On Location

Abstract

Combining a university methods course with math classes in an elementary school led to powerful learning experiences for the preservice teachers, the authors report. It also provided benefits for the elementary students and their teachers. ********** A GREAT deal of work goes into building learning experiences for preservice teachers of mathematics. This effort involves identifying and sequencing core mathematical tasks and concepts to be explored and investigating instructional strategies and related research on student thinking. It also involves examining technologies and new teaching materials. So that teachers can build on their own knowledge of mathematics, it involves planning discussions of and practice with mathematical problems ranging from simple to complex. It also involves designing tasks that hone preservice teachers' skills in listening and noticing, assessment, reflection, and lesson design. One of the most difficult challenges of preparing preservice teachers, though, is helping them make important connections between the work they read about--both theoretical and empirical--and instructional practices in real school classrooms. When done well, focused activities that build this link can have a powerful influence on these soon-to-be teachers. Laura Grandau is a math methods instructor, and Mark Landis and Kelly Ryan were preservice teachers in the math methods course described here. During one 15-week semester, we and other preservice teachers worked together in an elementary school learning how to teach mathematics. Nearly every meeting of this methods course took place at the school and involved practicing teachers and their students. The principal and the faculty welcomed us and were generous with their time and space. Together, the prospective teachers, the instructor, and the school's faculty and students created routines that allowed for observing, teaching, interviewing, and discussion. It was a rich opportunity that depended on good relationship-building, careful planning, flexibility, and genuine care for teacher development and student learning. The preservice teachers first learned about the school itself, its history, the surrounding community, and the current leadership teams and activities. Then we read and discussed literature on mathematics teaching and student thinking. We also became familiar with the mathematics curriculum used at the school and began our own mathematical problem-solving investigations. Next we zoomed in to the classroom level. During mathematics time, we entered classrooms to observe and later discuss the learning environment and group norms; strategies for managing students and materials; and the processes of knowing and delivering mathematics instruction, which include encouraging classroom talk about problem solving and listening to students' explanations of their mathematical thinking. Once each prospective teacher had become familiar with the inner workings of one or more mathematics classes, the practicing classroom teachers identified students--those whose mathematical thinking the classroom teachers wanted to know more about. After some initial study of Herbert Ginsburg's ideas about conducting clinical interviews (1) and some discussion of working closely with students, each prospective teacher conducted a one-on-one problem-solving interview with an individual focus student. The prospective teachers read research about the interview protocol and practiced administering it. They also talked briefly about this activity with their focus students' practicing teachers. Then they asked students to respond orally to leveled math problems that were designed to assess the children's understanding of early number concepts and problem-solving strategies. (2) After conducting these problem-solving interviews with their focus students, the preservice teachers and the methods instructor examined the children's responses and discussed the strategies the children used to solve number problems, as well as any confusions and misconceptions that arose. …