Visualization: a pathway to mathematical challenging tasks

Abstract

Mathematics learning is strongly dependent on the teacher and the tasks proposed to students (e.g. Doyle, 1988; Stein & Smith, 1998; Sullivan et al., 2013). Thus, the teacher must develop students’ mathematical understanding, creating situations to ensure that they have the opportunity to engage and be challenged in high-level thinking, through the tasks proposed. The teacher’s choices will determine the quality of students’ learning (e.g. Chapman, 2015; Stein & Smith, 1998). This implies the use of tasks that meet different ways of thinking displayed by the students, confronting them with multiple-solution tasks, that challenge them to see outside of the box, motivating them to learn and to work with each other. We are interested in visualization because it plays an important cognitive role in the teaching and learning of mathematics, as an aid to thinking, as a means of communicating mathematical ideas and as a useful tool in problemsolving (Arcavi, 2003). So, pre-service and in-service teacher training should promote an insight into the nature of mathematics and its teaching, meaning that teachers need to have different teaching and learning experiences similar to the ones they are expected to use with their own students (Ponte & Chapman, 2008; Vale & Barbosa, 2020).