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• 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

  251-268

  Katalin Fried

  Views:

  17

  Teachers 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.

• Using the computer to visualise graph-oriented problems

  15-32

  Erika Gyöngyösi

  Views:

  32

  The computer, if used more effectively, could bring advances that would improve mathematical education dramatically, not least with its ability to calculate quickly and display moving graphics. There is a gap between research results of the enthusiastic innovators in the field of information technology and the current weak integration of the use of computers into mathematics teaching.
  This paper examines what exactly the real potentials of using some mathematics computer software are to support mathematics teaching and learning in graph-oriented problems, more specifically we try to estimate the value added impact of computer use in the mathematics learning process.
  While electronic computation has been used by mathematicians for five decades, it has been in the hands of teachers and learners for at most three decades but the real breakthrough of decentralised and personalised micro-computer-based computing has been widely available for less than two decades. And it is the latter facility that has brought the greatest promise for computers in mathematics education. That computational aids overall do a better job of holding students' mathematical interest and challenging them to use their intellectual power to mathematical achievement than do traditional static media is unquestionable. The real question needing investigation concerns the circumstances where each is appropriate.
  A case study enabled a specification of advantages and obstacles of using computers in graph-oriented questions. Individual students' interviews revealed two less able students' reactions, difficulties and misinterpretations while using computers in mathematics learning.
  Among research outcomes is that the mathematical achievement of the two students observed improved and this makes teaching with computers an overriding priority for each defined teaching method.
  This paper may not have been realised without the valuable help of the Hungarian Eötvös State Grant.

• Mapping students’ motivation in a problem oriented mathematics classroom

  111-121

  Emőke Báró

  Views:

  65

  This 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

• Forming the concept of parameter with examples of problem solving

  201-215

  Katarzyna Wadoń-Kasprzak

  Views:

  31

  Pupils are encountering difficulties with learning algebra. In order for them to understand algebraic concepts, particularly the concept of parameter it was decided by the teacher of mathematics and Information Technology to integrate the teaching of these two subjects. The aim of this study is to investigate whether, and to what degree, software can be useful in process of forming the concept of parameter. This longitudinal study was conducted in a junior high school (13-16 year old children) using different computer programs.

• The use of different representations in teaching algebra, 9 th grade (14-15 years old)

  29-42

  Eszter Árokszállási

  Views:

  33

  Learning Algebra causes many difficulties for students. For most of them Algebra means rote memorizing and applying several rules without understanding them which is a great danger in teaching Algebra. Using only symbolic representations and neglecting the enactive and iconic ones is a great danger in teaching Algebra, too. The latter two have a primary importance for average students.
  In our study, we report about an action research carried out in a grade 9 class in a secondary school in Hungary.The results show that the use of enactive and iconic representations in algebra teaching develops the students' applicable knowledge, their problem solving knowledge and their problem solving ability.

• Maximum and minimum problems in secondary school education

  81-98

  Zsolt Fülöp

  Views:

  31

  The 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.

• Some problems of solving linear equation with fractions

  339-351

  Gordana Stankov

  Views:

  18

  The aim of this paper is to offer some possible ways of solving linear equations, using manipulative tools, in which the "−" sign is found in front of an algebraic fraction which has a binomial as a numerator. It is used at 8th grade.

• The application of modelling tasks in the classroom – why and how? with reflections on an EU teacher training course

  231-244

  Gabriella Ambrus

  Ödön Vancsó

  Balázs Koren

  Views:

  34

  The 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.

• Regula falsi in lower secondary school education

  169-194

  Zsolt Fülöp

  Views:

  36

  The 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.

• Models of impulsive phenomena: experiences with writing an interactive textbook

  333-345

  János Karsai

  Views:

  31

  "Take the textbook to computer" – is said quite often. Would it be so easy? If we start such a work, we meet a lot of trouble very soon. A book stored on a CD, read on the screen of computer and containing some hyperlinks does not become automatically electronic textbook. There are difficulties also in writing merely an electronic attachment to a classical book. In this paper, we deal with some important features (actually important from our point of view) of interactive mathematics textbooks, arising mathematical, didactical and technical problems. The "principles" are illustrated with examples taken from the book-CD "Models of Impulsive Phenomena".

• Preliminary e ects of mathematics curriculum development for primary school student teachers in Sárospatak Comenius Campus

  95-107

  Erika Gyöngyösi-Wiersum

  Views:

  31

  Hungarian 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.