Teachers, math, and reform: An investigation of learning in practice
Jose Aires Castro-Filho, The University of Texas at Austin, United States
The University of Texas at Austin . Awarded
This dissertation examined the possibility of professional development which focuses on developing teachers' content knowledge. Without a robust understanding of mathematics, teachers will not be able to teach higher level mathematics to all students. In addition, the study examined the feasibility of developing teachers' knowledge within their everyday practice and in the company of their colleagues. Learning content knowledge in the context of school teaching at the high school level has not been extensively explored in the literature. The study describes the development of teachers' content knowledge during the implementation of a reformed unit ranging from qualitative graphing to linear functions and simultaneous equations. Teachers also participated in discussions about students' outcomes.
The study was conducted at an urban high school in Austin, Texas. Eight math teachers were implementing a replacement unit in the Algebra I curriculum. The unit involved a transition from qualitative graphing to linear functions and simultaneous equations. Three different technologies were used by the teachers: a device called motion detector, a Java applet called Bank Account Interactive Diagram (Confrey & Maloney, 1998) and the software Function Probe II (Confrey & Maloney, 1998). Four of the Algebra I teachers were interviewed before and after three different lessons during the unit. All eight teachers were interviewed before and after the entire unit. Other data sources included videotaped observations of classes and professional development meetings.
The results of the study point to the following findings. (1) The curriculum materials and the technology used, created challenges for teachers' current understanding, especially in regard to the ideas of rates of changes and accumulation. When accompanied by the support of researchers and colleagues, these challenges were excellent learning opportunities for the teachers to reflect on and develop a deeper understanding of their ideas. (2) Teachers valued the materials and the approach, in particular, these three aspects: (a) the mathematical content of the unit, (b) the support from researchers, and (c) the collegial discussions about content knowledge. (3) Teachers benefited from discussions about students' outcomes. They changed from making claims based only on their experience to more carefully analyzing the available student data.
Castro-Filho, J.A. Teachers, math, and reform: An investigation of learning in practice. Ph.D. thesis, The University of Texas at Austin.
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