Mathematics Communication: Creating Opportunities to Learn
Tate, William, Teaching Children Mathematics
The importance of mathematics communication that builds on the lives and experiences of African American students in urban schools, thereby creating additional opportunities to learn and explore mathematics, is the focus of this article. Carter G. Woodson (1933) argued that mathematics pedagogy built on the African American students' experiences fostered two mathematics learning environments - within the school and outside of school. However, two disciplines with great influence on mathematics education - mathematics and psychology - place significant stress on objectivity and neutrality (Kilpatrick 1992). As a result, school mathematics has been tacitly constructed as a color-blind body of knowledge (Ernest 1991). Often, little consideration is given to the cultural appropriateness of mathematics pedagogy and communication (Secada 1993).
More recently, mathematics textbooks have included pictures of African Americans, and some mathematics textbooks include stories about Africans and African Americans who have contributed to the growth and development of mathematical knowledge. These efforts represent progress and should be encouraged and expanded. Yet these efforts are unlikely to prove sufficient to empower African American students to communicate with mathematics. Connecting the pedagogy of mathematics to the lived realities of African American students is essential to creating optimal opportunities to learn mathematics.
Understanding the Problem
What type of pedagogy must the African American child negotiate to be successful in mathematics education? More traditional mathematics pedagogy places great emphasis on whole-class instruction, with teachers modeling a method of solving a problem and the children listening to the explanation. This instruction is usually followed by having the students work alone on a set of problems from a textbook or worksheet (Stodolsky 1988). The goal of this teacher-directed model of pedagogy is for students to produce correct answers to a set of narrowly defined problems. In elementary schools, many teachers spend as much as 75 percent of mathematics class time on computational skills required to solve these narrowly defined problems (Porter 1989). Porter notes that the lack of attention paid to conceptual understanding, skills, and applications is problematic and should be addressed.
The aforementioned problems are applicable to all students. African American students can face additional barriers. For example, mathematics pedagogy for African American students is hampered by the following conditions of their school experiences: (1) persistent tracking, (2) less access than other students to the best qualified teachers of mathematics, and (3) fewer opportunities to use technology in school mathematics (NSB 1991; Piller 1992). Each of these barriers affects the nature of mathematics communication for the African American student. Ultimately, the African American student is given fewer opportunities to discuss and communicate with higher levels of mathematics (Secada 1992). Generally speaking, the three barriers listed previously are systemic and will require teachers to design strategies to influence schoolwide policy to change them.
Another potential barrier to mathematics communication is more directly connected to a teacher's decisions, that is, to the difficult pedagogical decision making and negotiation required to balance students' "voice" and the teacher's conceptions of appropriate mathematics. The term voice is used in this context to represent the students' efforts to communicate their experiences and traditions within the discourse of school mathematics. Stiff and Harvey (1988) argue that attempts by African American students to interject their voice in mathematics classes are often dismissed as "extraneous" matters. Moreover, the communication process is hindered by a legacy of mathematics instruction that looks to disconnect the learner from the mathematics (Ernest 1991). …