Abstract

INTRODUCTION One of the most troubling problems in urban education in the United States today is that African American children, particularly males, have been categorically underserved by public schools. Disproportionately large numbers of African American boys in our nation's inner-city schools are expelled, suspended, relegated to special education programs, and subsequently left with fewer personal resources than their European American peers. Clearly, combination of political, economic, and sociological factors contributes to the inability of teachers, schools, and schools systems to uniformly promote educational success among urban African American children. Part of the problem stems from an insufficient and incomplete knowledge base about these students' development and socialization. Many factors limit the creation of this knowledge base, including the visceral fear of African American males that is fed by demonized images of African American maleness in the popular media, and the general lack of access teacher preparation programs have to pedagogical expertise drawn from the culture, language, and history of African American people. Educators are not likely to develop pedagogical knowledge base of the critical aspects of class and culture for non-mainstream minority-group learners unless theory is developed that addresses how these students make sense of the curriculum in the context of their unique racial, ethnic, cultural, and political identities. More specifically, teachers cannot fully interpret the developmental learning of these students without an analysis and synthesis of the students' experiences with the curriculum and knowledge of how they position themselves in the culture of the classroom. This necessitates that teachers acquire deep understanding of the discourse routines and dynamics of the educational settings these students find themselves in. Developing an understanding of these issues as they relate to African American male students' academic achievement in mathematics is complicated by recent developments in mathematics curricula. A National Council of Teachers of Mathematics' (NCTM) (1989) document entitled Curriculum and Evaluation Standards for School Mathematics presently is transforming the instructional practices and classroom dynamics of mathematics learning in significant and positive ways. These standards emphasize developing learners' abilities to use mathematics in problem solving, reasoning, and communicating by engendering greater emphasis on understanding mathematics concepts than on achieving computational competence. They explicitly promote educational outcomes that include dispositions such as self-confidence in doing mathematics and valuing it as discipline. They further call for instruction that encourages students to: * articulate their reasons for using particular mathematics representation or solution, * summarize the meaning of the data they have collected, * describe how mathematical concepts are related to physical or pictorial models, and * justify arguments using deductive or inductive reasoning. Thus, the NCTM standards influence an important dimension of the classroom culture: the discourse of learning or math talk. Gee (1991) defines discourse as a socially accepted association among ways of using language, of thinking, and of acting that can be used to identify oneself as member of socially meaningful group or 'social network' (p. 3). However, to the degree that many urban African American students do not share mainstream, middle-class perspectives or assumptions about learning and teaching, these students may construct profoundly different subjective worlds than those anticipated by the teachers who teach to these standards (Kochman, 1981). The recent curricular innovations calling for greater emphasis on communication in mathematical reasoning (as articulated in the NCTM standards, for example), together with the fact that most instructional time is based on teacher-initiated talk (Goodlad, 1981), underscore the importance of classroom discourse as the foundation of children's classroom learning. …

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