The poster presents a didactical situation about the arithmetic mean and its representativity through use of graphics has like purpose that students obtain the mean of a data set beginning from its analysis in a graphic and that understand the effect that have above the mean a change in the data.
It’s required to be based on the four phases of Didactical Engineering (Artigue, 1995) as methodology for the design of the proposal; of these, at preliminary analysis phase were analyzed the cognitive, didactical and epistemological facts associate to the mean. Between identified difficulties in high school students, we focus on recognize its representativity and the effect that it has an atypical value or zero on the mean, in a data set (Batanero, 2001 and Mayén, Cobo, Batanero and Balderas, 2007).
On the other side, we found that the handling of graphics has been joined since ancient to the treatment of information. For example, the Egyptians realized census of the ground for a new repartition, the Babylonians sit in table’s clay registers about the moving of the stars and planets, solving a problem of estimation through the calculus of the total sum of the observations and divide for the number of data. In 1669, Huygens, extracting of Michael, F. and Denis, D. (2007), realized the first graphics of continues function and show who find the average of life remaining of a person of certain age.
Taking as reference the former mentioned, we consider the graphics use and interpretation at proposal activities, with the ending of generate understanding about the mean’s representativity, so as that students conjecture and present arguments to justify their results, make inferences and take decisions.
In the design of the activity we base in the three levels of questions proposed by Wainer, 1992, cited by Batanero (2001), for understanding of the measures of central position related with the extraction of the data directly of the graphics, with tendencies analysis and about the structure of presented data as a totality.
The activities were implemented in an experimental group and a control group of eight students, selected students have knowledge about the algorithm of the arithmetic mean and with the next level of a graphic translation: they can appreciate the purpose of this, describe a discrete portion of the data and recognize models and regularities in it. For evaluate the efficacy of this, it will design a test which will look if the student will be capable to apply the knowledge obtained in other context.
With this didactical situation it’s expected that students to succeed in the development of their abilities in order to understand the necessity of employ a central value and choose the most appropriate, to build a set of data that has a determinate average and to understand the effect that, above the arithmetic mean has a change in all data or in a part of them.
BIBLIOGRAPHY:
Artigue, M., Douady, R., Moreno, L. (1995). Ingeniería didáctica en educación matemática. Un esquema para la investigación y la innovación en la enseñanza y aprendizaje de las matemáticas. México: Editorial Iberoamerica.
Batanero, C. (2001). Didáctica de la Estadística. Granada: Grupo de Investigación en Educación Estadística.
Michael, F., Denis, D. (2007). Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization. Recover the 15 of October of 2007 the site web of the Departament of Mathematics of The University of York: http://maths.york.ac.uk/www/ResearchStats
Mayén, S., Cobo, B., Batanero, C. y Balderas, P. (2007). Comprensión de las medidas de posición central en estudiantes mexicanos de bachillerato. UNIÓN: Revista Iberoamericana de educación matemática 9, 187-201.