting from a classic geometric problem, an application is so created and few more nice properties are found and described. -
Die Stichprobe als ein Beispiel dafür, wie im Unterricht die klassische und die bayesianische Auffassung gleichzeitig dargestellt werden kann
133-150Views:159Teaching statistics and probability in the school is a new challenge of the Hungarian didactics. It means new tasks also for the teacher- and in service-teacher training. This paper contains an example to show how can be introduced the basic notion of the inference statistics, the point- and interval-estimation by an elementary problem of the public pole. There are two concurrent theories of the inference statistics the so called classical and the Bayesian Statistics. I would like to argue the importance of the simultaneously introduction of both methods making a comparison of the methods. The mathematical tool of our elementary model is combinatorial we use some important equations to reach our goal. The most important equation is proved by two different methods in the appendix of this paper. -
Our digital education habits in the light of their environmental impact: the role of green computing in education
69-86Views:302With the increasing use of IT tools, the environmental impacts they generate have also increased. Education is increasingly relying on digital tools to become a major emitter of CO2 itself. Therefore, the task of education is to teach future generations how to use IT tools efficiently while being environmentally aware. In addition to some forms of green computing, we show the level and ratio of those teachers who have corresponding IT knowledge in the Hungarian education. In this study, we present the justification of the problem through a case study, which estimates the Internet traffic of a website streaming popular educational resources. In addition, we will examine the extent to which national and international educational organization and guidance documents address the development of digital environmentally aware thinking. Based on the content of this study, we suggest some considerations for content developers to decide if they really need to create the digital content.
Subject Classification: 97P99, 94-06, 94-02
-
Maximum and minimum problems in secondary school education
81-98Views:218The aim of this paper is to offer some possible ways of solving extreme value problems by elementary methods with which the generally available method of differential calculus can be avoided. We line up some problems which can be solved by the usage of these elementary methods in secondary school education. The importance of the extremum problems is ignored in the regular curriculum; however they are in the main stream of competition problems – therefore they are useful tools in the selection and development of talented students. The extremum problem-solving by elementary methods means the replacement of the methods of differential calculus (which are quite stereotyped) by the elementary methods collected from different fields of Mathematics, such as elementary inequalities between geometric, arithmetic and square means, the codomain of the quadratic and trigonometric functions, etc. In the first part we show some patterns that students can imitate in solving similar problems. These patterns could also provide some ideas for Hungarian teachers on how to introduce this topic in their practice. In the second part we discuss the results of a survey carried out in two secondary schools and we formulate our conclusion concerning the improvement of students' performance in solving these kind of problems. -
Solving mathematical problems by using Maple factorization algorithms
293-297Views:178Computer 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. -
Taking learning styles into consideration in e-learning based education
385-396Views:109In improving electronic teaching material processes we should take the student's learning styles or methods into consideration. The ways learners receive information may be shared into three categories (modalities): visual, auditory, kinesthetic (tactile). In this paper I present some pedagogical questions of the electronic teaching-learning environment, offer a brief survey of the different learning style theories and emphasise the importance of the modalities in encoding information. The electronic teaching material should encourage the learner to choose an appropriate form of syllabus by which his knowledge can become more efficient. -
Application of computer algebra systems in automatic assessment of math skills
395-408Views:216Mathematics is one of those areas of education, where the student's progress is measured almost solely by testing his or her ability of problem solving. It has been two years now that the authors develop and use Web-based math courses where the assessment of student's progress is fully automatic. More than 150 types of problems in linear algebra and calculus have been implemented in the form of Java-driven tests. Those tests that involve symbolic computations are linked with Mathematica computational kernel through the Jlink mechanism. An individual test features random generation of an unlimited number of problems of a given type with difficulty level being controlled flat design time. Each test incorporates the evaluation of the student's solution. Various methods of grading can be set at design time, depending on the particular purpose that a test is used for (self-assessment or administrative exam). Each test is equipped with the correct solution presentation on demand. In those problems that involve a considerable amount of computational effort (e.g. Gauss elimination), additional special tools are offered in a test window so that the student can concentrate on the method of solution rather than on arithmetic computations. (Another obvious benefit is that the student is thus protected from the risk of frustrating computational errors). Individual tests can be combined into comprehensive exams whose parameters can be set up at design time (e.g., number of problems, difficulty level, grading system, time allowed for solution). The results of an exam can be automatically stored in a database with all authentication and security requirements satisfied. -
Teaching student teachers: various components of a complex task
55-72Views:104In this paper we summarize various aspects of teacher training and teaching student teachers (mainly concerning teachers of upper secondary school and High school). We stress several hints and recommendations to better achieve the obviously important aim: they should learn doing, understanding and teaching mathematics!
Of course, our view is particularly influenced by European traditions, but we think most of them equally apply to teacher training and teaching student teachers elsewhere. Neither is the paper meant to give an all sided overview about the problem field of teacher education as a whole, nor does it contain provocative, completely new ideas. We just want to describe our view of some aspects, based primarily on our personal experience in the mentioned field. -
Trigonometric identities via combinatorics
73-91Views:264In this paper we consider the combinatorial approach of the multi-angle formulas sin nΘ and cos nΘ. We describe a simple "drawing rule" for deriving the formulas immediately. We recall some theoretical background, historical remarks, and show some topics that is connected to this problem, as Chebyshev polynomials, matching polynomials, Lucas polynomial sequences.
Subject Classification: 05A19
-
Better understanding mathematics by algorithmic thinking and computer programming
295-305Views:317Tamás 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
-
Normalization based on dependency diagram
121-132Views:172Normalization is an important database planning method, although the understanding and application of this method brings up the utmost problem during data modelling. That is why we were looking for alternative normalization methods, from which the normalization with dependency diagram proved to be the most efficient. This was also confirmed by the statistical estimation of the carried out survey. -
A new approach for explaining Rhind's Recto – and its utility in teaching
337-355Views:129The Recto is a table in the Rhind Mathematical Papyrus (RMP) of ancient Egypt containing the unit fraction decompositions of fractions 2/n (3 ≤ n ≤ 101, n odd). To the question how (and why) the decompositions were made, there exists no generally accepted answer. The fact that in some other sources of Egyptian mathematics decompositions different from those in Recto exist makes the problem more difficult.
Researchers normally try to find the answer in some formulas by which the entries of the table were calculated [see e.g. 1, 42]. We are convinced that the correct answer is not hidden in formulas but in the characteristics of Egyptian mathematics namely those of fraction and division concepts. To study them is important not only from historical point of view but also from methodological one: how to develop fraction concept and how to make division easier. -
An interactive animation for learning sorting algorithms: How students reduced the number of comparisons in a sorting algorithm by playing a didactic game
45-62Views:223Learning programming and understanding algorithms is one of the hardest tasks for novice computer science students. One of the basic algorithms they learn during the introductory programming and algorithms courses are the sorting algorithms. Students like learning these and other algorithms by animations and didactic games, however, these animations are not educationally useful in every case. In this article, we present our educational sorting game, which can be used to introduce the topic of sorting algorithms. The didactic game can be used later too, as a demonstrative tool for explaining the more efficient, quicksort algorithm. We conducted a pedagogical experiment, in which we examined the process of development of sorting algorithms by students while they used the mentioned didactic game. The results showed that students were able to create an algorithm to solve the sorting problem, and they improved its effectiveness by reducing the number of comparisons in the algorithm. They were also able to understand the importance of the efficiency of algorithms when we demonstrated them the quicksort algorithm using the same tool after the experiment.
