Abstract:

There are presented our considerations related to the problems resulting in the process of implementation of the new curricula suggested by the New Math Reform in education as well as some results obtained in the framework of our research project “Implementation of the innovation strategies in order to attend the educational programs in Mathematics for different terminal areas at the Faculty of Sciences”, supported by the Research Department of Sciences at the Morelos State University”.

The New Math revolution can be dated to 1959, when on the Conference organized by the Organization for Economic Cooperation and Development there was promoted a reform on the content and methodology of secondary math education. Nowadays, there is no more teaching Euclidian geometry at school level due to the declaration announced at that conference by J. Dieudonné “Down with Euclid”. At another conference the motivations in terms of fundamental mathematical structures expressed by J. Dieudonnè turned out to be congruent with the discoveries of J. Piaget concerning to the Psychogenesis. The basic structures have been found basically the same.

Thus the reform was based on the fundamental structures common to cognitive process and to mathematics. Nevertheless the implementation of new curricula in classroom and textbooks was rather slow. There were some objections concerned to the formalism and abstraction of New Math with which there were no connection to reality and that the set theoretical algebra does not teach students to reason because the geometry was abandoned in favour of its algebraization. Nevertheless the reform was adopted in majority of the countries because the curricula bear a certain coherence reflecting the ideas of Erlangen Program proposed in 1982. An analysis of the problems arisen in the process of its implementation is still far from being satisfactory. Any evaluations to be made properly need some theoretical tools and should be based on some theoretical background. The principal trajectories which characterize the pertinence of teaching practice according to Onto Semiotic Approach (OSA) are treated in [1]. In our opinion the mathematical didactics should not be limited only to description, it should indicate improving the orchestration and development of study processes [1].

To evaluate the pertinence of the mathematical instruction process in teaching Geometry and to determine guidelines for improving the design of this process we propose such mathematical practices and interactions which are most appropriate to achieve the main objectives of the course. We focus on interactions of the theoretical ideas and operational practices which lead to better comprehension of geometry. The series of tasks designed to facilitate “institutional cognition” by means of directed instructions to develop deeper level of “Personal cognition” involving the sort problems with visualization and construction. Recent publications in Mathematics Educations demonstrate interest to the processes which permit articulate different parts of mathematics as well as mathematics with the extra mathematics reality, that are related directly to the complexity of the processes of teaching and learning.

References:
[1] Font, V., Rubio, N. y Contreras, Á. (2008). Procesos en matemáticas. Una perspectiva ontosemiótica. Acta Latinoamericana de Matemática Educativa 21, 706-714. Editorial: Comité Latinoamericano de Matemática Educativa.

Keywords:

Efficiency of teaching practice, Ontosemiotic Approach, New Math reform.