Characteristics of a learning environment to support prospective secondary mathematics teachers' noticing of students' thinking related to the limit concept

International audienceThe aim of this study is to describe changes in the way that prospective secondary school teachers notice students' mathematical thinking related to the limit concept in a learning environment designed ad hoc. The learning environment progressively nests the skills of attending to, interpreting and deciding as three interrelated skills of professional noticing. Results show characteristics of how prospective teachers gained expertise in the three skills since four out of five groups of prospective teachers interpreted students' mathematical reasoning attending to the mathematical elements of the dynamic conception of limit. The links between attending to and interpreting helped prospective teachers justify the teaching activities proposed to support the progression of students' mathematical reasoning: from a mathematical point of view or considering mathematical cognitive processes involved