GROUND ZERO - SEMIOTIC CONFLICTS IN THE MEASURES OF CENTRAL TENDENCY IN PROFESSIONAL EDUCATION

The Professional Education Mathematics Program addresses issues of numbers and geometry, including trigonometry; real functions and infinitesimal analysis; statistics and probabilities and discrete mathematics, structured in modules (Directorate General of Vocational Training, DGFV, 2004/05, p.3). According to the Professional Education Mathematics Program, statistics contribute to improving the ability to evaluate statements of a statistical nature, providing students/trainees with appropriate tools to reject certain advertisements, news or other information in which the interpretation of the data or the sampling was not correct (DGFV 2004/05, p.22). At the end of this topic, with duration of 27 hours, the students/trainees should know how to organize, represent and handle the data collected. In the context of educational research centered on the teaching practices of Mathematics and in the subject of statistics, this text aims to study the difficulties of students in measures of central tendency, where and in what form these difficulties arose. This study is part of a PhD work that is underway and, at this stage, we aimed to collect data to support a didactic intervention that will take place in the next school year.

In the present text we report a study on statistics, more precisely the contents of measures of central tendency – mode, median and mean – taught in the discipline of Mathematics of level IV vocational education (10th year, ages 15 to 17). In the study, students from three classes participated in a total of 51 students from a professional education school in Northern Portugal with the aim of evaluating knowledge in measures of central tendency by testing through a questionnaire built for this purpose with 10 questions and respective items. Although only the results of the analysis of three questions are presented, this analysis was based on the Ontosemiotic Approach of Godino and colleagues (2009) and was based on the concept of semiotic conflict. For Godino et al. (2007): “A semiotic conflict is any disparity or difference of interpretation between the meanings ascribed to an expression by two subjects (persons or institutions)".

The detection of these conflicts, of students in the measures of central tendency, will base a didactic intervention that will take place in the future. In terms of results, we could find that the conflicts related to representations, conceptual conflicts and procedural conflicts referred by Mayén, Diaz and Batanero (2009) were detected as described in several reviewed literature.