# The Pedagogical Institute of Chile

We give two extracts below. The first short extract is taken from E D Rojas and F Oteiza, Chile: The Context and Pedagogy of Mathematics Teaching and Learning, in

*Bruce R Vogeli, Hector Rosario and Patrick Scott (eds.), Mathematics And Its Teaching In The Southern Americas: With An Introduction By Ubiratan D'ambrosio*(World Scientific Publishing Co, 2014), 89-114. The second short extract is taken from C Gutiérrez and F Gutiérrez, Carlos Grandjot, tres décadas de matemáticas en Chile: 1930-1960,*Boletín de la Asociación Matemática Venezolana***11**(1) (2004), 55-84.**1. The Pedagogical Institute of Chile**

In 1889, President Jose Manuel Balmaceda signed the bill that created the Pedagogical Institute, the first secondary teacher education institution in Latin America. Teacher education in secondary mathematics was one of the central fields of concentration. The institution was created by the government as part of its 1889 secondary educational reform modelling the concentric approach to education. Since then, the concentric system has been the model framing the Chilean educational system. In a concentric approach, learning is conceived to occur in phases from basic principles to the more complex. The same cycles are repeated two or more times, or the curriculum is revised again every few years, which enables students to gain deeper knowledge and understanding of the topic.

To staff the Pedagogical Institute, the government recruited thirty scholars with doctoral degrees from Germany; fifteen of them were mathematicians. The first two mathematics professors at the Pedagogical Institute were Reinaldo Von Lilienthal, who, after a couple of months returned to Germany, and Augusto Tafelmacher, who retired in 1907. The way mathematics teachers were prepared in Chile was mostly determined by this German team. In a way, the operational definition of mathematics curricula in the country was tailored in textbooks developed by some of them. Algebra and geometry were taught until the 1960s on the basis of books written by Pröshle and Pöenisch.

With the arrival of the German professors in 1889 to start the Pedagogical Institute, mathematics in Chile acquired a new dimension. Tafelmacher and Pöenisch, both with doctorates in exact sciences, gave mathematics a new dimension as a cultural and autonomous discipline, defining it as a "corpus of knowledge" at the service of teaching, a characteristic that it had in Europe from the beginning of the century. Tafelmacher and Pöenisch were passionate and devoted to teaching, and they influenced and prepared a legion of "discipulos" who spread that passion and devotion all over the country. Another German mathematician, Carlos Grandjot, founder of the Instituto de Chile (1930) also shared with pride his services as a professor of mathematics in the institutions of teacher education in the Republic. His courses included

*matemáticas elementales y superiores*, philosophy and physics at the Pedagogical Institute. He also participated in the foundation and development of institutions that cultivated mathematics as a science at the national level. Grandjot was the founder and first president of the

*Sociedad Matemática*

*de Chile*[Mathematical Society of Chile], in 1953. In 1957 he also founded the

*Instituto de Investigaciones Matemáticas*[Institute for Mathematical Research], based at the Universidad de Chile, during the presidency (Rectoria) of Juan Gomez Millas.

In addition to going in-depth in his lessons on calculus, Grandjot introduced in 1936 in the Pedagogical Institute programme, a course on differential geometry. The course,

*Geometría Diferencial*, gave way to one on

*Análisis Vectorial*, and

*Fundamentos de la Matemática o Axiomática*became an elective course in the dual degree programme. The programme graduated teacher candidates with specialisation in both Mathematics and Physics "

*Profesor de Matemáticas y Físico*". Later after some reforms, the degree was extended to nine semesters.

Among Grandjot's most outstanding disciples in Chile were Dr Rolando Chuaqui and Professor Cesar Abuauad. Dr Chuaqui studied medicine and later earned his Ph.D. in

*Lógica y Metodología de la Ciencia*at California Berkeley in USA (1965). After his return from Berkeley, Dr Chuaqui became a professor at the

*Facultad de Ciencias - Universidad de Chile*. In 1969 he accepted a position as Dean of the Department of "

*Ciencias Exactas*" [Mathematics, Physics and Chemistry], at the

*Pontificia Universidad Católica de Chile*. Soon after, he developed the first

*Programa de Post-grado en Ciencias Exactas*(PEPCE) in Chile, the first Mathematics Doctoral program in the country. His contribution as a researcher in the field of logic is internationally known.

Cesar Abuauad taught the first official courses of this "new science" at the Pedagogical Institute of the University of Chile in 1956:

*Algebra abstracta and Lógica y Fundamentos de las Matemáticas*(modern mathematics), disciplines that Grandjot had introduced in Chile.

**2. Carlos Grandjot**

If the development of science in Chile, in particular that of mathematics, is viewed in perspective, it can be concluded that they have had to travel a long and rocky road to reach full maturity. There are many actors who have intervened in this process, including several foreigners who made Chile their second homeland. Carlos Grandjot is one of them. To understand his contribution to mathematics in Chile, it is necessary to have in view a picture, albeit a synoptic one, of the development of this discipline in the country. Its origins go back to the last years of the Colony, more precisely to the Mathematics Chair installed in 1758 at the Royal University of San Felipe, and to the Mathematics Course of the San Luis Academy inaugurated in 1799. With the dawn of Independence, both institutions were integrated into the National Institute, founded in 1813, from which the first mathematicians of the Republic graduated in 1824. The contents of these courses depended on the criteria of the teacher and were dictated based on notes written by the teacher himself. It was up to Andrés Antonio Gorbea, a Spanish engineer who arrived in Chile in 1826, to organise the teaching of mathematics in the European style. He drafted a programme that became official in 1831 and adopted for his classes a text written for the École Polytechnique, an institution whose spirit was to cultivate mathematics as a "useful" science. Within this spirit, mathematics was maintained in Chile until the end of the nineteenth century. Its development channel was the School of Engineering.

With the arrival of German teachers in 1889 to start up the Pedagogical Institute, mathematics acquired a new dimension. Tafelmacher and Pöenisch, both doctorates in exact sciences, set up mathematics as an autonomous and cultural discipline, as a "corpus" of knowledge at the service of teaching, a character that it had had in Europe since the beginning of the century. They wrote the syllabus and teaching texts and published articles on current issues in the

*Annals*of the University of Chile. This new facet of mathematics caused an impact among some intellectuals. Valentín Letelier commented in 1895 in his book

*The Fight for Culture*: "It had been so many years since Chile had written about mathematics, that the last school generations had been educated in the idea that this science was mummified and did not lend itself to further development."

The impulse of Pöenisch and Tafelmacher was basically centred on teaching; They formed a legion of self-sacrificing disciples that spread throughout all areas of the national territory, which made Pöenisch say in 1929, when already retired: "the teaching of the field is entrusted to people who know and they can fulfil their duties ... their preparation and work spirit give me the right to rest easy." Notwithstanding this just satisfaction of the Master, let us observe that a mature science, in addition to its facets as a "useful" science and as a "corpus" of knowledge - at that time well organised in Chile - requires a third aspect in order not to stagnate and stimulate its development. This aspect is science as a creative process. It was up to Carlos Grandjot to be a pioneer and first actor in the incorporation of this third channel of development of Chilean exact sciences.

Since his arrival in the country, Grandjot participated in the creation of institutions for the progress and cultivation of national science. He was a founding professor at the Institute of Chile (1930); of the first Mathematical Society of Chile (1953) of which he was its first president, and of the Institute of Mathematical Research (1957), among others. From his chair, he made known and promoted avant-garde mathematics and modern physics among his students, sometimes with success and others times without it, but always with enthusiasm. He collaborated closely with the academic authorities in the institutionalisation of scientific research and in the necessary international contacts with centres of excellence to activate it in Chile.

...

Dr Grandjot, as his students called him, arrived in Chile on 1 May 1929, from Germany, hired by the Government to "provide his services as a Mathematics Professor in the educational establishments of the Republic. He would have the obligation to serve up to fifteen hours a week of classes, including seminars." Upon arriving, he began teaching "classes on Higher and Elementary Mathematics, Philosophy and Physics at the Pedagogical Institute of the University of Chile." The contract had a duration of two years to start from 9 April 1929. He renewed the contract successively, until he was surprised to still be in Chile by the beginning of the Second World War. This somehow sealed his fate and he decided to stay in Chile and become a national, which allowed three other university schools, in addition to the Pedagogical School, to enjoy his services: the School of Engineering of the Pontifical Catholic University of Chile, since 1933; the School of Engineering of the University of Chile in its Complements of Higher Mathematics course, starting in 1945; and the School of Architecture of the aforementioned Catholic University since 1953.

Last Updated November 2022