Professional Noticing: A Component of the Mathematics Teacher’s Professional Practice

In this paper, I characterize the notion of «teaching competency» as being able to use knowledge in a pertinent way to carry out mathematics teaching tasks. One aspect of teaching competency is the teacher’s «professional noticing» of students’ mathematical thinking. This feature of teacher competency involves the cognitive ability to identify and interpret the salient features of the students’ output in order to make informed decisions. This construct is illustrated using a context in which the prospective teachers are learning to interpret the students’ answers to linear and nonlinear problems (in order to recognize the students’ development of proportional reasoning). In this context, when prospective teachers use increasingly more explicit mathematics elements and features of the development of mathematical understanding to describe and interpret the students’ mathematical thinking is considered as evidence of the development of professional awareness