"Teaching Mathematics for Understanding in Urban Settings: A Model that Integrates Knowledge, Skills, and Dispositions toward Students"

Abstract

International studies reveal that lessons in the United States involve less mathematical connections between concepts and procedures compared to lessons taught in countries where student achievement is higher (Stigler & Hiebert,1999; Hiebert et al., 2003). Although U.S. teachers present just as many rich problems as the teachers in the other countries, they often reduce the conceptual aspects of the problems to computations and algorithms during alesson. Hence, the main goal of this project was to provide teachers in an U.S. urban setting opportunities to develop mathematical knowledge and pedagogical skills necessary to teach mathematics for understanding. We developed a two-year video-based PD program that featured two main goals:

(1) to deepen teachers' understanding of 6th-grade mathematics concepts and
(2) to develop their ability to teach in ways that are responsive to student thinking by maintaining the cognitive demand of the mathematical task.

The PD model was designed to integrate mathematics knowledge and teaching skills through a multi-dimensional analysis of videotaped lessons. The PD program consisted of 40 hours paced according to the district instructional guide. All 6th-grade teachers and their students from 5 high-poverty and low-performing middle schools participated in the study. Teachers were randomly assigned to either a treatment or a control group. During year 1, the treatment group participated in the PD program, while the control group did not. During Year 2, the control and the treatment groups participated in the PD program.

Various measures were used to assess the effectiveness of the program. This AERA presentation focuses on our analyses of videotapes of lessons taught by the participating teachers. These videotapes allowed us to study the impact of the PD program on teachers' classroom practice. The videotapes illustrate how knowledge, dispositions, and skills intersect in ways that either afford or limit students from participating in mathematics lessons. Through the presentation of selected episodes from teachers' videotaped lessons, we will illustrate various interrelations among

(1) knowledge of mathematical concepts and of ways students understand these concepts,
(2)knowledge of instructional routines that are responsive to student thinking, and
(3) dispositions toward students.

These examples indicate that all three elements of teaching are necessary for students to develop mathematical meaning. More importantly, teachers who did not believe in students' ability to reason mathematically exhibited low expectations for their students in the video. Teachers lacking positive dispositions for students were not capable of applying their mathematics knowledge and teaching skills to their full potential. Thus, we argue that the last element of our framework-dispositions toward students-although often excluded from models for teacher learning, should be explicitly integrated in professional development experiences.