Prospective Teachers’ Use of Conceptual Advances of Learning Trajectories to Develop Their Teaching Competence in the Context of Pattern Generalization

(1) Background: This research shows how the identification of conceptual advances (CA) that determine transition between stages a progression model in learning trajectory will help prospective primary teachers (PPT) to develop teaching competence “professional noticing students’ mathematical thinking”. Conceptual are key moments construction structures and involve change way students understand relationships. (2) Methods: A module has been designed which Teaching Degree analyze responses education tasks pattern generalization from use advances. (3) Results: The results show professional can be developed suitable environments. (4) Conclusions: recognition helps interpret thinking trajectories effective tools structure noticing.