The research is aimed at strengthening skills of high school mathematical thought. It has two stages, the first is analytic type, central activity consists in analyzing the plan and curricula of secondary school and obtain the processual and conceptual vision  of teaching and learning algebra, this in addition to observe teaching practices in the area of mathematics and interviewing students and teachers on the subject. The information obtained will give an overview of the process of linking the teaching of algebra, arithmetic geometry, measurement and interpretation of information; this will help take guidelines for the design and implementation of a course workshop aimed at teachers of secondary education.

The second phase considers the analysis of the establishing of the practice of teachers who give the area of mathematics to determine how the relationship between their strategies and learning of arithmetic and algebra is established, based on this design and implement intervention into practice strategies. A follow-up is carried out to check the progress of the ability of the students respond to problematic situations evidenced through an increase in its curricular achievements. Finally, the research team, will develop and distribute a text for teachers of mathematics in which the successful experiences of teachers will be recovered, that includes the designed software, detailed strategy and new proposals.

Objetive

Strengthen the learning of algebra of the students of the third grade in secondary school in the field of developing the mathematical thinking in three different secondary schools in Guadalajara metropolitan area through a teaching strategy based on articulation and organization and transit of arithmetic and geometry and interpreting information and processes of measurement, to the algebraic language.

It is essential to consider that basic education is between critical and difficult processes, as the transition from arithmetic to algebra, if this process is given in an appropriate manner allows to support the transition from the stage of concrete operations to the formal thinking. Velazquez (2000).  One der factors determinants is to consider the fundamentals, processes, concepts of arithmetic to strengthen learning of algebra, in a constructivist framework.

 The student goes through stages in the process of formation, same coincide with algebraic numerical aspects development stages, according to Piaget, and Collis (1990), are: the final stage of concrete operations, the concrete generalization or early formal and the formal operations, which have the ability to build concepts and develop algebraic processes. It is important to consider algebra and arithmetic as an integral form of learning that relate to each other, form a vision of one of the main sectors of mathematics.

Memoirs of the 17TH week Regional research and teaching in mathematics, mosaics mathematicians No. 20, 2007 Department of mathematics, University of Sonora, Mexico., pp. 101-106. Manuel Velázquez Fidela, 2004, mathematical instruction to mathematical education the mathematics of the 20th century: a look at 101 articles), pp. 129-134. Garcia, Rolando and Piaget, Jean, 2000 towards a logic of meanings?, editorial Gedisa, Madrid. Pycior, H., 1981, George Peacock and the British Origins of Symbolical Algebra. Article, 1981, history mathematics. Nidditch, town house(Ph), the development of mathematical logic, ed. Chair, Madrid, 1987 Miles, M. B. and Huberman, 1994, M. a. Qualitative Data Analysis: An ExpandedSourcebook. Thousand Oaks-California Olfos, Soto, Silva, 2009 "renewal of the teaching of the Algebra elementary: A contribution from didactics, Elementary algebra teaching renovation: contribution from the didactic Pontificia Universidad Católica, Chile Montero Jaime Martínez, 2008, basic skills in mathematics, A new practice, Wolters Kluwer, Spain"