History and Hermeneutics for Mathematics Education
Storia
ed Ermeneutica per la Didattica della Matematica
Mathematics Education
Main papers (by G.T. Bagni)
³Bagni, G.T. (2006), Some Cognitive
Difficulties Related to the Representations of two Major Concepts of Set Theory. Educational Studies in Mathematics,
62, 3, 259280 (in English) http://dx.doi.org/10.1007/s1064900685453
³Bagni,
G.T. (2004), Functions:
processes, properties, objects [pdf]. In: Mariotti, M.A. (Ed.), Proceedings of CERME3, 28 February3
March 2993,
³Bagni, G.T. (2004), Una experiencia
didáctica sobre funciones en la
escuela secundaria [pdf]. Revista
Latinoamericana de Investigación en Matemática Educativa, 7, 1, 524
(in Spanish)
³Bagni,
G.T. (2000), Simple
rules and general rules in some High School students’ mistakes [pdf]. Journal für Mathematik Didaktik,
21, 2, 124138 (in English)
³Gagatsis, A.
& Bagni, G.T. (2000), Classical
vs. Vector and Cartesian Geometry in problem solving in Greece and in Italy
[pdf].
Gagatsis, A. & Al. (Eds.), Learning and assessment in Mathematics and
Science, Department of Education, University of Cyprus, Nicosia,
171196 (in English)
³Bagni,
G.T. (1998), Visualization
and Didactics of Mathematics in High School: an experimental research [pdf]. Scientia
Paedagogica Experimentalis, XXXV, 1, 161180 (in English)
Selected papers (by G.T. Bagni)
Representation
registers:
Continuità
e discontinuità [pdf] (
Two wellknown analytical examples allow
us to introduce some educational reflections with reference to mathematical
curricula if
Dimostrare
e convincere [pdf] (
The proof is often considered the essential moment of doing Mathematics,
from the didactical point of view as well. With no intention to deny the
primary relevance of the proof, the paper reminds us that proofs themselves are
only one side of the mathematical work. In fact, there is a predemosntrative
phase, of relevant importance, usually left to intuitive capacity. Those ideas
have repercussions on the conception and the role of demonstration, as it is
shown through experiences carried out in some higher secondary schools
Learning, problem solving, representative registers [pdf] (
We analyse the behaviour of High School pupils (aged 1719 years) with reference
to some exercises in Trigonometry and in Analytic Geometry; an experimental
research considered 196 pupils. In particular, as regard strategies and
educational implications, we conclude that many pupils try to solve a problem
only in the sector explicitly considered: and sometimes this is a remarkable
obstacle to reach good performances and it is ineffective for the development
of the ability to coordinate different registers of representation
Una
riflessione sulla visualizzazione [pdf] (2002, SFIDA
Some experimental researches dealing with pupils aging 1619 years allow
us to state that identifying a function with its Cartesian diagram can cause educational
problems: if we consider teaching (only) in the sense of the production of
semiotic representations we we grant a privilege to particular aspects of the
general concept, to the detriment of others
Apprendimento
del concetto di funzione [pdf] (2002,
SFIDA
Some aspects of the learning of real functions are investigated. As
regard action views, objectoriented and propertyoriented approaches, many
works indicate that the role of representations is fundamental. We propose a
case study and conclude that, in order to make it possible the reification, it
is important to analyze teacher’s role in the institutionalization
Didactics of Analysis:
Euclid’s proof and Eratosthenes’ sieve [pdf] (
The idea of infinity in the learning of mathematics in classroom
practice is investigated, referred to
L’infinitesimo
e lo studio dell’analisi [pdf] (
In this paper the idea of infinitesimal in the learning of mathematics
in classroom practice is investigated, referred to
Interpretazione
categoriale di una misconcezione [pdf]
(
In this paper an important misconception about infinite sets is
described with reference to the categories. Moreover operational and structural
conceptions of mathematics are related to the categories
Limite e visualizzazione
[pdf] (
The concept of limit in the learning of mathematics is investigated, referred
to
Integral and measure [pdf] (
The status of the concepts of continuity of the set of the real numbers
and the idea of integral is investigated, with reference to
Insiemi infiniti di numeri
reali [pdf] (
In the first part of this paper, the idea of continuity of the set of the
real numbers in the learning of mathematics is investigated, referred to
Didactics of Probability:
A paradox of Probability [pdf] (
An informal point of view can be important and interesting in order to
introduce the concept of Probability. In this paper we describe an experimental
research activity about a first approach to Probability: we presented to
students aged 1617 years a short test based upon a well known paradox. The
greater part of the pupils considered by intuition
Zara game and teaching of Probability [pdf] (
This work deals with a first approach to probability from an informal
point of view. We presented to students aged 17
Statistics and Measuring [pdf] (
Measuring is a very common activity, belonging to pupils’ everyday experience.
We consider that an informal point of view is really important, and in our
opinion it can be effective, in order to introduce some basic concepts of
Statistics. In this paper we describe an experimental research activity: we
presented to students aged 1718 years a short test based upon a common
measuring activity. The greater part of the pupils showed difficulties in the
interpretation of the role of standard deviation
Didactic contract and affective
elements:
Irrational inequalities: learning, contract [pdf] (
Disequazioni
irrazionali: apprendimento, contratto [pdf] (
We investigate by a test the learning of an important “chapter” of the
mathematical education in the High School (in particular, referred to pupils
aged 1617 years). Many students are conditioned from didactical contract to
apply always the “standard” rules given by the teacher, and this behaviour can
be harmful: resolutions are mechanical, not creative and sometimes they becomes
more complicated
Trigonometric functions: learning, contract [pdf] (
In this paper the influence of the didactical contract on the students in
the learning of mathematics is investigated, referred to the introduction of
trigonometric functions, in
Esercizi
standard e contratto didattico [pdf]
(
In this paper the ideas of imaginary number and of domain of a function
in the learning of mathematics in classroom practice are investigated, referred
to
Gli immaginari nella pratica
didattica [pdf] (
The idea of imaginary numbers in the learning of mathematics in
classroom practice is investigated, referred to
Influence of text’s mental images upon resolutions
[pdf] (
As regards pupils’ approach to problem solving, several Authors stated
that pupils dealing with a given problem create a mental model of the proposed
situation; but a recent work proved that the full possibility to imagine a
situation does not help pupils. In this paper (dealing with pupils aged 1316
years), we show that, sometimes, this full possibility can constitute a real
obstacle to the acceptation of a correct resolution
Puntini... [pdf] (
Some reflections concerning the formal
rigor are based upon a test proposed to some High School and university
students
“Impossible” problems in students’ behaviour [pdf] (
The behaviour of High School students is investigated, with reference to
some “impossible” problems (in particular we examined students aged 1719
years). We conclude that some cases of “impossibility” are improperly
“extended” to similar exercises: the influence of didactic and experimental
contracts is remarkable in students’ behaviour
Che
cos’è? [pdf] (
In this paper some models associated to the idea of straight line and of
circle in the learning of mathematics are investigated, referred to
Other educational papers:
L’opera
di G. Pick: un’esperienza didattica [pdf] (
G. Pick’s work: an educational experience [pdf] (
In this paper the original article (
Alice
e lo Stregatto colorano il piano [pdf]
(
In this work we propose some elementary considerations about the least
number of colours needed in order to colour R^{2} being any couple of point whose distance is 1
associated to two different colours. It is an open problem (2003)
Logica
e linguaggio nella pratica didattica [pdf] (2003, SFIDA
We consider a problem related to the use of quantifiers in the High
School (students aging 1819), particularly dealing with existential
quantifiers, and we propose a case study based upon an analytical example. We
conclude that many students encounter obstacles with main logical concepts,
particularly when considered propositions are expressed by a formal language.
Symbols and language are linked with a wider sociocultural dimension, so the
presence of basic Logic in High Schools curricula must be considered as an
important point
Download resources (by
Calcolo
combinatorio 2 (High School)
Statistica
2 (High School)
Successioni (High School)
Laboratorio
di Geometria 2 (High School)
Laboratorio
di Geometria 3 (High School)
Download
“Appunti di Didattica della Matematica”
(G.T. Bagni, Editor, in Italian, pdf files)
Appunti
di Didattica della Matematica

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