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Analysis of the affective factors of learning mathematics among teacher trainees
225-254Views:37The Hungarian National Core Curricula gives primacy to the development of abilities and the practical application of knowledge. The task of the training programme is primarily to prepare teacher trainees for the teaching and educating profession. As teachers, they are going to plan, organize, help, guide, control and evaluate the learning of mathematics of individuals and groups of students from the age of 6 to 10 (12), and cultivate their mathematical skills, thinking and positive attitude towards any mathematical activities. In order to train educators who are able to meet the above requirements on high standard, it is necessary to update the teacher training programme based on the trainees' preliminary knowledge and motivation level.
The key to learn about the child's mind and achieve conscious development is the systematization of factual knowledge and methodological awareness. The modern, flexible approach to subject pedagogy, based on pedagogy, psychology and epistemology, qualifies trainees to educate learners who understand and like mathematics. Therefore, it is essential to develop the trainees' positive approach to mathematics and arouse their demand for continuous professional improvement. (Programme of the four-year primary school teacher training, 1995.)
In our research we are looking for ways of ascertaining the starting parameters which have influence on the planning of the studies of mathematics and subject pedagogy. In this article we introduce a questionnaire by the means of which we collected information on the trainees' attitude and its changing towards mathematics. With the help of the analysis of the answers we paint a picture of the ELTE TÓFK (Eötvös Loránd University, Faculty of Elementary and Nursery School Teacher's Training) third year students' attitude to the subject, and we compare it to the tendencies noticed in the mass education. The energy invested in learning is influenced by the assumption of the relevance and importance of the subjects. Therefore we considered it also our task to reveal. Besides the students' attitude toward mathematics and their assumption about their own competence we have collected data also on their performance in the subject. Summarising the research results we show the advantages of the questionnaire, and summarise the observations which would indicate need for methodological changes in the mathematics teacher training. -
Teaching student teachers: various components of a complex task
55-72Views:26In 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. -
The mathematics teacher trainee as an assistant teacher
295-306Views:23The experiment described in the article aims to answer two needs at once: that of assistant teachers in schools, and that of a more practical training of mathematics teachers. The answer suggested is a model of school experience where mathematics teacher trainees work as assistant teachers in schools. An attempt to realize this model is described, and it is evaluated positively. -
Developing a method to determine teachers’ and pupils’ activities during a mathematics lesson
25-43Views:37Third-graders from nineteen classrooms (N = 316) were asked to draw a picture on a mathematics lesson. Based on these drawings we have developed a data analysing method that allows us to find out how pupils present both their teacher's and their classmates' activities in their drawings. Two inventories were formed that contain, respectively, teachers' and pupils' activities during a mathematics lesson as seen in the pupils' drawings. The first inventory contains 14 separate items organized into six groups that contain teacher activities like asking questions and giving feedback on mathematics. Ten of the items are related to teaching and the rest contain items like keeping order in addition to the teacher's location in the classroom. Respectively, pupils' activities are organized into five groups that contain altogether 22 items. These contain the activities of a single pupil, and also pupil-teacher and pupil-pupil discussions on mathematics. -
E-learning in teacher training
277-294Views:10A research has been organised with three Colleges taking part during the academic year of 2002-03. These institutions were
• The Teacher's Training College of Baja
• Eszerházy Károly College of Eger
• The College of Nyíregyháza
The aim of the research was to reveal differences between results of students studying in the traditional way and of students using e-learning.
The survey has been carried out among students of PE (physical education). A distance educational programme (Basics of Gymnastics) developoed before launching the survey served as basis for the survey [5]. The results of the research were first presented at the Agria-Média Conference in 2004. After analysing the results the findings were presented at the 3rd International Conference on Education and Information Systems in Orlando, Florida in July 2005.
This paper tries to reveal the structure of the e-learning programme, the environment of the research and the latest results found after the final analyses of the research. -
Evaluating admission procedures for teacher education in Finland
231-243Views:34In 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. -
Why some children fail? Analyzing a test and the possible signs of learning disorders in an answer sheet: dedicated to the memory of Julianna Szendrei
251-268Views:17Teachers and educators in mathematics try to uncover the background of the mistakes their students make for their own and their students' benefit. Doing this they can improve their teaching qualities, and help the cognitive development of their pupils. However, this improvement does not always support their students with learning disorders, since their problem is not caused by wrong attitude or lack of diligence. Therefore, it is the interest of a conscientious teacher to recognize whether the weaker performance of a student is caused by learning disorders, so the helping teacher can give useful advices. Although the teacher is not entirely responsible for the diagnosis, but (s)he should be be familiar with the possible symptoms in order to make suggestions whether or not to take the necessary test of the learning disorders.
In this article, through examining a test and the answer sheet of a single student, I show some signs that might be caused by learning disorders. -
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. -
Dynamic methods in teaching geometry at different levels
1-13Views:37In this paper we summarize and illustrate our experiences on DGS-aided teaching geometry of the courses "Computer in mathematics" and "Mathematical software" held for students at Juhász Gyula Teacher Training College of University of Szeged. Furthermore, we show examples from our grammar school experiences too. The figures in this paper were made by using Cinderella ([19]) and Euklides ([21]). -
Outstanding mathematicians in the 20th century: András Rapcsák (1914-1993)
99-110Views:27In this paper we commemorate the life and work of András Rapcsák on the occasion of the centenary of his birth. He was an outstanding professor and a scholar teacher. He was head of the Department of Geometry (1958-1973) and the director of the Institute of Mathematics at the University of Debrecen (Hungary). He played an important role in the life of the University of Debrecen. He was the rector of this university between 1966 and 1973.
At the beginning of his career he taught at secondary schools in several towns. He wrote mathematical schoolbooks with coauthors. He also taught at Teacher's College in Debrecen and in Eger.
He became to interested in differential geometry under the influence of Ottó Varga. The fields of his research were line-element spaces and related areas. He was elected an Ordinary Member of the Hungarian Academy of Science in 1965. He wrote 21 papers, 8 school and textbooks and 3 articles in didactics of mathematics. -
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 polygons in the secondary school: a four country comparative study
29-65Views:38This study presents the analysis of four sequences of videotaped lessons on polygons in lower secondary schools (grades 7 and 8) taught by four different teachers in four different countries (Belgium, Flanders, England, Hungary and Spain). Our study is a part of the METE project (Mathematics Educational Traditions in Europe). The aims and methodology of the project are described briefly in the introduction. In the next section of this paper we describe various perspectives on teaching and learning polygons which were derived from the literature, concerning the objectives, conceptual aspects and didactic tools of the topic. The next two sections introduce the main outcomes of our study, a quantitative analysis of the collected data and a qualitative description linked to the perspectives on teaching polygons. We conclude by discussing some principal ideas related to the theoretical and educational significance of this research work. -
Die Stichprobe als ein Beispiel dafür, wie im Unterricht die klassische und die bayesianische Auffassung gleichzeitig dargestellt werden kann
133-150Views:30Teaching 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. -
A differentiated e-learning teaching program in mathematics
299-308Views:39The intelligent online interactions between students and teacher are still not assured because of the fact that a learning management system could not play the role of a teacher in producing a chain of deduction. Furthermore, managing a course in existing e-learning systems has not yet guaranteed the differentiated teaching because it does not enable students to appropriately learn at their corresponding levels. In this paper, we would like to introduce a differentiated e-learning course in Vietnam. We also present some designing principles for such courses and propose some typical situations in teaching mathematics aimed at helping high school students individualize their online learning in mathematics. -
The role of representations constructed by students in learning how to solve the transportation problem
129-148Views:107The purpose of the research presented in this paper was to study the role of concrete and table representations created by students in learning how to solve an optimization problem called the transportation problem. This topic was learned in collaborative groups using table representations suggested by teachers in 2021. In 2022, the researchers decided to enrich the students’ learning environment with concrete objects and urged the students to use them to present the problem to be solved. The students did it successfully and, to be able to record it in their notebooks, they constructed a table representation by themselves without any help from their teacher. After that, they managed to solve the problem by manipulating the objects. At the same time, each step in the solution was presented with changes in the table. The students were assessed before (pre-test) and after collaborative learning (test) in both academic years. The pre-test results were similar, but the test results were better in 2022. Therefore, it can be concluded that using concrete and table representations constructed by students in learning how to solve transportation problems makes collaborative learning more constructivist and more effective than when they use only table representations suggested by their teachers.
Subject Classification: 97M10, 97M40
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Let's learn database programming in an active way
213-228Views:22This paper introduces how I applied the "learning by doing" method in the education of advanced knowledge of database systems in Software Engineering BSc program. The first goal of my method is to enable the students to use the PL/SQL and SQL as a skill, namely they get a practical competence which can be immediately used in business. In the laboratory the students independently practise the material learnt on the lecture. They get feedback for all their activities from the teacher. A software system helps administer the solutions, automatically verifies the syntax of them and helps the teacher to evaluate them. The paper summarises the results of three semesters. In the last year I compared the active learning method with the traditional method. I asked the students in a voluntary survey about the active learning method. -
How to teach computer programming if our goal is the International Olympiad in Informatics
13-25Views:35Nowadays if a student in Hungary (age between 17-20 years old) wants to be the member of the Hungarian selected team (has four members) to participate in the International Olympiad in Informatics (IOI), first, he has to qualify himself in the first fifteen of the National Secondary School Competition (OKTV) in the programming category after the III. round. Then he should be in the first four place after the sixth round of the Selection Competition. Being successful is necessary that the student wants to start studying computer programming at least in the 9th school year and he needs a teacher who prepares him. In the last nine years three students of the author have participated in five Olympics and two of them won gold and bronze medals. This article wants to demonstrate the methods that a teacher needs to use to teach students in 9th school year for computer programming, to be the member of the Hungarian National Team after three or four years. -
The application of modelling tasks in the classroom – why and how? with reflections on an EU teacher training course
231-244Views:34The 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. -
Preliminary e ects of mathematics curriculum development for primary school student teachers in Sárospatak Comenius Campus
95-107Views:30Hungarian students' mathematics performance has been getting weaker in the past few years. A possible solution to stop this tendency is to develop curriculum. Therefore, Hungarian researchers have been refining a particular framework of curriculum development in primary school teacher training programmes. The national curriculum is designed on the assumption that learning can be broken into a sequence of levels and students can evenly succeed in gaining knowledge at successive levels. In this paper, we want to discuss how to reduce students' difficulties with different background to grow competence at successive levels. -
The requirements in statistics education – comparison of PISA mathematical tasks and tasks from the mathematical textbooks in the field of statistics
263-275Views:34This 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. -
Psychology - an inherent part of mathematics education
1-18Views:146On the chronology of individual stations of psychology and their effect on mathematics education designed as working document for use in teacher training.
The article is structured as a literature survey which covers the numerous movements of psychology towards mathematics education. The current role of psychology in mathematics education documented by different statements and models of mathematics education should provide a basis for the subsequent investigations. A longitudinal analysis pausing at essential marks takes centre of the continuative considerations. The observed space of time in the chapter covers a wide range. It starts with the separation of psychology from philosophy as a self-contained discipline in the middle of the 19th and ends with the beginning of the 21st century. Each stop states the names of the originators and the branches of psychology they founded. These stops are accompanied by short descriptions of each single research objective on the one hand, and their contributions to mathematics education on the other hand. For this purpose, context-relevant publications in mathematics education are integrated and analysed. The evaluation of the influence of concepts of psychology on teaching technology in mathematics is addressed repeatedly and of great importance. The layout of this paper is designed for the use as a template for a unit in teacher-training courses. The conclusion of the article where the author refers to experiences when teaching elements of psychology in mathematics education courses at several universities in Austria is intended for a proof on behalf of the requested use.Subject Classification: 01A70, 01-XX, 97-03, 97D80
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Report on the "English Language Section of Varga Tamás Days 2009"
169-175Views:31The 9th English Language Section as a part of the Varga Tamás Days was organised by the Department of Mathematics Education at the Teacher Training Institute of the Eötvös Loránd University. We report on the talks and the following discussions in this section. -
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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How to use our own program evaluation system to streamline teaching computer programming
73-80Views:34During computer programming contests the use of automatic evaluation systems is becoming more and more frequent. In said systems the contestants are allowed to submit their source code that will be evaluated with the results reported back to them. According to this report the contestant can realise for what test cases his program works properly and for what cases does it fail. This kind of on-line evaluation system is used for example in the International Olympiad in Informatics (IOI), in the final round of the Nemes Tihamér National Programming Competition, and in the Selection Competition for IOI in Hungary. A contest management system can be used for other purposes apart from this singular example. A well-developed evaluation system can foster not only the teaching of computer programming and the preparation of students for programming contests but the teacher's work as well. -
Report on "English Language Section of Varga Tamás Days": annual meeting, 11–12 November, 2005, Budapest, Hungary
217-223Views:36The Department of Mathematics Education at Teacher Training Institute of Eötvös University organised the 5th English Language Section as a part of Varga Tamás Methodical Days. We discuss the activities based on the authors' abstracts.