Prospective mathematics teachers' learning about high school students' understanding of limit concept

The goal of this study is to characterize how do prospective teachers develop the noticing skill in relation to the teaching and learning of the limit of a function at a point. Twenty-five prospective teachers participated in a learning environment designed ad hoc considering the related nature of the skills of identifying, interpreting and deciding how to respond that conceptualize the skill of noticing students' mathematical thinking. Results indicate that the development of prospective teachers noticing implicated the recognition of the mathematical elements that are relevant in the concept understanding, the consideration of different progressions in the students' learning, and the proposal and justification of instructional decisions focused on enhancing students' cognitive processes that can articulate the concept understanding, beyond curricular references.