Developing Secondary Mathematics Content Knowledge for Teaching in Secondary Mathematics and Science Teachers
This study investigated secondary mathematics teachers' teaching practice. The subjects were enrolled in a three-hour graduate mathematics education course and an accompanying one-hour, school-based PLC for secondary mathematics and science teachers. The course was designed to support teachers' in developing deep and connected understanding of key mathematics ideas of the algebra through precalculus strand of secondary mathematics. Ideas of quantity, covariation, and function were explored in a science context. Tasks were designed to promote meaning making and specific reasoning abilities that have been reported to be foundational for understanding key ideas of calculus (Carlson, Jacobs, Coe, Larsen, Hsu, 2002). The goal of the learning communities was to promote teachers' reflection on the effect of their practice on student learning and to assist teachers in learning to develop conceptually based and inquiry focused lessons.
Our course design was informed by previous data that had revealed that bringing teachers to understand fundamental ideas of secondary mathematics such as rate of change, linearity and exponential growth is complex. Teachers need sustained engagement with activities that support their constructing deep and flexible understanding of these ideas. This required that our project staff clarify for themselves the proccesses of acquiring an understanding the fundamental concepts central to secondary mathematics. As one example, our attempts to unpack the reasoning abilities, understandings and notational issues related to unerstanding exponential functions has led to a dissertation study that produced an exponential function framework that articulates and illustrates these ideas and abilities.
Agendas and tasks for the PLC meetings are developed by project staff for the purpose of supporting teachers in learning to examine and support their own students' understanding of these key ideas. As an example, teachers interview students to inquire and characterize their student understanding of ideas such as rate of change and exponential growth. They also develop lessons (with assistance from project staff) to support their students in learning these fundamental ideas deeply.