The research report investigates connections between five 3rd garde students (one African American boy, one African American girl, one Caucasian girl, one Asian boy, and one Middle Eastern boy) belief, attitudes, and practices about mathematics and their parents' expectations. In addition, the study examines the relationships between the social interaction of these five students on mathematics learning and their mathematical dispositions. In search of a viable understanding of the above situations, constructivist inquiry was used. In this paper we discuss students' attitudes and beliefs towards themselves and towards mathematics, parents' expectations, classroom social norms and sociomathematical norms, and the teacher's role for establishing classroom culture.
Culture, Social Interaction, and Mathematics Learning***
In any culture, people share language, place, traditions, and ways or organizing, interpreting, conceptualizing, and giving meaning to their physical and social world. National Council of Teachers of Mathematics (NCTM, 2001a) acknowledges the importance of culturally relevant mathematics by stating that "social condition, social tradition or culture, and social goals influence student learning ... However, a student's social traditions or culture may either coincide or conflict with classroom norms for student activity, student conduct, and student-teacher interactions" (p. 7). In the case of conflict between a student's culture and classroom social norms, the student may or may not accept the classroom social norms and may or may not be able to adapt to the school environment. Therefore, that conflict may impact the student's learning mathematics. On the other hand, a sensitive teacher may observe the student's cultural patterns and develop activities that accommodate the student's learning. In this type of situation, the student and the teacher come to a mutual understanding and agreement. NCTM (2000a, 2000b, 2000c; 2001a, 2001b, 2001c) suggests recognizing and valuing students' cultural heritage significantly influences students' mathematical learning.
In this study, we use social interaction to mean norms and values negotiated and established implicitly and/or explicitly by the members of a local community (i.e., teacher, students, and parents). In this sense, understanding students' backgrounds is crucial for mathematics teaching and learning. As D'Ambrosio (2001) observed, "An important component of mathematics education today should be to reaffirm, and in some instances to restore, the cultural dignity of children" (p. 308).
There is a body of research focusing on the notion of ethnomathematics. According to this perspective, contributions made by people from various non-European cultures (i.e. Arabs, Asians, Hispanics, African Americans, etc.) for mathematics advancement have not been given the attention they deserve (Ascher, 1994; Bishop, 1991; D'Ambrosio, 2001; Frankenstein, 1995; Nunes, 1992; Orey & Rosa, 2001; Secada, 1992; Zaslavsky, 1973). Zaslavsky (1973) asserted that the study of ethnomathematics would benefit all students who "learn to respect and appreciate the contributions of peoples in all parts of the world" (p. 309).
This research study focuses on five 3rd grade students' (one African American boy, on African American girl, one Caucasian girl, one Asian boy, and one Middle Eastern boy) beliefs and practices towards mathematics learning as they interacted with each other in problem solving, reasoning, communication, and mathematical representations. In addition, the study explored their parents' beliefs and values about education and attempted to examine the relationship between parents' expectations of their children's mathematics education and students' mathematics learning.
The five students were selected within a larger classroom community of 28 students. They had been working together from the beginning of the school year and were comfortable expressing their feelings and views among themselves. …