This was a workshop designed to acquaint the participants with a broad spectrum of mathematical ideas and viewpoints presented in a manuscript written, in the 18th century, by the Portuguese priest (and very influential scholar during the reform of the University of Coimbra) José Monteiro
da Rocha, as an introduction to a mathematics course.

Based on both Monteiro da Rocha’s life and on his own comments on the teaching and learning of mathematics in Portugal, we have strong reasons to date this unpublished manuscript around 1760.

At that time, the study of mathematics as well as the study of other areas, was at such a low level that some scholars were quite concerned with the learning content as well as the methods of learning; as a consequence we can find some important suggestions for dealing with these problems. An example
of this is Luı́s António de Verney’s « Verdadeiro Método de Estudar » (« True Method of Studying »), published in 1750 which acquired quite a large circulation and, even nowadays, is used as a source of research. Less known than Verney’s work, and other similar texts produced all over Europe at that
time, is the above cited manuscript by Monteiro da Rocha. In this work he echoed his concern with the teaching and learning of mathematics, emphasysing the lack of teachers of mathematics while, in his own words, « waking up his nationals from the lethargic state [in which they were living] ». In particular he suggested « writing in vulgar language » (i.e. Portuguese instead of Latin) for spreading mathematical knowledge among Portuguese citizens and he stimulated the national pride by reporting on the example of Portugal’s « glorious maritime discoveries ».

In the present workshop:

i) We presented a brief summary on the life and works of José Monteiro da Rocha, referring, in particular, to his activity in designing and writing the rules for the big reform of the University of Coimbra (1772) where, for the first time, a Faculty of Mathematics was created in Portugal.

We also referred to his activity as a professor of the same university and his relationships with the academics of Real Academia das Ciências de Lisboa; we will also report on the international spreading of some of his works on Astronomy.

ii) We referred to the ideas/models presented in other textbooks of Monteiro da Rocha’s times.

iii) We proposed the analysis of some specific parts of the above cited introduction, by reading them from an English version of the original manuscript distributed to the participants.

iv) We lead a follow-up discussion/reflection on

– The actuality of da Rocha’s ideas, for example on his understanding of what is mathematical knowledge;

– The development/history of the models for presenting/introducing mathematics textbooks;

– The historical-didactical facts that we can learn/apply, at the present time where there is an acknowledged decrease of interest in studying mathematics.