Developing pre-service teachers’ noticing of students’ understanding of the derivative concept

This research study examines the development of the ability of pre-service teachers to notice signs of students’ understanding of the derivative concept. It analyses preservice teachers’ interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results indicate that the development of this skill is linked to pre-service teachers’ progressive understanding of the mathematical elements that students use to solve problems. We have used these results to make some suggestions for teacher training programmes.

Changes in how prospective teachers anticipate secondary students’ answers

This study focuses on how prospective teachers learn about students’ mathematical thinking when (i) anticipating secondary students’ answers reflecting different characteristics of understanding and (ii) propose new activities in relation to the classification of quadrilaterals. The data were collected from forty-eight prospective secondary school teachers enrolled in an initial training programme. The results indicate three changes in how the prospective teachers anticipate secondary students’ answers in relation to the role given to a perceptual or relational perspective of the classification of quadrilaterals. These changes are described considering how prospective teachers grasp the students’ understanding of the inclusive relation among quadrilaterals as a conceptual advance. We argue that prospective teachers’ learning was promoted after participating in a structured environment where they had the opportunity to discuss how to recognize the features of student’s understanding.