| As the teacher and researcher, I studied systematically my own teaching for a one-semester class in algebra to a group of 9th grade students in an inner-city high school. I explored four research questions. First, I looked at the differences between a numerical pattern approach to algebra and the district's mandated algebra that uses a standard algebra textbook. Second, I looked at how students interacted with the algebra content using a numerical pattern approach. Third, I looked at my own instructional practice and grounded some decision making process made in the moment of teaching. Fourth, I looked at the planning required to teach algebra in this environment. I used Stein, Smith, Henningsen, and Silver's (2000) Task Analysis Guide to examine the cognitive demand for the tasks and Michigan Department of Education's (2006) Curriculum Guide to examine the algebra content for the tasks. I used Lee's (2007) Cultural Modeling Project framework and Cohen, Raudenbush, and Ball's (2003) instructional triangle framework to investigate the interactions between teacher, content, and students. I audio taped 23 classroom enactments, kept a personal journal, kept all lesson plans, and collected students' assessments and notebooks. My analysis showed that the district mandated textbook was dominated by a high percentage of low-level cognitive demand tasks, targeted 40 standards and had few connections between them. The teacher generated tasks, which used a numerical pattern approach, was not dominated by low-level demand tasks, targeted 18 standards, and had more connections between them. Contrary to portraits of inner-city schools mathematics classroom, in the lessons analyzed, the students and I discussed the mathematics. Students questioned their "known" mathematics, chose appropriate problem solving strategies, and contributed to the building and teaching of the numerical pattern approach to algebra. During the weekend, I used students' assessments as a guide for weekly lesson plans and modified my lesson plans in the midst of teaching to fit the needs of my students. I present three implications for this study: (1) reconceptualization of the content, (2) using students as resources, and (3) management of the chaos of teaching. These implications can be adapted to teachers working in difficult teaching environment. I also provide strategies on how to implement a numerical pattern approach to teach ninth grade algebra. |
