So When Do We Teach Mathematics? Vital Elements of Professional Development for High School Mathematics Teachers in an Urban Context.

It is our belief (university professors/researchers), and the finding of many studies, that effective professional development can be an invaluable foundation for high-quality, reform-oriented teaching that leads to improved student learning and achievement (e.g., Darling-Hammond, 2000; US Dept. of Education, 2000). Furthermore, teachers serve as the primary catalyst for change in students' learning (Borko & Putnam, 1995). However, given the plethora of research and anecdotes related to successful programs that ultimately lead to student achievement, how to design professional development within a given context remains a challenging endeavor. Research suggests the following be included in successful professional development efforts: (1) university and school collaborative partnerships, in which teacher educators play an important role in the development of thinking and independence (Little, 2002; Putman & Borko, 2000); (2) opportunity for teachers to reflect in a collaborative format (Farmer, Gerretson, & Lassak, 2003); (3) guided help with the study of curriculum, assessment, and instruction (Newmann, Secada, & Wehlage, 1995); (4) modeling of practices that promote effective student learning; and (5) opportunities to negotiate learning within the context of the own practice and classroom (Wilson & Berne, 1999). Although there exist lists of what should be incorporated in professional development programs, rarely does this literature explore how to embed these components within the realities of the urban school context. Teacher development is further complicated by the federal- and state-level expectations for teachers to become highly qualified (No Child Left Behind, 2001). Mandates emphasize content knowledge and make it imperative for all teachers to have an opportunity to work toward initial and continuing certifications within a unified program. Within content knowledge, mathematics is identified as an essential component of K-12 foundation (U.S. Department of Education, 2003). Thus, within professional development, there must be more emphasis on mathematics content knowledge. Teachers' thinking about mathematics teaching and learning are challenged by expectations and ideals endorsed by current reform efforts in mathematics education (e.g., NCTM, 2000). Such recommendations call for an approach to mathematics teaching that allows students to communicate, problem solve, and engage in conceptual mathematics. Teachers are asked to teach in ways that promote an integrated, connected view of mathematics, rather than a procedural, rule-based view. This shift toward inquiry-based instruction assumes teachers view mathematics as a tool for thought, rather than a set of rules and procedures to be memorized. However, teachers are unlikely to make adjustments in their thinking without intervention and deliberate support (Richardson & Anders, 1994). Given this understanding, professional development efforts must intentionally provide experiences that will assist teachers in learning new ways of thinking about mathematics and its teaching (Farmer, Gerretson, & Lassak, 2003). Within a stronger focus on content knowledge, programs must also examine the type of mathematical content that is explored, as well as the explicit links they make to pedagogy. Hill, Rowan, and Ball (2005) found that teachers' mathematical knowledge was significantly related to student achievement gains in elementary classrooms (p. 371). Ball, Lubienski, and Mewborn (2001) cite the importance of knowing mathematics for teaching, which encompasses all of the knowledge required to teach mathematics effectively. From a professional development standpoint, this perspective suggests that programs should provide opportunities for teachers to learn mathematics around specific content and teaching situations that may arise in practice. Designing professional development becomes increasingly complex when layered with issues specific to inner-city settings. …