Background:
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.

Material and methods:
The data were collected from forty-eight prospective secondary school teachers enrolled in an initial training programme.

Results:
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.

Conclusions:
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