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