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• What can we learn from Tamás Varga’s work regarding the arithmetic-algebra transition?

  39-50

  Gyöngyi Szanyi

  Zsuzsanna Jánvári

  Views:

  73

  Tamás 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

• The transition problem in Hungary: curricular approach

  1-16

  Éva Erdélyi

  András Dukán

  Csaba Szabó

  Views:

  117

  The curricular background of the transition problem from highschool to universty is analysed in Hungary. While students finish their mathematical studies successfully at highschool, pass their final exams, this knowledge seems to disappear at their first year at university. We investigate the mathematical knowledge expected by the Hungarian universities and compare it to expectations of the National Core Curriculum. Based on the levelling tests of four universities we created a seven problem test for highschool students containing very basic problems required both by the universities and the National Core Curriculum. We analyse the results of the test.

  Subject Classification: D34, D35

• Regula falsi in lower secondary school education II

  121-142

  Zsolt Fülöp

  Views:

  92

  The aim of this paper is to investigate the pupils' word problem solving strategies in lower secondary school education. Students prior experiences with solving word problems by arithmetic methods can create serious difficulties in the transition from arithmetic to algebra. The arithmetical methods are mainly based on manipulation with numbers. When pupils are faced with the methods of algebra they often have difficulty in formulating algebraic equations to represent the information given in word problems. Their troubles are manifested in the meaning they give to the unknown, their interpretation what an equation is, and the methods they choose to set up and solve equations. Therefore they mainly use arithmetical and numerical checking methods to solve word problems. In this situation it is necessary to introduce alternative methods which make the transition from arithmetic to algebra more smooth. In the following we will give a detailed presentation of the false position method. In our opinion this method is useful in the lower secondary school educational processes, especially to reduce the great number of random trial-and-error problem solving attempts among the lower secondary school pupils. We will also show the results of some problem solving activities among grade 6-8 pupils. We analysed their problem solving strategies and we compared our findings with the results of other research works.

  Subject Classification: 97-03, 97-11, 97B10, 97B50, 97D40, 97F10, 97H10, 97H20, 97H30, 97N10, 97N20

• Analyse d’obstacles lies a la notion de fonction reciproque

  43-61

  Susana Murillo-López

  André Antibi

  Views:

  3

  L'article présente une réflexion sur les difficultés éventuelles des étudiants au cours de l'étude des fonctions réciproques. Nous nous intéressons à l'enseignement de cette notion dans le cadre de la transition entre le lycée et la première année d'université en France. L'article résume la façon de présenter de nos jours le concept de fonction réciproque dans le curriculum français. Nous présentons des propositions d'enseignement issues de quelques travaux de recherche anglophones. Cela nous permet de mettre en lumière l'existence d'obstacles dans l'apprentissage et de difficultés dans l'enseignement de cette notion.

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

  95-107

  Erika Gyöngyösi-Wiersum

  Views:

  28

  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.

• Transition from arithmetic to algebra in primary school education

  225-248

  Zsolt Fülöp

  Views:

  29

  The main aim of this paper is to report a study that explores the thinking strategies and the most frequent errors of Hungarian grade 5-8 students in solving some problems involving arithmetical first-degree equations. The present study also aims at identifying the main arithmetical strategies attempted to solve a problem that can be solved algebraically. The analysis focuses on the shifts from arithmetic computations to algebraic thinking and procedures. Our second aim was to identify the main difficulties which students face when they have to deal with mathematical word problems. The errors made by students were categorized by stages in the problem solving process. The students' written works were analyzed seeking for patterns and regularities concerning both of the methods used by the students and the errors which occured in the problem solving process. In this paper, three prominent error types and their causes are discussed.

• Fostering engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks

  1-14

  Giovannina Albano

  Agnese Ilaria Telloni

  Views:

  94

  We designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics.

  Subject Classification: 97U70, 97H60