History and Hermeneutics for Mathematics Education

Storia ed Ermeneutica per la Didattica della Matematica




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, 453-468 (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, 45-62 (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, Dordrecht, 63-66 (in English)

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, Dordrecht, 82-86 (in English)

³Bagni, G.T. (2000), The role of the History of Mathematics in Mathematics Education: reflections and examples [pdf]. Proceedings of CERME-1, II, 220-231 (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 XVII-XVIII centuries:


Formal models: an historical example [pdf] (2001, in English)

I Riccati e le equazioni differenziali [pdf] (1995, in Italian)

I Riccati e G.M. Ciassi [pdf] (2003, in Italian)


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] (1994, in Italian)

P. Aproino (1586-1638) e pi greco [pdf] (1995, in Italian)

G. Riccati e G. Tartini [pdf] (1998, in Italian)

Storia delle Scienze per la Didattica [pdf] (2002, in Italian)

La Schola Riccatiana [pdf] (forthcoming, in Italian)

Selected papers (by G.T. Bagni)


Storia e Geografia della Matematica [pdf] (2004, in Italian)

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] (1995, in Italian)

A brief history of the continued fractions, from Euclidean Algorithm to the results by Lagrange and Galois

Il “gruppo moltiplicativo di Bombelli” [pdf] (2000, in Italian)

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] (2001, in Italian)

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] (2001, in Italian)

Two arithmetic and algebraic historical examples are related to Secondary School mathematical curricula

Larte de labbacho (1478) [pdf] (2002, in Italian)

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] (1995, in English)

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] (1995, in Italian)

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] (2000, in Italian)

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] (2001, in Italian)

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] (1994, in Italian)

A brief history of “pi” allow us to introduce some reflections by Paolo Aproino (1586-1638) concerning the approximation of a circle by a sequence of regular polygons

Figure simili nella Geometria degli Indivisibili [pdf] (1999, in Italian)

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] (1996, in Italian)

Some analytical techniques and examples by Jacques and Jean Bernoulli are presented and their educational importance is underlined

Il metodo di esaustione [pdf] (1997, in Italian)

The history of exhaustion method, since Anaxagoras to Leibniz, summarizes the historical roots of mathematical analysis

Attualità di Leonhard Euler [pdf] (1997, in Italian)

Some analytical and algebraic techniques by Leonhard Euler are presented and their educational importance is underlined

Il “nulla geometrico” di G. Torelli [pdf] (1998, in Italian)

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] (2001, in Italian)

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 la Didattica della Matematica

(G.T. Bagni, Editor, in Italian, pdf files)


Libri e idee. Appunti di Storia della Matematica



History and Hermeneutics

for Mathematics Education

(Giorgio T. Bagni, Editor)


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