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Metaphors Frame Classroom Cultures That Can Empower Students

The having of wonderful ideas is ... the essence of intellectual development. And ... the essence of pedagogy [is] to give ... the occasion to have ... wonderful ideas. (Duckworth, 1987, p 1.) A substantial number of educational studies have on how teacher beliefs about cultural and curricular issues influence educational practice (e.g., Carr & Kemmis, 1986; Bishop, 1991; Saxe, 1991). In particular, Bishop (1991) said culture is a "powerful stimulant for educational thinking" (p. 4). But what are important components embedded in any study of school culture? Is culture about the students and teachers, or does it pertain only to their beliefs? Is it about the society, the school system, or the classroom? Bishop addressed these questions by asserting that "culture consists of a complex of shared understandings [that] serves as a medium through which individual human minds interact in communication with one another" (p. 5). What are important foci for teachers, textbook authors, or researchers interested in curriculum? Carr and Kemmis (1986) identified aspects of curriculum that range from specific acts of teaching and learning to programs across entire school years. Frameworks for curricular study can be found in materials, in educational policies and practices, and in historical circumstances. The purpose of this article is to probe teacher beliefs about the cultures and curricula of mathematics classrooms. By examining the case of a teacher in New York City - his teaching practices and the resulting learning environment fostered there - certain pedagogical and epistemological beliefs can be highlighted. We explore what we mean by the "culture of a classroom" by applying Lakoff and Johnson's (1980) framework for metaphorical reasoning. But, before we consider the relationship between culture and metaphor, let us examine some polar beliefs concerning teaching and learning middle school mathematics. Beliefs Bishop (1991), discussing social aspects of mathematics education, poignantly stated the ramifications of student and teacher interactions in the classroom: At the pedagogical level, the social influences on the child's mathematical education are more easily identified with the teacher and the rest of the classroom group. The teacher and the group mould, in interaction, the values [that] the child will receive concerning mathematics. Through activities, with reinforcement and negotiation, the child becomes enculturated into ways of thinking, behaving, feeling and valuing. A "mathematics classroom" is already defined in such a way that only certain kinds of activities are possible and, therefore, certain kinds of values developed. (p. 15) From Bishop's cultural perspective on mathematics instruction and implied beliefs, the techniquesoriented curriculum is problematic. Teachers viewing mathematics education through this lens see children learning mathematics through the mastery of techniques and memorization of formulas and algorithms. Progress is measured by an accumulation of correct answers on time-constrained tests on which students are expected to demonstrate their catalogs of formulas and rules; correct answers are emphasized. "Associations are strengthened through repetition with prompt reinforcement of correct responses and the extinction of 'wrong' responses" (Wheatley, 1991, p. 14). Middle school teacher William Mack (a pseudonym) described an alternative to this techniques-oriented classroom environment for teaching and learning mathematics. In describing a cooperative, problem-solving learning environment, he speaks of creating an atmosphere in which making mistakes is part of the learning process. A critical component of children's learning is the responsibility they all share in helping each other in their learning groups. To learn to work together, they have to be taught group skills. In the culture of this classroom, children are not graded for correct answers alone. …