# ABOUT THE DEVELOPING OF MATHEMATICAL THINKING IN CHILDREN: A WORKSHOP EXPERIENCE WITH MEXICAN STUDENTS

Abbreviations: SEP-Public Education Secretary, IEBEM-Institute of Basic Education of the Morelos State, ENLACE- National Assessment of Academic Achievement in Schools

The problem of the development of the mathematical logic thinking at the early stages of the intellectual formation is a generalized problem. In our country, this has been reported through the results of the ENLACE (http://www.enlace.sep.gob.mx/) test in Mathematics, at National level by SEP-Mexico.

With the intention of improving this situation, a pilot project has been set by the IEBEM-Mexico, for the rather large group of regular and outstanding students, of primary and secondary level who are supposed to perform an interest toward mathematics, in order to prepare them for the mathematical competitions organized for these levels, by the Mexican Academy of Sciences.

In this sense, we implemented a workshop, directed by a group of professors of the Faculty of Sciences of the Morelos State University, which were graduated students interested in the mathematical education.

Teachers implemented innovative strategies, in the sense that, they do not use typical problems in their designs, like those implemented in the past in training for the Mathematical Olympiads. Instead, they employed strategies that provided students freedom to experimenting, through the use of different manipulatives, to help pupils to overcome difficulties, taking care at the same time, maintaining the link with the various topics and objectives from the official program in mathematics.

Observations in this workshop suggest, between other things that, one way ensuring that students learn concepts and terminology, procedures for problem solving, argumentations, etc. is through experience and the accompaniment. Through experiments and game activities, the students gradually develop various skills and mobilize a set of cognitive resources, needed for solving problems. This is generally described by the following observations:

- The employment of manipulatives and pictorial representations, which refer to objects of everyday life, helps motivate the student to the solution of problems and maintain his attention. In addition, some types of tools and representations have a special effect on the student, because they seem determinant in the solution of a specific problem.

- Group activities that promote collaborative work, instead individual work, contribute to: a) a major visualization of the elements and their relations, the interchange of ideas, etc. involved in a problem solution; and b) allow us identify some characteristics, like the boys that seems to have major spatial visualization than the girls, which by their side, tend to follow patterns in the solution of problems, etc. in behalf the teachers.

Along with this, in this work we are looking for theoretical background related to collaborative learning, development of individual learning styles, pedagogical situations, etc., that help us to re-direct the activities, in order to obtain more efficient lines of action in the program of development of logic mathematics thinking, through problem solving.