Interactions between teacher and student need to be appropriate to the student and the content, regardless of the student’s social class, ethnicity, language, or gender. Effective teachers often make use of their students’ interests to engage them in academic tasks. Effective teachers of urban African American students do so by making use of the culture of their students. They demonstrate an understanding of their students’ backgrounds and experiences, link classroom content to those experiences, use familiar cultural patterns, and focus on the child.33 High expectations for all students without regard to their social class, ethnicity, or gender can also pay high dividends. For example, low-achieving minority students can do as well as other students when placed in more demanding programs.34 Also, in a study of teachers in schools serving children of poverty, higher achievement results were obtained when teachers placed more emphasis on meaning in their mathematics classrooms.35 Because the quality of the interaction of teacher and student around the content is so critical to the success of instruction, the most successful teachers are not merely sensitive to the cultural diversity of their students but use that diversity to enrich the learning experiences they provide to the class as a whole.36

Communities of Learners

Creating classrooms that function as communities of learners has been the focus of much recent research and scholarship in mathematics education.37 In the research on teaching and learning mathematics with understanding, four features of the social culture of the classroom have been identified.38 The first is that ideas and methods are valued. Ideas expressed by any student warrant respect and response and have the potential to contribute to everyone’s learning.

A second feature of a classroom community of learners is that students have autonomy in choosing and sharing their methods of solving problems. Students recognize that many strategies are likely to exist for solving a problem, they respect the methods used by others and that others need to understand their own methods, and they are given the freedom to explore alternatives and to share their thinking with the rest of the class. Notice how Mr. Hernandez has three other students besides Michelle share their solutions to the grid problem. Ms. Kaye has five students present their solution methods. She also engages the class in a discussion of the similarities and differences between the various methods. In contrast, Ms. Lawrence and Mr. Angelo, although they call on students to answer questions, are more

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