Teachers need to develop “mathematical knowledge for teaching” (MKT)—the mathematical knowledge, skills, and habits of mind that are inherent in the work of teaching. The level of a teacher’s MKT has a big effect on children’s mathematics learning (Hill, Rowan, & Ball, 2005).
Teaching also involves skill in anticipating and interpreting students’ ideas and ways of thinking about mathematics. When professional development is grounded in explicit attention to student thinking, it has been shown to impact student learning (Fennema et al., 1996).
Proficient teaching requires a repertoire of practices, routines, and techniques that enable teachers to effectively and efficiently help all students learn mathematics. Teachers benefit from direct work on these practices and the development of skill in parsing and describing their craft (Grossman & McDonald, 2008).
LEARNING FROM OWN PRACTICES
Developing teaching expertise is a career-long process. While teachers may serendipitously learn from their experiences, professional learning should not be left to chance. The idea that teachers need to learn more effectively from their day-to-day work has been consistently noted in research and educational theory (e.g. Dewey, 1916; Schön, 1983; Lampert, 2010) and, more generally, the ability to critically examine one’s own change efforts over time is key component to improvement (Bryk, Gomez, Grunow, Lemahieu, 2015).