Developing and Using Mathematical Knowledge for Teaching Fractions: A Case Study of Preservice Teachers
Date of Award
Dissertation - Restricted
Doctor of Philosophy (PhD)
Pink, William T.
One emerging theme in mathematics education examines the mathematical knowledge needed for teaching (Ball & Bass, 2003; Ball, Hill, & Bass, 2005a; Hill, Rowan, & Ball, 2005; Hill, Ball, & Schilling, 2008). Most recently, mathematical knowledge for teaching is defined by researchers as "the mathematical knowledge used to carry out the work of teaching mathematics" (Hill et al., 2005, p. 373). First and foremost, mathematical knowledge for teaching means that teachers demonstrate conceptual and procedural understanding of the mathematics topics they teach. Moreover, mathematical knowledge for teaching means that teachers who demonstrate competence in their own understanding of mathematical topics also know how to explain those concepts to students (Hill et al., 2005). Therefore, mathematical knowledge for teaching includes both teacher knowledge of and competence with the subject matter as well as a particular set of pedagogical skills that allows teachers to make decisions about the mathematics they teach in their classrooms. These decisions facilitate and promote student understanding of and achievement in mathematics...