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Examining relation between talent and competence through an experiment among 11th grade students
17-34Views:120The areas of competencies that are formable, that are to be formed and developed by teaching mathematics are well-usable in recognizing talent. We can examine the competencies of a student, we can examine the competencies required to solve a certain exercise, or what competencies an exercise improves.
I studied two exercises of a test taken by students of the IT specialty segment of class 11.d of Jedlik Ányos High School, a class that I teach. These exercises were parts of the thematic unit of Combinatorics and Graph Theory. I analysed what competencies a gifted student has, and what competencies I need to improve while teaching mathematics. I summarized my experience about the solutions of the students, the ways I can take care of the gifted students, and what to do to the less gifted ones. -
Teaching of problem-solving strategies in mathematics in secondary schools
139-164Views:85In the Hungarian mathematics education there is no explicit teaching of problem-solving strategies. The best students can abstract the strategies from the solutions of concrete problems, but for the average students it is not enough. In our article we report about a developmental research. The topic of the research was the explicit teaching of two basic strategies (forward method, backward method). Based on our experiences we state that it is possible to increase the effectivity of students' problemsolving achievement by teaching the problem-solving strategies explicitly. -
Levels of students' understanding on infinity
317-337Views:164Here 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. -
Compositions of dilations and isometries in calculator-based dynamic geometry
257-266Views:89In an exploratory study pre-service elementary school teachers constructed dilations and isometries for figures drawn and transformed using dynamic geometry on calculators. Observational and self assessments of the constructed images showed that the future teachers developed high levels of confidence in their abilities to construct compositions of the geometric transformations. Scores on follow-up assessment items indicated that the prospective teachers' levels of expertise corresponded to their levels of confidence. Conclusions indicated that dynamic geometry on the calculator was an appropriate technology, but one that required careful planning, to develop these future teachers' expertise with the compositions. -
Process or object? Ways of solving mathematical problems using CAS
117-132Views:65Graphing and symbol manipulating calculators are now a part of mathematics education in many countries. In Norway symbol manipulating calculators have been used at various exams in upper secondary education. An important finding in mathematics education is the duality of mathematical entities – processes and objects. Building on the theoretical development by Anna Sfard and others, the students' solutions on exam problems in upper secondary education are discussed with reference to procedural and structural knowledge. -
Smartphones and QR-codes in education - a QR-code learning path for Boolean operations
111-120Views:104During 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. -
Ein anderer Weg bei dem Logarithmusunterricht: Ein entwickelndes Unterrichtsexperiment
1-16Views:63In my developmental experiment I tried to fusion the expectations of the Hungarian education and the realistic mathematics education. The duration of this experiment was 33 lectures long. In this article I try to show how were introduced the definition, the rules of logarithm with real life problems and the outcome of the experiment. -
Differentiated instruction not only for Mathematics teachers
163-182Views:254The 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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Mapping students’ motivation in a problem oriented mathematics classroom
111-121Views:173This research focuses on mapping students’ motivation by implementing problem-solving activities, namely how the problem-oriented approach affects the students’ commitment, motivation, and attitude to learning. As a practicing teacher, the author faced difficulties with motivation and sought to improve her practice in the form of action research as described in this paper. Based on the literature, the author describes sources of motivation as task interest, social environment, opportunity to discover, knowing why, using objects, and helping others. The author discusses the effect of problem-oriented teaching on the motivation of 7th-grade students. In this paper, the results of two lessons are presented.
Subject Classification: 97C20, 97D40, 97D50, 97D60
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Outstanding mathematicians in the 20th century: András Rapcsák (1914-1993)
99-110Views:134In 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. -
The time spent on board games pays off: links between board game playing and competency motivation
119-131Views:292The impact playing has on the development of thinking is an important topic of psychology of learning, brain research and mathematics didactics.
Our research is also connected to the aforementioned topic. We investigated the effects of playing board games on competence motivation and the development of mathematical competencies.
In this paper, we present the results of an experiment carried out in a secondary school class.
The experimental group spent one of three weekly mathematics lessons playing board games.
Apart from the several advantages of playing games in general, we can conclude that, based on the results of the national competence measurement, the mathematical competence of the students developed properly.
The readiness and the progress of the pupils were compared on the basis of input and output tests and an initial knowledge measurement and, at the same time, we compared their level of mathematical competence with the results of the national competence
measurement.Subject Classification: 97C70, 97D40
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The effects of chess education on mathematical problem solving performance
153-168Views:169We investigate the connection between the "queen of sciences" (mathematics) and the "royal game" (chess) with respect to the development of mathematical problem solving ability in primary school education (classes 1-8, age 7-15) where facultative chess education is present. The records of the 2014 year's entrance exam in mathematics – obligatory for the enrollment to secondary grammar schools in Hungary – are compared for the whole national database and for the results of a group containing chess-player students. The problems in the tests are classified with respect to the competencies needed to solve them. For the evaluation of the results we used standard mathematical statistical methods. -
Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: 31 March – 2 April, 2023 Oradea, Romania
83-107Views:311The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Oradea, Romania, at Partium Christian University, from 31 March to 2 April, 2023. It was organized by the Doctoral School of Mathematical and Computational Sciences of the University of Debrecen and Partium Christian University. The 85 participants – including 18 PhD students – came from 9 countries and represented 30 institutions of higher and secondary education. There were 4 plenary and 53 session talks in the program.
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Why do we complicate the solution of the problem? reflection of Finnish students and teachers on a mathematical summer camp
405-415Views:147This paper deals with reactions and reflections of Finnish secondary school students and teachers on Hungarian mathematics teaching culture. The experiences were collected at a mathematics summer camp in Hungary. -
Teaching student teachers: various components of a complex task
55-72Views:74In 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. -
14 to 18-year-old Hungarian high-school students' view of mathematicians appearing in the media - a case study
183-194Views:101One way to develop positive attitude toward STEM subjects that popular media, including movies and films can be engaged to promote more positive and inclusive STEM images. The movie Hidden numbers offers an opportunity to explore the representations of scholars, especially mathematicians within a biographical drama. Focusing on 5 characters, this article first discusses whether these characters fit into stereotypical scientist image or not. Secondly, we examine how high school students evaluate these characters. We argue that this movie is suitable to promote positive attitude toward STEM subjects. -
Maximum and minimum problems in secondary school education
81-98Views:130The 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. -
Conversion between different symbolic representations of rational numbers among 9th-grade students
29-45Views:186Our research involved nearly 800 ninth-grade secondary school students (aged 14-15) during the first weeks of the 2023/2024 school year. Less than 40% of students solved the text problems related to common fractions and percentages correctly. In terms of student solutions, pupils showed a higher success rate when the text of the problem contained common fractions, and the solution had to be given as a percentage. In this case, the success rate of switching between different symbolic representations of rational numbers (common fraction, percentage) was also higher. Observation of the methods used to solve also suggests that the majority of students are not flexible enough when it comes to switching between different representations.
Subject Classification: 97F80, 97D70
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The influence of computer on examining trigonometric functions
111-123Views:103In this paper the influence of computer on examining trigonometric functions was analyzed throughout the results questionnaire. The students, as usual, had to examine two trigonometric functions, both were given with the appropriate instructions. Three groups were tested. Two of those three groups were prepared with the help of computer and the third one was taught without computer. From the analysis of the questionnaire it follows that the computer has a great influence on understanding of the connections between the graph and very complex calculations. -
Katalin Juhász (1952-2012)
1-2Views:67Katalin Juhász was born in 1952, in Tarnaméra (Hungary), where she also completed her primary school studies. She finished Erzsébet Szilágyi Highschool, Eger, in 1971 and she graduated in mathematics from Lajos Kossuth University (KLTE), Debrecen, in 1976. That year she married a physicist and together they brought up their son. -
Les mathématiques dans le grand public et dans l'enseignement: quelques éléments d'une analyse didactique
195-216Views:91The paper looks for reaction of the public at large that is people out of educational system, concerning the mathematical exercises. We can see some results about:
• impact of terms on the motivation
• the effects of the traditional didactic on the method to resolve a problem.
Résumé. Cet article cherche la réactions du grand public c.a.d. de personnes hors systéme scolaire, de nombreuses années aprés avoir terminé leurs études vis á vis des exercises mathématiques.
Nous présentons quelques résultats concernant les points suivants:
– l'impact de l'« habillage » d'un énoncé sur la motivation
– les effets de l'absence d'un contrat didactique traditionnel sur la maniére de résoudre un probléme. -
On four-dimensional crystallographic groups
391-404Views:99In his paper [12] S. S. Ryshkov gave the group of integral automorphisms of some quadratic forms (according to Dade [6]). These groups can be considered as maximal point groups of some four-dimensional translation lattices in E^4. The maximal reflection group of each point group, its fundamental domain, then the reflection group in the whole symmetry group of the lattice and its fundamental domain will be discussed. This program will be carried out first on group T. G. Maxwell [9] raised the question whether group T was a reflection group. He conjectured that it was not. We proved that he had been right. We shall answer this question for other groups as well. Finally we shall give the location of the considered groups in the tables of monograph [4]. We hope that our elementary method will be useful in studying linear algebra and analytic geometry. Futhermore, 4-dimensional geometry with some visualisation helps in better understanding important concepts in higher-dimensional mathematics, in general. -
Exploring the basic concepts of Calculus through a case study on motion in gravitational space
111-132Views:184In universities, the Calculus course presents significant challenges year after year. In this article, we will demonstrate how to use methods of Realistic Mathematics Education (RME) to introduce the concepts of limits, differentiation, and integration based on high school kinematics and dynamics knowledge. All mathematical concepts are coherently built upon experiences, experiments, and fundamental dynamics knowledge related to motion in a gravitational field. With the help of worksheets created using GeoGebra or Microsoft Excel, students can conduct digital experiments and later independently visualize and relate abstract concepts to practical applications, thereby facilitating their understanding.
Subject Classification: 97D40, 97I40, 97M50
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Pupils' meta-discursive reflection on their cooperation in mathematics: a case study
147-169Views:108This article addresses the issue of how 10–11 year old pupils in pairs can actively get involved in reforming their behavior as they reflect on their interaction in order to solve mathematical problems. We studied the opportunities offered for the development of meta-discursive reflection in a pair of pupils in two alternative environments: (1) pupils' observations and discussions on their video-recorded cooperation and (2) pupils' participation in playing and acting in a drama. The results of the research revealed three levels of the pupils' meta-discursive reflection on their interaction: (1) focusing on the achievement of personal goals, (2) focusing on partners' responsibility and (3) focusing on mutual responsibility. Both environments helped the pupils to improve their socio-mathematical interaction. -
Looking back on Pólya’s teaching of problem solving
207-217Views:423This article is a personal reflection on Pólya's work on problem solving, supported by a re-reading of some of his books and viewing his film Let Us Teach Guessing. Pólya's work has had lasting impact on the goals of school mathematics, especially in establishing solving problems (including non-routine problems) as a major goal and in establishing the elements of how to teach for problem solving. His work demonstrated the importance of choosing rich problems for students to explore, equipping them with some heuristic strategies and metacognitive awareness of the problem solving process, and promoting 'looking back' as a way of learning from the problem solving experience. The ideas are all still influential. What has changed most is the nature of classrooms, with the subsequent appreciation of a supporting yet challenging classroom where students work collaboratively and play an active role in classroom discussion.
Subject Classification: 97D50, 97A30
