With the advent of reform-based curricula and recommendations related to the teaching of mathematics from the National Council of Teachers of Mathematics (NCTM, 2000), teachers need access to ongoing professional development which models ways in which teachers are now asked to teach (Ball & Cohen, 1999; M.S. Smith, 2001). An extended professional development program was implemented with teachers of grades 3 through 5. This program sought to model reform-based teaching techniques and advocated hands-on, manipulative based activities for the mathematics classroom. The results of this preliminary qualitative study are presented here. Changes in teacher practice were documented through a Grounded Theory approach to data analysis (Glaser & Strauss, 1967). A framework for identifying stages of teacher change was developed.
Professional development of teachers has long been used as an avenue for imparting new teaching techniques to inservice teachers. With the advent of reform-based curricula and recommendations related to the teaching of mathematics from the National Council of Teachers of Mathematics (NCTM) (2000), teachers need access to ongoing professional development which models ways in which teachers are now asked to teach (Ball & Cohen, 1999; M.S. Smith, 2001). "The professional culture of mathematics education must be transformed and requires extensive changes in teachers' deeply held beliefs, knowledge, and habits of practice" (Kitchen, 2003, p. 3). These changes take place through ongoing professional development. Although the need for teachers to change their practices to be more in line with reform-based ideas and curricula is recognized, little research has investigated the support teachers need to make changes in their practice (Kitchen, 2003). Hoban (2002) states, "clearly we need a new way of thinking about educational change that takes into account the complex nature of teaching, teacher learning, and the change process" (Hoban, 2002, p. 21).
This paper presents the results of a preliminary qualitative study in which an extended professional development program was implemented with teachers of grades 3 through 5 in an effort to effect change in their teaching practices as well as their attitudes toward manipulative use in the classroom. This research study led to the development of stages of teacher change and the identification of perceived barriers to manipulative use in the elementary school classroom. The stages of teacher change will be discussed here. The primary method for investigating the efficacy of this process was Grounded Theory (Glaser & Strauss, 1967), a qualitative research approach which attempts to generate a theoretical framework through data collection and analysis pertaining to the participants' experiences in order to find themes, in this case related to teacher actions in the classroom. Data analyzed included transcripts from teacher interviews and focus groups, informal interviews with the school principal and mathematics specialist, classroom observations of teachers interacting with their students, and anecdotal notes from model teaching experiences.
Content Knowledge of Teachers
In her comparison of United States and Chinese elementary school teachers, Ma (1999) found that the U.S. teachers were lacking in their ability to diagnose children's errors and misconceptions to a degree that intervention could take place on a conceptual level. Many U.S. teachers provided explanations for student misconceptions that were procedural in nature while the Chinese teachers provided both procedural and conceptual explanations of student errors and ways of connecting the misconception. Chinese teachers were often more able to provide multiple representations of mathematical ideas whereas many of the U.S. teachers were only able to provide one or two representations of the same mathematical concepts. Additionally, Cohen, Hill, and Kennedy (2002) found that in order for students to understand particular content, their teachers must also have an understanding of the content. …