The aim of this research is to characterize profiles of the teaching competence "noticing students' mathematical thinking" in the context of the pattern generalization. Prospective primary teachers were asked to describe and interpret the answers of three primary students to three linear pattern generalization problems. Five profiles for this competence have been identified. Prospective teachers named various mathematical elements to describe the students' answers but did not always use them to interpret the understanding of pattern generalization of each student. Furthermore, this teaching competence ranges from the PPTs who could not recognize the understanding of the primary students to those capable of recognizing degrees of primary students' understanding. Our findings allow one to generate descriptors of the development of this teaching competence and provide information for the design of interventions in teacher education addressed to support the recognition of evidence of students' mathematical understanding.