Abstract:

This work is theoretically supported by the Ontosemiotic Approach (OSA) of Godino and collaborators to analyze the components of the didactic suitability of the didactic intervention first task in the vocational education mathematics, level IV (ages 16-18). This level is the equivalent to secondary education (grades 10 to 12, ages 16-18) in Portugal.

According to Godino and colleagues (2016, 2020) we analyzed the six components of the didactic suitability (DS):
a) Epistemic suitability measures the representativeness and interconnections of the implemented meaning as regards a previously intended reference meaning;
b) Cognitive suitability is the extent to which the implemented meaning is perceived by the students, and whether the personal meanings achieved is close to the intended meaning;
c) Emotional suitability is related to the students' involvement (interest, motivation, and so on) in the study process;
d) Mediational suitability depends on the availability and adequacy of material and temporal resources in the teaching process;
e) Interactive suitability depends on the extent to which the didactical configurations and classroom discourse served to identify and solve semiotic conflicts that appeared along the instructional process;
f) Ecological suitability is the extent to which the teaching process fit the school and society educational process, and took into account other factors influencing the setting in which it was developed.

The didactical intervention – in Mathematics level IV, statistical classes' module – used tasks that allowed students to study and practice the central tendency measures' theme. Project work motivated the students to use their "own" data. During the intervention, students learned by themselves, were supported by the teacher during the classes and could do their statistical investigation. This research is part of broader work and has a qualitative paradigm with an interpretive and exploratory aim. This paper presents the first task, "Discovering Error: Statistical Graph Reviews," and analyzes students' solutions and dialogs. The task will be given and aimed to lead students to interpret the statistical information presented graphically and make them check its errors. That interpretation is intended to develop students' critical thinking so that they, as citizens, can interpret the statistical information provided in their daily lives.

A qualitative paradigm (interpretive aim ) and exploratory descriptive were adopted. Nevertheless, we present dialogues and examples of the students' work during the task. The research questions were: What were the levels of each component of that didactic suitability? What was the global didactic suitability of this first task? In this work, the six components of DS by Godino et al. (2016, 2020) were framed by Andrade (2014) as analysis tools and adapted for this first task analysis of the intervention. From the results, this first task attained its designed aims. High levels of Epistemic, Cognitive, Emotional and Mediational suitabilities were found. Concerning the Ecological suitability, it was moderate since the students complained about the lack of time to complete the task, and it was not possible to use technology during the classes.

Keywords:

Statistics, task, ontosemiotic approach, didactic suitability.