Professional Development for Middle School Mathematics Teachers to Help them Respond to NCTM Standards

The Curriculum and Evaluation Standards for School Mathematics were created to promote change in the teaching and learning of mathematics (National Council of Teachers of Mathematics, 1989, p. 2) so that K-12 students would have mathematical power. Although the Standards envision a curriculum reflecting the scope of relevant mathematics and taking advantage of the power of technology, most middle school classrooms remain unchanged from the drill-and-practice classrooms of the 1970s (Niess & Erickson, 1992). Change is coming slowly and unevenly (Garet & Mills, 1995), despite many national group endorsements of the Standards, intensive discussions about reform, and funding of projects to help educators update instruction to reflect the Standards (Edwards, 1994). The Standards were designed to fundamentally restructure how teachers teach mathematics and what they teach (National Council of Teachers of Mathematics, 1989, p. 251). The Standards identify strongly held beliefs of teachers as major barriers to the implementation of such change (National Council of Teachers of Mathematics, 1989). Cooney (1987) agrees that changes the Standards authors envisioned will be difficult to achieve because of the beliefs teachers have about mathematics. He offers the role of authority to help the framing of questions about teachers' beliefs and response to change (Cooney, 1994). A person's orientation toward authority is an important consideration in studying current reform movements in mathematics education. Much research exists that indicates many teachers teach mathematics from a rigid, dualistic view of the world in which every question has an answer from an authority (Brown, Cooney, & Jones, 1990). Studying teacher beliefs about mathematics and their roles as teachers can provide critical information for affecting these beliefs. Such a rigid view is incompatible with the Standards, which require teachers to be reflective and adaptive. Teachers must see the world as contextual and knowledge acquisition as constructivist (Cooney, 1994, p. 628). Numerous researchers (Copes, 1979; Helms, 1989; Kesler, 1985; McGalliard, 1983; Meyerson, 1978; Owens, 1987; Stonewater & Oprea, 1988) have used Perry's theory of intellectual development (Perry, 1970) in studies of mathematics teacher education. Basing his theory on interviews with Harvard students during the 1950s and 1960s, Perry identified a hierarchy of nine positions from which people interpret their world. People move from believing every question has an answer from an authority to realizing that knowledge is a personal structure that all people must build in light of their own experiences. Perry identified a critical point at which individuals move from seeing authority as something or someone out there to seeing authority as an internal agent (Perry, 1970). At this point, teachers move from passively accepting the word of an authority (professor, textbook, NCTM) to accepting themselves as authoritative. Copes (1979) adapted Perry's scheme for his study of conceptions of mathematical knowledge. He condensed the nine positions into four categories. The first is dualism (Perry Levels 1-2) at which a person thinks every question has an answer, every problem has a solution, and an authority is someone who knows these answers. The second state is multiplism (Perry Levels 3-4) at which individuals think all questions have many answers and all individuals have the right to their opinion about which answer is better. The third level is relativism (Perry Levels 5-6) at which persons think all answers are not equally valuable and must be judged by standards such as validity and elegance. The fourth level is commitment (Perry Levels 7- 9) at which individuals realize knowledge is not something out there to be gotten, many decisions involve uncertainty and risk, and all decisions require actively building knowledge via personal experience. The Perry scheme with its key concept of authority provides a lens for understanding how teachers view mathematics and teaching and how they might move from one level to the next. …