No time like the present: reflecting on equity in school mathematics

Theory Into Practice, Summer, 2003 by Celia Rousseau, William F. Tate

Mathematics education has traditionally paid little attention to teacher reflection about equity. In this article, we argue that the time has come to move equity from the margins to the mainstream in mathematics education and make it a focus of teacher reflection. To illustrate the need for a focus on equity, we describe the beliefs of a group of high school mathematics teachers. We argue that the teachers' views of equity and race blocked substantive reflection about the nature of their instructional practices and the impact of those practices on students of color in their classes. We submit that this case is important because it highlights some of the assumptions that must be challenge in an effort to promote the kind of reflective practice that can contribute to the realization of opportunity to learn school mathematics.

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THE PURPOSE OF THIS ARTICLE is to describe framework to support teachers' reflection about school mathematics and traditionally underserved students. Despite recent gains in achievement, many students of colorare not performing at acceptable levels in school mathematics. One examination of national trend studies, college admission exams, and advanced placement tests indicated that for a 15-year period beginning in 1982, all demographic groups have improved in mathematics achievement--specifically in basic skills (Tate, 1997). Further, the mathematics achievement gap was slowly closing between White students and students of color (i.e., African American and Hispanic students) on assessments of basic skills. Unfortunately, across many national surveys of student achievement, African American and Hispanic students remain largely overrepresented in the lower tails of achievement distributions and underrepresented in the upper tails of these distributions. This trend does not appear to be changing in any noticeable fashion.

Perhaps the success associated with the basic skills performance of African American and Hispanic students can inform our understanding of how to support the implementation of more demanding mathematics goals for these and other underperforming demographic groups. The positive achievement gains shown in the area of basic skills demonstrates that when teachers and administrators agreed on a common goal in school mathematics, were goal oriented, and were given sufficient institutional support to achieve the goal, students would learn the mathematics taught. However, we also speculate that the success (albeit limited) of the basic skills movement was related, at least in part, to teachers' beliefs about their students. Many of the goals and teaching strategies linked to the basic skills movement were consistent with teachers' perceptions of students' ability and how best to teach largely poor, urban students of color (Strickland & Ascher, 1992). As the vision of what it means to be mathematically literate in U.S. society has shifted from knowledge associated with a strictly basic skills curriculum to a more demanding standard, the limits of past practice and low teacher expectations about school mathematics become increasingly apparent.

For the first time in the history of the United States, all studentsare being challenged by state and local standards to learn mathematics skills once offered only to "college capable" students. Further, many students face challenging assessments in mathematics with real consequences for advancement in the school system. These policy directives place new demands on teachers to teach content that was purposefully restricted to an elite few in just the past decade. For example, the state of Texas has called for a graduation exit examination that includes content from algebra and geometry courses. During the 1980s, a Texas high school graduate could have completed the mathematics graduation requirement without taking a single algebra course. Today, a Texas high school student must complete three years of mathematics including algebra and geometry. Further, the student must demonstrate mastery of this content on a state mandated assessment. Nearly every state has adopted more demanding standards in school mathematics (Massel, 1994). It is this context that suggests the need for serious teacher reflection about practice, pedagogy, and policy in school mathematics.

Reflecting on What?

Insightful reflection about practice is a function of teachers' knowledge about the subject matter and the learner. The Cognitively Guided Instruction (CGI) studies and other long-term studies of mathematics teaching support the idea that teachers' knowledge of students' reasoning--when it is integrated, robust, and a part of the established mathematics curriculum--can positively affect the teaching and learning of traditionally underserved students (Campbell 1996; Carey, Fennema, Carpenter, & Franke, 1995; Silver & Stein, 1996). A similar argument can be made for teachers' understanding of students' cultural backgrounds. For example, Knapp (1995) found that many teachers in high-poverty schools who placed the greatest emphasis on meaning in mathematics instruction treated cultural background as a resource for learning. More explicitly, the teachers were able to sustain students' engagement with academic work and link students' world of experience to the world of school-based learning. The nexus of subject matter and the learner provides a starting point for our discussion of equity, mathematics instruction, and the reflection process.