Using the Performance Assessment for California Teachers to Examine Pre Service Teachers' Conceptions of Teaching Mathematics for Understanding
Motivated by a concern about the low performance of American students in mathematics, the National Research Council published the report Adding It Up: Helping Children Learn Mathematics (2001) This report summarizes a core body of research revealing that U.S. students continue to perform poorly in mathematics. While they can carry out straightforward procedures, American students demonstrate limited understanding of mathematical concepts and are unable to apply their knowledge to solve novel problems. This report also explains that the preparation of elementary and middle school teachers falls short of equipping future teachers with the knowledge they need to help students develop mathematical proficiency. Thus, a key challenge for mathematics teacher education is to prepare prospective teachers to teach mathematics for understanding. As Philipp (2008) describes, meeting this challenge is difficult because "teachers lack the depth and flexibility of mathematical understanding and the corresponding beliefs they need to teach for proficiency (NRC, 2001)" (p. 3) Moreover, given the persistence of traditional teaching practices in American teaching, prospective teachers have had few, if any, opportunities to participate in classrooms that promote learning mathematics for understanding (Lortie, 1975; Zeichner Liston, 1987)