Editorial

Ogni articolo é preceduto da un breve commento in italiano e dall'abstract in inglese.

(Every article is preceded by a brief comment in Italian and from the abstract in English)

1. L'articolo di apertura dei Quaderni, di Hanène Abrougui, analizza alcuni errori frequenti nell'insegnamento/apprendimento dei decimali in Tunisia in situazione di formazione degli insegnanti. Viene esibita una analisi qualitativa di un lavoro sperimentale fatto con gli allievi.

Abstract

A constant important error of the students of the sixth year of the teaching of base in the tests of mathematics has made the formation of the teachers of this level necessary to drain.  In  this formation, there are interested to the conceptions of the teachers on you number decimal, notion largely studied during the 5° year and of the 6° year of the school of base. To specify the theoretical framework, introduces the results of the study gotten beginning from a questionnaire. They shows that the dominant conception of the teachers of 5° and 6° year it is that a decimal is a "number with comma", conception that is not to the origin of the confusions between a decimal and a rational decimal. Besides as fraction is frequent also the conception of the decimal one of which the denominator is a power of 10. This conception induces, to the times, the not recognition of the decimal number, written in the form of a fraction of which the denominator differs of a power of 10. Our analysis has finally shown a lack in the dominion of the knowledges on the structure of the whole D and the ownerships of the decimal ones, this it brings to direct the formation, in the future toward a study deepened particularly more of this whole and the study of other numerical sets whole as Q, R, R-Q, C,… in general way.

2. L'articolo di Lucia Földesiová analizza la relazione tra l'insegnamento della geometria solida e vettoriale in Slovacchia. Sono analizzate alcune metodologie  e proposte didattiche.

Abstract

The problem of teaching mathematics at secondary school is the continuity of mathematics content and the content of other subjects. The abstract mostly focuses on the relation between solid geometry from the vector calculus point of view and the synthetic approach to teaching of solid geometry. Findings from the experiment will enable I have carried out to specify the formulation of the tasks but also some methodical activities of the running experiment.

3. L'articolo di Stefanos Keisoglou e Panayotis Spyrou analizzano il rapporto con i processi di matematizzazione attraverso l'utilizzo di strumenti didattici per il laboratorio di matematica sia concreti che virtuali. Gli strumenti hanno una giustificazione storica. La sperimentazione é condotta in Grecia attraverso analisi qualitative.

Abstract

In this article we present the design and the pilot run of a rich learning environment that lays emphasis on the mediation of tools. In this environment two artifacts are functionally combined: a device in which the basic ways of measuring a height have been incorporated and the computer through which students can study a dynamic simulation of the device. The device was a product of a combination of functional characteristics of devices that have emerged historically. The discovery of how to use the instrument arises through a process of mathematization, which is completed in two phases, out of which the first pertains to the similarity of right triangles and the other one to the trigonometric tangent. The research highlights the distinct contributions of each of the tools in the process of mathematization and aims to assess the effect on the learning process of their concerted presence. The research ends with a schematization articulating connections between the two stages, which we present in the final table. 

4. L'articolo di Michaela REGECOVÁ analizza alcuni problemi riguardanti l'insegnamento/apprendimento della geometria in Slovacchia riguardanti specificatamente il calcolo vettoriale e la geometria analitica. L'analisi comparativa su tre gruppi di allievi é prevalentemente qualitativa.

Abstract

The use of the analytical method and the vectorial calculation in the resolution of the exercises of the planimetria and the stereometria is a fundamental problem near the students of the secondary schools. In general, in the secondary teaching, the method of the calculation and the construction is used. In this article, I propose previously an analysis of a geometric exercise and the experimentation effected with three groups of students. The results of our experimentation show the necessity to increase the quality of the level of the secondary teaching of the vectorial calculation in the analytical geometry, new ideas are given for new searches.

5. Questo articolo classico sul "Caso di Gael" rappresenta un inedito. Viene presentato per la prima volta nella tesi di dottorato di Guy Brousseau. Questa versione é risistemata assieme a Virginia Warfield in lingua francese. La versione inglese é apparsa in Mathematical Behavior, n°18 (1), 1-46, octobre 1999.

Abstract

The Theory of Didactical Situations has had a central position in French mathematics education research since the early seventies.  A major component of this theory is the didactical contract, a completely implicit but highly powerful aspect of the relationship between teacher and student.  In this article we relate the series of tutorial sessions which provoked the original formulation of that theory, and in which the theory was validated by its first application.

Gaël was an intelligent child who was failing exclusively in mathematics.  He was one of nine cases studied between 1980 and 1985 (at the Bordeaux COREM). After observing him in class and offering him various learning situations, both didactical and adidactical, we arrived at the hypothesis that Gaël was implementing an strategy  of avoidance of the "conflict of knowing" which we characterized as "hysteroid type avoidance", whereas the others exhibited "obsessional type avoidance" (note that these behaviors should not be confused with the psychiatric categories of the same name, which are serious personality disorders.)  It was possible to offer psychological explanations for this behavior, but they did not provide the means for correcting the avoidance, and they focused the interest of the researchers on a characteristic of the child or on his competencies, rather than remaining at the level of his behavior and the conditions which provoked it or which might modify it.  This behavior demonstrated the refusal, conscious or not, of the child to accept his share of the decision-making responsibilities in a didactical situation and hence to learn while working with an adult.

It made it possible for the experimenters to explore and understand the constraints of the didactical situation, interpreted as a "didactical contract".  It is the simulacrum of a contract, an illusion, intangible and necessarily broken, but a fiction which is necessary in order for the two protagonists, the teacher and the learner, to engage in and carry out the didactical dialectic.  The didactical means to get a student to enter into such a contract is devolution.  It is not a pedagogical device, because it depends in an essential way on the content. It consists of putting the student into a relationship with a milieu from which the teacher is able to exclude herself, at least partially (adidactical situation).  The mechanism implemented was devised to engage Gaël progressively but explicitly in a challenge in which the teacher could be "on the student's side."

This situation subsequently revealed itself to be one of the fundamental situations of subtraction.

6. L'articolo di Angelo Bonura e Leonide Russo propone un percorso didattico che vede coinvolte la Matematica, la Fisica e l’Economia aziendale e ha riguardato la costruzione e l’uso di modelli analitici lineari per la risoluzione di problemi  concreti di tipo fisico ed economico. Il lavoro èproposto é stato sperimentato in una scuola secondaria superiore di Palermo.

Abstract

The poor levels of learning in mathematics and sciences of the Italian pupils, as recent statistical researches show, are probably to attribute to a dogmatic and few stimulating method of  teaching.

With reference to this, we describe a didactic experience (in which more scientific subjects of study have been connected) that, making use of methods planned in order to increase the interest and motivation of the students, has given rise to a notable improvement of their learning levels.

This experience has interested subjects such as Maths, Physics and Economics and it has concerned the creation and the use of linear analytical models for the solution of physical and economical problems.

The methodology has been based on the didactics for problems of J. Dewey, in which the introduction of analytical method arises from need to solve problems, made more effective by means of cooperative learning strategies.

The appraisal of the outcomes of the experimentation has been carried out by introducing two indexes of learning, the first relative to the interest and motivation (wish to learn), the second to the performance, and by comparing the distribution of the levels of the students at the  beginning and at the end of the didactic experience.

The obtained results are very satisfactory because the growth of pupils’ motivation has also given a notable increase of their levels of competence.

 

7. L'articolo compara metodologie differenti nell'insegnamento della statistica in alcune città italiane. Lo studio sperimentale si avvale degli strumenti dell'analisi implicativa di varaibili per l'analisi dei dati.

            Abstract

The objective of the present work is that to analyze some results of a test of profit administered to pupils of the junior high school after a period of lessons of statistic effected by the teacher of mathematics. The study analyzes, through the analysis implicative, analogies and differences of performance of the pupils both in comparison to the territorial context (four centers involved in the experimentation, Padova, Palermo, Perugia and Roma), both to the used didactic methodology (approach directed to the data, DOA, and DOA combined with the method of the Cooperative Learning). Besides, an analysis of the profiles of learning is introduced previously on the base of hypothesis and considerations.

8. Una conferenza su "Guerra e Matematica" di J.HØYRUP  chiude il numero 13 dei Quaderni. Una rassegna dei continui rapporti tra matematica e guerra in una visione olistica del fenomeno. Il percorso storico é affrontato dall'antichità ai nostri giorni.