History and Hermeneutics for Mathematics Education
Storia
ed Ermeneutica per
History for Mathematics Education
Main papers (by G.T. Bagni)
³Bagni,
G.T. (2005), The historical roots of limit notion. Cognitive
development and development of representation registers [pdf]. Canadian Journal of Science, Mathematics
and Technology Education 5:4, 453468 (in English)
³Bagni, G.T. (2001), La introducción de la historia de las matemáticas en la enseñanza de los números
complejos. Una investigación
experimental en la educación media
superior [pdf]. Revista
Latinoamericana de Investigación en Matemática Educativa, 4, 1, 4562
(in Spanish)
³Barbin, E.; Bagni, G.T.; Grugnetti, L.; Kronfellner, M.;
Lakoma, E. & Menghini, M. (2000), Integrating
history: research perspectives [pdf]. In: Fauvel, J. & van Maanen, J. (Eds.), History in Mathematics Education. The ICMI Study, Kluwer Academic Publishers,
³Bagni, G.T. (2000), Difficulties
with series in history and in the classroom [pdf]. In: Fauvel, J. & van
Maanen, J. (Eds.), History in
Mathematics Education. The ICMI Study, Kluwer Academic Publishers,
³Bagni, G.T.
(2000), The role of the
History of Mathematics in Mathematics Education: reflections and examples [pdf]. Proceedings
of CERME1, II, 220231 (in English)
Mathematics, Culture, Society in an historical period
(by G.T. Bagni)
Using the History into Mathematics
Education. An example: the Marca Trevigiana in XVIIXVIII centuries:
Formal
models: an historical example [pdf] (
I Riccati e le equazioni differenziali
[pdf] (
I Riccati e G.M. Ciassi [pdf] (
G. Riccati, “Del Contrappunto” (1762) (original text)
V. Riccati, “Del Cuneo, Lettera Postuma” to
G.B. Nicolai (original text)
Other
works:
I logaritmi dei numeri negativi [pdf] (
P. Aproino (15861638) e pi greco [pdf] (
G. Riccati e G. Tartini [pdf] (
Storia delle Scienze per la Didattica
[pdf] (
La Schola Riccatiana [pdf] (forthcoming, in Italian)
Selected papers (by G.T. Bagni)
Storia e Geografia della Matematica [pdf] (
The presentation of some results by
Srinivasa Ramanujan allows us to introduce many questions related to the
geography of mathematics
History
of Algebra:
Frazioni continue discendenti e
ascendenti [pdf] (
A brief history of the continued
fractions, from Euclidean Algorithm to the results by Lagrange and Galois
Il “gruppo moltiplicativo di Bombelli”
[pdf] (
The historical study of Algebra allows us to point out the
features of the group of the fourth roots of the unit
Dai coniglietti alla sezione aurea [pdf] (
An historical path between some mathematical
subjects of High School, in particular Fibonacci sequence and continued
fractions
History
of Arithmetics:
Dalla Storia alla Didattica della
Matematica [pdf] (
Two arithmetic and algebraic historical
examples are related to Secondary School mathematical curricula
Larte de
labbacho (1478) [pdf] (
The first mathematical book printed after Gutenberg
is an arithmetical handbook published in Treviso, 1478
History of Number Theory and Logics:
Prime
numbers and quadratic polynomials [pdf] (
A celebrated Eulerian example allows us
to introduce a brief study of prime values of quadratic polynomials, with
elementary methods
La Funzione Zeta di Riemann [pdf] (
Some issues related to the function Zeta
(Z), studied by Euler and by Riemann, are presented; in particular, the proof
(Apéry, 1978) of the irrationality of Z(3) is introduced
Matematica e Bellezza [pdf] (
The comparison of different proofs of the
theorem according to which prime numbers are infinitely many can be referred to
some reflections concerning mathematics and beauty
Le relazioni simul e ordo
di P. Mengoli [pdf] (
In a treatise by Pietro Mengoli (1675)
we find an important relation that can be related to the order nowadays
introduced by Lindenbaum Algebras
History
of Geometry:
Approssimazione, poligoni, circonferenza
[pdf] (
A brief history of “pi” allow us to
introduce some reflections by Paolo Aproino (15861638) concerning the
approximation of a circle by a sequence of regular polygons
Figure simili nella Geometria degli
Indivisibili [pdf] (
After an historical section devoted to the
role of similar figures in Cavalieri’s work, we present the result of an
experimental research making reference to Euclid, Apollonius and Bonaventura
Cavalieri, dealing with pupils con allievi della classe II media
History of Analysis:
Attualità
di Jacques e Jean Bernoulli [pdf] (
Some analytical techniques and examples
by Jacques and Jean Bernoulli are presented and their educational importance is
underlined
Il metodo di esaustione [pdf] (
The history of exhaustion method, since
Anaxagoras to Leibniz, summarizes the historical roots of mathematical analysis
Attualità di Leonhard Euler [pdf] (
Some analytical and algebraic techniques
by Leonhard Euler are presented and their educational importance is underlined
Il “nulla geometrico” di G. Torelli [pdf] (
Some ideas expressed in a book by
Giuseppe Torelli (1758) allow us to introduce some reflections on potential and
actual infinitesimal
Infinito e infinitesimo potenziale e
attuale [pdf] (
A brief history of infinitely great and
infinitely small reflects the features of the different historical periods
considered
Download
Libri e idee. Appunti di Storia per
(G.T. Bagni, Editor, in Italian, pdf files)
Libri e idee. Appunti di
Storia della Matematica

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