Abstract:

The interpretation of statistical graphics appearing in communication media is part of the statistical literacy or culture that every citizen might have for their self-development in modern society.Then, a deep knowledge of the difficulties of this interpretation is essential, since a biased or poorly constructed graphic will prevent the information to be read correctly by the citizen that has to interpret it. As shown in Gal (2002), a consumer of statistical data not only needs some statistical skills, but also some linguistic abilities; a good knowledge of the scope, criticism and mathematical experience are also required. Hence, data users must be acquainted with the essential mathematics concepts involved in the development of certain statistic indicators, as well as the mathematical connection between these summary statistics, the graphs or tables, and the raw data from which they are constructed.
Both reading and constructing statistical graphs require several elements to identify and understand labels of the edges, scales, area in the construction of a histogram, proportionality, operations, among others (Curcio, 1987).
The aim of this research is assessing the fourth graph reading level, described by Curcio (1989), and Friel, Curcio and Bright (2001), concerning with critical assessment of the data collection methods, their validity and reliability, in a sample consisting of 171 primary school prospective teachers. To this end, from a biased graph taken from press, we elaborated a questionnaire with open questions. This questionnaire evaluates the correct interpretation, together with the extraction of main conclusions, of a bar graph whose understanding requires enough mathematical skill concerning proportionality.
We carried out a quantitative and qualitative analysis based on the onto-semiotic approach’s methodologies (Godino, Batanero & Font, 2007), in particular the priori analysis of the tasks and the notion of critical semiotic functions (Contreras et al. 2017). This analysis provided that 67% of the participants identified the information represented in the graph as correct. A more detailed study of the arguments given to justify the correctness of the graphic show that 39% of the students associate this correctness to the clarity of the graphic, a 7% to the existence of a proportionality relation of the data represented in the axes, another 7% to the source, and the rest gave no argument at all. Consequently, since prospective teachers of primary school will be in charge to prepare statistically literate citizens, we conclude that is important to increase their statistical comprehension in order to be able to expand this knowledge in their students.

References
Contreras, J. M, Molina-Portillo, E. Godino, J. D., Rodríguez-Pérez, C. y Arteaga, P. (2017). Funciones semióticas críticas en el uso de diagramas de barras por los medios de comunicación. En J. M. Contreras, P. Arteaga, G. R. Cañadas, M. M. Gea, B. Giacomone y M. M. López-Martín (Eds.), Actas del Segundo CIVEOS.
Curcio, F. R. (1987). Comprehension of mathematical relationships expressed in graphs. Journal for Research in Mathematics Education, 18(5), 382-393.
Curcio, F. R. (1989). Developing graph comprehension. Reston, VA: N.C.T.M.
Friel, S., Curcio, F., & Bright, G. (2001). Making sense of graphs: critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education 32(2), 124-158.

Keywords:

Statistical literacy, statistical graphs, prospective teachers.