Continued Statistics Teachers' Formation at Colegio de Ciencias y Humanidades, Mexico
Hugo M. Hernandez¹, Roberto Avila¹, Veronica Y. Kataoka²
¹Statistics Departament - Principal's Office, Sciences and Humanities School-National Autonomus University of Mexico, México City, DF, Mexico; ²Programa de Pόs-Graduação em Educação Matemática, Universidade Bandeirante de São Paulo, São Paulo, Brazil

In Mexico, most of in-service Statistics teachers didn't study a major related to education; they are mathematicians, engineers, actuaries, so most of them need pedagogical formation, based on concepts and practice. The Colegio de Ciencias y Humanidades (CCH, Mexico), as an educative institution, concerned about teachers' formation, gives to them 20-hours or 40-hours courses twice a year. In one of these courses for statistics, lectured by the two first authors, didactical sequences are shown, asking teachers to solve them, in order to “experience” the sequence from a student's point of view, and to realize how that sequence may work didactically. These courses are divided into three stages. This work aims to show the didactical sequence, “Mόnica's random walks” (MRW), as an example of the activities given in the course for Statistic teachers at CCH, Vallejo, Mexico. The MRW sequence allows to work with probability concepts such as events, sample space, single event probability, to explore the difference between random and deterministic experiments, to approach probability from relative frequencies, to calculate theoretical probability from a tree diagram, and to compare observed and expected patterns (CAZORLA, SANTANA; 2006). At first stage, it's dicussed that this sequence is based on Brousseau's theory of Didactic Situations (1996) and has been studied by researchers under Godino's Onto-semiotic theory (2002) and Chevellard's Anthropology of Didactis theory (1992). In second stage, the teachers solve the four sections and 23 questions in the activity. At the third stage, teachers with some knowledge about software Fathom already, are asked to reply 1000 times the experiment in MRW. They also have to realize the shape of distribution. They also have to compare results between 30 coin tossings in the environment physical-experimental and the theoretical probability with their results by Fathom simulation. By the results obtained, we belive this proposal for continued teachers' formation at CCH may help them in conceptual and didactical contents of the sequences, and in knowing theories in Education as well.

Brousseau, G. (1996) Fundamentos e Métodos da Didáctica da Matemática. In: Brun, Jaean (Org.). Didáctica das matemáticas. Lisboa: Instituto Piaget.

Cazorla, I. M., Santana, E. R. dos S. (2006). Tratamento da Informação para o Ensino Fundamental e Médio (1rd. ed., v.1). Itabuna, Bahia, Brasil: Via Litterarum.

Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques, 12 (1), 73-112.

Godino, J. D. (2002) Un enfoque ontolόgico y semiόtico de la cogniciόn matemática, In: Recherches en didactique des Mathématiques, 14, n 3, p. 325-355.

Keywords: Statistics Teachers' formation; Probability; Didactical sequence; Mônica's random walks

Biography: High-school statistics teacher for almost 17 years. Master degree in Math Education, focused in Statistics Education. Author of several books, articles and scholar programs in Statistics. Current head of the Statistics Department at his campus, and current ISPL Country Coordinator for Mexico.