Influences from the Royaumont-seminar in 1959 on primary school arithmetic in Iceland

Abstract

A seminar on new thinking in school mathematics was held in Royaumont, France in 1959. At the seminar, the European proponents for reform of school mathematics met representatives of the New Math movement in the United States. Some of the European participants were members of the Bourbaki-group of mathematicians who worked on presenting all mathematics in a unified modern way, mathematique moderne. One of the final recommendations of the seminar was that each country could reform its mathematics teaching according to its own needs; establishing as much cooperation as possible was recommended, however. The Nordic participants at the Royaumont Seminar agreed upon cooperation on reform of mathematics teaching and presented their ideas to governmental bodies. The issue was taken up in the Nordic Council, which decided to set up a committee under its Culture Commission. Each of four countries – Denmark, Finland, Norway and Sweden – appointed four persons to the Nordic Committee for Modernizing Mathematics Teaching, NKMM. 

The Nordic Committee’s task was to analyse the current situation in mathematics education, to work out curriculum plans and to write experimental texts. The committee appointed several teams of writers. The focus was on mathematical content, and the teaching of seventh to twelfth grades was its main object. However, it was decided to handle mathematics courses throughout the primary level, and for that purpose the committee contacted extra experts for the first to sixth grades of primary school.  

Writing sessions were arranged in summer 1961. Some texts were ready that autumn, and others were to be so successively until the beginning of 1966. A Danish author, Agnete Bundgaard, and her Finnish collaborator wrote a textbook series for the primary level. The work was translated into Icelandic and published, nearly simultaneously with its Danish publication. Denmark was one of the countries which went the furthest when it came to introducing the Bourbaki tradition into university programs, and eventually also into high school programs (Karp, 2015). 

In this paper, the text of the Bundgaard textbook series in its Icelandic version is analysed with respect to presentations on arithmetic education at the Royaumont seminar, mainly by Professor Gustave Choquet, and the final recommendations of the seminar. These are compared to previous and later arithmetic textbooks in use. The questions posed concerned which ideas from the seminar were implemented in the primary level textbook series, whether the ideas were new in Iceland, and whether they survived the first wave of enthusiasm for the New Math and became a permanent contribution to school mathematics in Iceland.

The results of the comparison of the Bundgaard series with four other textbook series, two previous to it and two later ones, show that the declared intention of the reform movement to emphasise the structure of the number system and build its presentation on set-theoretical concepts was duly followed in the Bundgaard-textbook series. 

The new topics in the Bundgaard series were primarily the use of set theoretical concepts and notations for building up the number concept and understanding of operations through repeated reference to the axioms of the number field, see mynd [figures] 1–11, even if negative numbers were missing. The axioms were carefully introduced with respect to structure. One can, therefore, state that the Bundgaard series went far towards meeting the mathematicians’ demands. In later textbooks these concepts appeared more as aids to calculations than emphasizing structure, which gradually faded away.

Building up the system of natural numbers from prime numbers and divisibility and emphasizing mental arithmetic were revived topics that have survived in the school curriculum to this day. Approximation and estimation have also become permanent contributions to school mathematics in Iceland. What did not become permanent was replaced by an introduction to statistics and probability, discussed at Royaumont but less recommended for primary level, and by the use of variables and solving simple equations.