"This is the First Time I've Done This": Exploring secondary prospective mathematics teachers' noticing of students' mathematical thinking

This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students' mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program. These skills (attending, interpreting, and responding) are defined as teachers' professional noticing of students' thinking. Results indicate that seniors respond to students' thinking in significantly different ways from juniors and sophomores. Converging the data highlighted inconsistencies in how participants' were making sense of students' mathematical thinking, as well as in participants' self-identified strengths and weaknesses.