Page 126 - Textos de Matemática Vol. 34

116 JAIME CARVALHO E SILVA
textbook was highly praised in Portugal (it won a prize of the Academy of Sciences) and abroad (it was very favourably reviewed in several journals, namely the Bulletin of the American Mathematical Society).
Apart from the 25 original mathematics textbooks edited by the University of Coimbra during the 19th century, several dozen small pedagogical notes were pub- lished in the academic journal “O Instituto”. This number is not enough for what is needed in a Mathematics Faculty, but represents nevertheless a notable advance- ment of the mathematics studies in Portugal.
4. The methods
The 1772 Statutes of University define with a considerable detail which kind of work the students should do in the classroom. There were vocal, practical and written exercises. The approval was obtained only in a final oral examination, so the goal of these exercises was to help the students memorise the “Elementary truths of the lessons”, to get a perfect understanding of proofs, and so that students would be able to “combine for themselves the said truths, search new uses for them and to investigate other unknown truths”. These goals are quite ambitious. In order to achieve these goals the Statutes describe in detail the kind of exercises that students were supposed to do. The vocal exercises would be done daily, weekly and monthly and should include situations where the Professor would place the student “in the path of the inventors” by showing them how to conjecture something and how mathematicians try to prove that conjecture, giving the students a detailed idea of “evolution of mathematical discoveries”. In the practical exercises the students should “add always theory and practice”. In the written exercises students should do routine exercises and also small dissertations:
Every month there will be a General Exercise. For it the Professors will choose a theme that asks for discussion and gives opportunity for a brief dissertation.
We know the dissertations were a common practice (see examples in [9]), at least till the beginning of the 20th century. And these dissertations were not only exercises in the classroom; they were part of the final examinations; students had to choose for the final examination a
Dissertation that he should have written about some subject related to the lessons of the same year and similar to the ones the Professors will choose for the exercises every month.
One important methodological aspect pointed out by the 1772 Statutes was the use of History of Mathematics in the teaching: