# The School Mathematics Curriculum

The preparation of mathematics teachers should be considered in the larger school curricular context. Venezuela, Costa Rica and the Dominican Republic each have a mandatory, official, national curriculum. In Colombia, however, there are general orientations that are followed in the different regions of the country, but an identical national curriculum for all does not exist.

With respect to mathematics, all these countries experienced in their own way the “Modern Mathematics” reform, which had emerged as a possible solution to an important problem for mathematics education: closing the gap between the mathematical practice of professional university research mathematicians, and the mathematics in elementary and secondary schools. Using the language of sets and with perspectives taken from university mathematics there was a desire to integrate mathematics as a single discipline. It was proposed that modern symbolism be adopted, that the use of graphs be given greater importance, that much of traditional algebra be eliminated, and that something extremely serious be modified and practically eliminated: traditional Euclidean Geometry. A famous war cry of some of the reformers was “Euclid must go” (J. Dieudonne). The reform began in Europe (especially France) and the United States. Later it was expanded to Latin America and other latitudes. Textbooks and curricular changes were the main mechanisms to drive the reform. The reform failed to achieve its initial objectives and was rejected by many educators, students, and even parents. Nevertheless, the actions and ideas that the reform promoted were dominant for almost 30 years. In different ways all of these countries backed away from the reform in the 1980s and 1990s as they were influenced by constructivism, systems theory or curricular models based on competencies.

During the 1970s and well into the 1980s much of the school mathematics curriculum in Colombia was determined by “Modern Mathematics”. It is perhaps noteworthy that the *1st Inter-American Conference on Mathematics Education *(IACME I) was held in Bogota, Colombia, in December of 1961. Its main purpose was to promote the development of the modern mathematics reform in the Americas (Ruiz and Barrantes 2011). Afterwards Colombia experienced the influence of “systems theory” until the second half of the 1990s. At the time they began to emphasize the construction of knowledge and the development of thinking using “problem situations”, interdisciplinarity, action research, and a perspective based on competencies. In Colombia there are two seminal documents that orient school mathematics: *Curricular Guidelines for Mathematics* and *Basic Standards for Mathematical Competencies,* published in 1998 and 2006, respectively. These should be considered complementary. The lack of a specified national curriculum is being debated in the country.

In Venezuela the influence of modern mathematics was also felt. In 1965 the Pedagogical Institute (a very influential institution in that country) also assumed that reform model in the first three and that same year national mathematics programs with that orientation were officially approved. Venezuelans participated in the first three *Inter-American Conferences on Mathematics Education* and organized the fourth. This wave continued until 1980 when a national education law broke with modern mathematics and adopted the international perspective of “*Back to the Basics*”.

The modern mathematics reform also influenced mathematics programs in the Dominican Republic where a translation of the books of the *School Mathematics Study Group* (*SMSG*) from United States was used in teacher preparation, and later on in some high schools.

In Costa Rica, as in the other countries considered, modern mathematics dominated the school curriculum beginning in 1964 when new programs with this orientation were officially approved. The universities adopted teacher preparation processes based on the new orientation. It was not until the middle of the 1990s that the modern mathematics model was officially replaced, although it had already been largely abandoned in practice. The next strong influence was constructivism (although the approach was very general), and many dimensions of behaviorism continued to exist (particularly with respect to assessment). In 2012 there was an authentic revolution in mathematics education. A new national curriculum was approved based on problem solving with an emphasis on real contexts, and that introduced an innovative vision of the use of competencies.