Abstract:

The use of technology in school, confronts students and teacher with issues that until then had been unusual, making a specific set of difficulties arise. The choice of the viewing window, being essential in obtaining any graphical representation, appears in the literature as one of the great difficulties that students face. The problems during direct input of values or while conducting zooms, as well as the difficulties dealing with partial or incomplete views of graphs are reported in numerous studies. However, we know very little about what the teacher does to help students overcome these difficulties. Being clearly recognized the influence of the role of the teacher on student learning, it is particularly important to know how the teacher guides and supports students on the choice of the viewing window. Existing research suggests that the teacher should continuously draw students’ attention to possible difficulties that may arise, and carefully sequence the contact of students with potentially problematic situations, preventing them from occurring too early. Assuming that the management of this question is complex for the teacher, these are however results that say very little about the teacher’s practice.

In this sense, this study aims to know and understand the teacher's options regarding the way students interact with the viewing window during the study of functions in mathematics at high school level.

The study adopts a qualitative and interpretative methodological approach, undertaking one teacher case study. Data were collected by semi-structured interviews, class observation, and documental data gathering. 14 lessons of 90 minutes were observed and recorded, with interviews conducted before and after each class, intending to know what the teacher planned for that class and the underlying reasons and, afterwards, how he sees the events that took place on the class. Data analysis was conducted in an interpretative way.

The achieved results suggest a conscious concern of the teacher to minimize the contact of students with problematic situations in what regards to the viewing window. In an initial phase, this concern is reflected in the implementation of tasks were the use of the standard window is a good option, even in cases where real situations are involved. Later, the choice of tasks evolves to include situations where the standard window is not the best choice, although it still allows solving the task. Near the end of the study of the subject, the teacher prepares a task including a partial or incomplete graph representation (but easy to identify in the standard window). This global strategy ultimately leads to the students disinterest on teacher suggestions and alerts, because they are unable to see their usefulness once they can always solve the task on the standard window.
The findings of this study recognize the importance of carefully sequence the students’ contact with situations in which the choice of the window is more complex, but raise questions concerning how this confrontation should occur, suggesting that it is necessary to consider situations where it is actually needed to face the difficulties, and placing a strong emphasis on the tasks proposed by the teacher. These findings also highlight the importance of identifying stages on teacher work with students around the viewing window and of including this knowledge in teacher education.

Keywords:

Graphing calculator, viewing window, teacher's knowledge and practice.