A framework for identifying stages of teacher change resulting from extended mathematics professional development.

Andreasen, Janet B. ; Swan, Bonnie A. ; Dixon, Juli K. 等

Abstract

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.

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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. This content-specific understanding should be a by-product of any professional development program that focuses on how students understand mathematics.

With this understanding that U.S. teachers are lacking what Ma (1999) referred to as profound understanding of fundamental mathematics (PUFM), professional development should focus on giving teachers opportunities to develop both their own pedagogical content knowledge and PUFM. This can be done through professional development opportunities that focus on both content-specific knowledge of the teacher and methods of teaching. Focusing on the content that the teachers should know conceptually, including that which is above the levels they are teaching, should help to develop deeper content knowledge. An additional focus on methods and strategies for teaching along with common student misconceptions and error patterns (Ashlock, 2005) should help to improve the teacher's pedagogical content knowledge.

"Teaching necessarily begins with a teacher's understanding of what this to be learned and how it is to be taught" (Shulman, 1987, p. 7). Since the late 1980s, efforts have been made to define the type of mathematical knowledge required for teaching mathematics at various levels. Shulman (1986) began the efforts to make a distinction between general knowledge of content and what he termed pedagogical content knowledge--that knowledge of student misconceptions, typical errors, multiple representations effective in teaching, and familiarity with topics children find interesting or difficult. Further research into the field of mathematics with regards to pedagogical content knowledge has shown that what teachers of mathematics needed to understand about the mathematics being taught in their classrooms was substantially different from the mathematics the everyday person needed to understand (Ball, 1990a, 1991; Leinhardt & Smith, 1985).

Professional Development Standards

Professional development in practice takes on many different forms--from one-day workshops about specific teaching strategy to extended professional development devoted to increasing teachers' skills and comfort level with the subject area. There is a push by the U.S. Department of Education and the National Science Foundation for the latter of these professional development models to be adopted (National Science Board, 2004). It is believed that extended, long-term professional development is the most effective way of sustaining change in local schools (Cwikla, 2004).

Standards for professional development have been developed by various researchers. Hill (2004) conducted a synthesis of this research and eight standards an practices related to professional development were compiled. These included that high-quality professional development should include the following key aspects:

1. Active or inquiry learning;

2. Examples for classroom practice;

3. Collaboration on the part of the participants;

4. Modeling of effective and relevant pedagogy;

5. Opportunities for reflection, practice, and feedback;

6. A focus on the content involve;

7. A focus on student learning of the content; and

8. Teacher choice and involvement in planning.

In the professional development sessions Hill observed, nearly all that were deemed to be of high quality involved teachers engaging in mathematical activity in similar manners to what their students might be expected to do.

In addition to these professional development standards, the National Council of Teachers of Mathematics (NCTM) advocates that teachers of mathematics must have access to professional development and that the primary focus of professional development for teachers of mathematics should be that of helping teachers teach mathematics to their students using strategies advocate by NCTM in the Standards (NCTM, 2000). NCTM also advocates that professional development programs must emphasize building teacher content knowledge, pedagogical knowledge, and knowledge of student thinking.

Change Process

The most immediate and most significant outcome of any successful professional development program is that of having a positive impact in changing teachers' knowledge and practice (Guskey & Sparks, 2002). According to Joyce and Showers (1988) "teachers can be wonderful learners. They can master just about any kind of teaching strategy or implement almost any technique as long as adequate training is provided" (p. 2). Yet while most teachers have a deep and strong desire to improve teaching and learning, many professional development programs seem unsuccessful at changing teacher practice.

Despite well intentioned efforts to provide professional development, only about half (52%) of teachers from Title I schools sampled by the National Longitudinal Survey of Schools (NLSS) who received training in a given content area said that professional development led them to change their teaching practices. About 4% reported professional development had little or no impact; and 44% reported it confirmed what they already did (Kirby, Naftel, McCombs, Berends, & Murray, 2003). The NLSS report also showed that professional development was likely to result in changing teacher practice when it was sustained, intensive, and promoted a coherence in the teachers' professional development (Garet et al., 1999; Garet, Porter, Desimone, Birman, & Yoon, 2001; Kirby et al., 2003; Parsad, 2001).

One model for teacher change, introduced by Guskey (1986), suggests that significant change in teachers' beliefs and attitudes is likely to take place only after a teacher has experimented and evidenced changes in student learning outcomes. In other words, "the model implies that change in teachers' beliefs and attitudes is primarily a result, rather than a cause, of change in the learning outcomes of students" (Guskey, 1986, p. 9). This intrinsic goal of helping students learn and meet achievement goals is well cited (Goodlad, 1984; Leithwood, Jantzi, & Aitken, 1999; Lortie, 1975).

Guskey's (1986) model of the teacher change process is illustrated by outcomes listed in the following order: (a) staff development, (b) change in teachers' classroom practices, (c) change in student learning outcomes, and, (d) change in teachers' beliefs. He supports his model with the work of Bolster (1983), who suggested that efforts to improve education will likely be unsuccessful unless they encompass the idea that a teacher's knowledge of teaching is validated practically with verification. Without that validation, change is not likely to occur. This idea was also supported by Crandall (1983). Stemming from his model, Guskey suggests three guiding principals essential to planning effective professional development programs: (a) recognize that change is a gradual and difficult process for teachers, (b) ensure that teachers receive regular feedback on student learning progress; and, (c) provide continued support and follow-up after the initial training.

Resistance to change is a large part of the gap between knowledge and practice, and between vision and reality. In an article published in the Journal of Staff Development, Janas (1998) explains that "resistance is not always an negative force" and that durability and complexity of managing resistance, can be met with a proactive approach by staff development organizer. Janas cites three strategies for combating resistance to change: (a) being aware of resistance--knowing that it is a fearful response to change and a natural part of any change process, (b) identifying sources and types of resistance--knowing that it is a normal and valued function of existence; and (c) developing strategies to minimizing resistance before it evolves into a barrier to progress. These strategies can help teachers to realize that professional development is not something that is done "to them" but "with them".

Methodology

The design of the study was qualitative in nature and focused on the following research question:

 In what ways can inservice elementary school teachers' practices
 change throughout participation in an extended mathematics
 professional development program?

Sources of data included audio tapes of the pre- and post-teacher interviews and three focus groups; field notes from classroom observations; anecdotal notes from model teaching; and anecdotal notes of conversations with participants, the principal and the mathematics specialist. Data analysis focused on using a Grounded Theory approach to find themes related to teacher attitudes and use of manipulatives in the classroom (Glaser & Strauss, 1967).

School Setting

The study took place at an urban public elementary school in central Florida. The principal of the school had recognized the need for mathematics professional development and had approached the university faculty in the fall. According to state-wide standardized test results, 34% of third graders, 35% of fourth graders, and 24% of fifth graders at the school were at or above grade level in mathematics. This was below the state average at all levels. The elementary school had thirty-five classroom teachers, a support staff of four teachers, and three special area teachers. Student enrollment was 619 students. Twenty-eight percent were African American, 35.8% were Caucasian, 34.2% were Hispanic, and 0.9% were Asian. The children were from predominantly low- to middle-income urban families. Approximately 80% of the students were eligible for free-and-reduced lunch, making the school eligible for Title I funding.

Participants

Participants in this study were nine elementary public school teachers of grades three through five who participated in a series of professional development workshops related to mathematics instruction in elementary school. The workshops focused on improving the content-specific knowledge of the teachers as well as providing activities that could be taken back to classrooms in an effort to improve students' understanding of the mathematics. Nearly all activities used manipulatives in some manner. The participating teachers included seven females and two males with a range of two years to over 25 years of teaching experience (See Table 1).

Research Team

The research team consisted of two doctoral students in mathematics education and one mathematics education faculty from a local university. The faculty member provided guidance and assistance in planning the professional development workshops and facilitated one workshop. The doctoral students facilitated the remaining workshops which met alternating Fridays from January through April of 2004. Each member of the research team was involved in all phases of the project.

Procedures

The professional development program was scheduled for January through April 2004 during teachers' paid time. Prior to the first workshop, all participating teachers were interviewed. Individual interviews were scheduled at the teacher's convenience so as not to interfere with teaching duties. Prior to asking the interview questions, each teacher was presented with a short introduction and description of the study. They were told that in addition to pre- and post-interviews, they would be observed in their classrooms, and asked to participate in several focus groups. Ten teachers agreed to participate in the study; however, one teacher did not complete the professional development. The interview consisted of the following questions:

1. What does a typical day in your classroom look like as it relates to mathematics?

2. What is your specific use of manipulatives in the classroom?

3. How would you describe your typical teaching style?

The interviews were audio taped and later transcribed.

Six all-day workshops followed over a period of three months during the teachers regularly scheduled workdays. Three of the sessions began with an informal focus group which was audio taped and later transcribed. During these focus groups, participants had the opportunity to reflect on and discuss their feelings and experiences about the use of manipulatives and the topics that had been covered in previous workshops. Four or five of the focus group questions were asked in each session with all of the questions being used at least once in the three focus groups. Teachers willingly participated, although, not all teachers were present for all the focus groups due to time constraints and outside factors. The questions included:

1. In what ways has your use of manipulatives influenced your effectiveness as a teacher?

2. After your attempts to integrate manipulatives into your classroom, what things have you learned on your own? What things would you do differently?

3. What specific activities have been occurring in your classroom related to manipulative use?

4. What barriers do you see in implementing manipulative use into your classroom?

5. Do you think manipulatives can be used to complement the curriculum you teach? If so, in what ways? If not, why?

6. In what ways has your view of teaching changed as a result of this professional development?

7. In what ways have you seen changes in your students as a result of this professional development?

The number of teachers at each focus group ranged from 5 to 9. At the first focus group, questions 2, 4, and 5 were used. At the second focus group, questions 3 and 5 were asked. At the third and final focus group, questions 1, 6, and 7 were asked. Questions six and seven were only asked at the final focus group to ascertain changes in views of teaching and/or in student behavior or achievement as a result of the professional development project.

Professional Development Sessions

Each workshop focused on a different standard based on the recommendations of the National Council of Teachers of Mathematics (NCTM, 2000). Activities were selected based on needs of the teachers and students at the school, availability of manipulatives, and the effort to improve individual teacher's content-specific knowledge and pedagogical content knowledge related to mathematics. Some activities were designed to take back and implement in the classroom while others were designed to challenge teachers' mathematical thinking. Different manipulatives were used in the course of the professional development including, but not limited to, pattern blocks, Cruisenaires[R] rods, two-color counters, base-ten blocks, Unifix[R] cubes, and fraction circles. Children's literature connections were used in each workshop as requested by the teachers.

All the sessions incorporated hands-on activities and teachers were encouraged to work with one another in small groups. The introductory workshop focused on problem solving in an attempt to cause the teachers to think about the mathematics they teacher in different ways. Additionally, there were activities using base-ten blocks to multiply and divide whole numbers. Teacher input into future workshop sessions was also gathered at this time and incorporated into later workshops.

The second session focused on number sense and operation. This session included using base-ten blocks for addition and subtraction, comparing whole numbers with place value, finding patterns on the hundreds chart, and an analysis of student error patterns in whole number computation.

The third session focused on fractions. Since the participants were teaching grades 3-5, fractions were a tremendously important concept. The teachers requested an entire session devoted to fractions and this included finding least common multiples and greatest common factor using Cuisenaire[R] rods, representing various fractions on the geoboard, making fraction kits out of construction paper, and looking at area, set, and linear models of fractions.

The fourth session focused on algebraic thinking. This included an emphasis on developing and generalizing patterns, logical reasoning, Handson Equations[R] (Borenson, 1997), and using the graphing calculator and motion detection to reproduce various types of graphs (Hogan, 2001). Patterns included both repeating and growing patterns and the generalizations of each.

The fifth session focused on measurement. This included an extended time of conducting a Mini-Measurement Olympics (Campopiano, 1987) with the metric system, discovering relationship between areas and volumes of geometric shapes and solids, finding time using a "one-handed clock" (P. E. Smith, 1987), counting money, and making change.

The final session dealt with probability and statistics including predictions, area models for probability, experimental versus theoretical probabilities, and games of chance versus games of choice. This session ended with measurement activities that were remaining from session five.

Classroom Observations

Observations were conducted in each participant's classroom once or twice during the course of the project. Most of the observations were conducted during the last half of the project. The participants were aware that the observation was to take place and they were scheduled at the convenience of the teachers. It appeared that some teachers had planned special lessons for the observations while others planned lessons they would have taught regardless of the observation. Several teachers indicated that they designed the feedback of the researchers related to the observations, while others were not as interested in gaining feedback from an outside observer. Field notes were taken throughout the observation and the research team members met regarding the observations. The classroom observations provided validation of the conclusions made from the transcripts of interviews and focus groups.

Model Teaching

One model teaching session was conducted in each participant's classroom toward the conclusion of the professional development project. Teachers had a choice of how involved they became in the process with some teachers actively involved and others just observing. Much of this time was spent with students working in small groups using different hands-on tools. Fourth- and fifth-grade students explored the relationship between fractions and percents using transparent hundred grids, beads, and paper plates. Third grade students investigated probability with a game involving graphing the results of fair and unfair spinners and then predicting from the graph which spinner was used. The sessions were approximately one hour in length. The focus of the model teaching included demonstrating good questioning of students to lead them to discover and share various solutions to complex problems as well as demonstrating how manipulatives could be used to assist in teaching mathematical concepts and encouraging students to construct their own knowledge. Questioning techniques included asking leading questions to elicit student response and incorporating higher order questions. Students were asked to explain their thinking and provide ways for their classmates to understand the mathematics that was being addressed. During the professional development sessions, time had been devoted to discussing error patterns common to elementary school students and the importance of recognizing student errors.

Post-Interviews

At the conclusion of the professional development project, the participants were again interviewed to ascertain their belief and attitudes and to determine any changes that may have occurred during the professional development. The questions asked were identical to the pre-interview with the addition of the following question:

How has your teaching practice changed as a result of this professional development?

Data Analysis

To determine what changes, if any, in teacher practice and attitude related to manipulative use occurred during the training, as well as frequency of use, the data were analyzed using an objectivist approach to Grounded Theory (Glaser & Strauss, 1967). Data were in the form of transcripts from nine pre- and post-interviews, and three focus groups-one at the beginning of the series of workshops, one at the midway point, and another at the end. Other data came from field notes of classroom observations and anecdotal notes taken from informal conversations, Anecdotal notes from model teaching experiences were also examined. All transcripts were analyzed for emerging themes using a constant comparison analysis of the data where transcripts were read-and-reread and grouped-and-regrouped to determine the emerging themes (Glaser & Strauss, 1967). Field notes from classroom observations and anecdotal notes from model teaching were used to verify and validate the themes found in the interviews and focus groups. Themes related to the stages which teachers progress through in changing practice emerged from the data.

Stages in changing practice

This study revealed that teachers may progress through specific stages in making changes in their practice including a resistance to change, talking about changing practice, mimicking, and then actually changing a practice.

The first stage teachers encountered was a resistance to changing practice. Teachers were opposed to making changes to their teaching practices, particularly those who had been teaching for many years. The teachers were comfortable with the way they had been teaching and were slow to change those practices (Thompson, 1992). For example, John said "so it's a gradual process, and sometimes we dig our heels in, but it's something we have to change with the tides, I guess." Joan said about her typical classroom teaching style, that "when [students are] learning a new idea or concept, or it's a new chapter that we're starting, I want everyone focused and in tuned to what I'm giving as far as direct instruction." Interestingly, this statement occurred immediately after talking about the need for hands-on materials in teaching mathematics. Joan, like many others, desired to teach "her way" which resulted in little opportunity for students to experience hands-on mathematics instruction. She was willing to use manipulatives, but only after she had instructed the class directly and only if her students used them in certain ways. Manipulatives were not used for exploration or learning new material. This was evidenced in the model teaching in her classroom as well. Her students were reluctant to use manipulatives to express their opinion and she was a passive observer in the classroom.

The second stage that emerged was beginning to talk about changing practice, without evidence in their classroom. In this stage, teachers' perceptions of their practice began to change. They started talking about what "they might do" in the future. Joan's plans were representative of other teachers as they entered this stage when she said, "Hopefully next year, I'll be able to sit down with my team and kind of plan out how we're going to use the manipulatives." The teachers began to talk about the steps they were taking to begin to make changes in their practice. Beth indicated "I'm exploring things a little bit more," but the implementation in her classroom was lagging behind. Perhaps part of this was due to the desire to be the expert in the classroom and not being willing to try new ideas until they reach that expert level. Joan illustrated this desire when she said, "I want to be able to understand it for myself before I try to teach them." It was evident from classroom observations that some teachers were talking about changing but their teaching methods were not reflecting this change.

The third stage which emerged was that of mimicking. The teachers began to use the activities exactly as they had done in the workshops. At this stage, they were not willing or able to find or invent new ideas or activities and copied what was done in the workshops exactly as it was presented to them. For example, Sarah reported that she "started using your loops and beans" and Joan had the feeling that "it's important to get the activity that you presented us along with a handout so we can go back and see how these manipulatives were used." She was relying completely on what was given in the workshop and not modifying it or expanding on it in any way. She wanted to be completely prepared for anything students might do in the classroom through these activities, and wanted "anything else that you can give us--you know, get the lessons together, along with the manipulative, and know how you're going to use them beforehand." Some teachers reported using manipulatives that they had not used before due to the workshop. Steve, a second year teacher, reported using "base-ten blocks for the first time in my entire career as a result of using them [in the workshops]." Most, but not all, of the teachers reached the mimicking stage through the process of participating in the professional development project. Classroom observations validated this in that some teachers mimicked activities from the workshops for the observations. Many of these teachers were passive observers for the model teaching experience.

The final stage that emerged was that of actually changing practice where teachers took what they learned and applied it in their classroom with their students. They did more than just repeat activities given in the workshops. There was evidence that they found and/or developed their own lessons that incorporated the philosophy of teaching advocated in the professional development experience. Only two teachers in this study reached this stage. Those teachers began to realize that the ways in which they had taught in the past were not always effective and began to change some of their practices. Sue reported that "before ... I used the materials, I held the materials (primarily for demonstration purposes]. Now ... I put forth more of an effort to find enough for my kids; and before, if I didn't have enough pattern blocks, I modeled on the board because our school didn't have plenty of manipulatives. But now I find a way to make paper pattern blocks or ... to find ways to bring it into the classroom I guess. But before I wasn't like that." She began to find ways to get the materials into the students' hands and began to make the time to ensure that her students had what they needed for the lessons she had planned. Observations of these two teachers in their classrooms validated this stage and they were willing and active participants in the modeling teaching experiences.

Conclusions

Through the process of this professional development project, a descriptive model for the progression of teacher change was developed. It was found that teachers may progress through at least four stages in making changes in their practice. These stages included:

1. Resistance to change -- Teachers in this stage are opposed to making changes to their teaching practices. These teachers are comfortable doing things "the way they have always been done."

2. Talking about changing practice -- Teachers perceptions in this stage are beginning to change. They are beginning to talk about what they "might do" and seem willing try out new ideas however little or no evidence exists to show any change has actually occurred in their teaching practice. Here it is difficult to ascertain whether these teachers are just trying to impress their peers or if they are genuine in their desire to adopt a new way of teaching.

3. Mimicking -- Evidence showed teachers were using materials and activities that they had been introduced to the professional development; however, few if any modifications were made and little was done to expand on what they had learned.

4. Changing Practice -- In this last stage teachers take what they learn and apply it in their classroom with their students. Here there is evidence that they have found and have developed their own lessons that incorporated change.

The teachers in this study were found to be at varying places along this progression. Many bridged the gap to a new stage as a result of the professional development study. Most teachers were at least to the mimicking stage by the end of the project. Two teachers reached the stage of actually changing practice; however, there was some evidence that changes were beginning to take place before the professional development began.

In discussing professional development with the teachers involved and examining their feedback from the various sessions, it was found that professional development interventions should include experiences to help teachers to bridge for their students and themselves the transition from concrete representation of ideas, as in the case with hands-on manipulative-based lessons, to the more abstract. Many of the teachers were willing to start to make changes, but lacked the pedagogical content knowledge required to effectively bridge the gap from the concrete to the abstract for their students. They were often unable to bridge that gap for themselves. The professional development experience needed a more concerted effort to help the teachers to bridge that gap. The teachers not only needed to understand the necessity of transitioning from concrete to abstract for their students (Van de Walle, 2004), they needed to be exposed to examples of activities that bridge that gap. Since many teachers seemed to be at the mimicking stage of making changes, these activities are necessary to help them to see the need to make those transitions. Without the example to follow, many teachers were caught in a paradox of wanting to implement more hands-on, manipulative-based activities but now knowing how to help the students to see the connections to the abstract mathematics they were required to understand (Ball & Cohen, 1999; Hoban, 2002).

In summary, with regard to these stages, almost all of the teachers by the end of the semester were either talking about changing practice or were in the mimicking stage. In the focus groups and the interviews at the end of the project all the teachers gave the impression that they were doing things differently but in reality very little evidence existed to support anything past the mimicking stage. It was difficult to ascertain why the teachers did not progress further. It was also difficult to determine just how much of this was due to the common perception of a "lack of planning time." In the end, only two of the teachers reached the stage of changing practice where they began to develop and investigate their own ideas to further their own and their students' experiences with hands-on learning that incorporated the philosophy of teaching advocated in the professional development. Further research with more participants and at varying sites is needed to substantiate this model.

Professional development should address these issues and the stages of teacher change can be informative in planning for professional development experiences. The implications of this model include the ability to design professional development workshops to facilitate teachers moving past the mimicking stage into actually changing practice. Professional development needs to include more opportunity for developing individualized and personalized lessons. Further research into the efficacy of this type of professional development is needed. Model teaching proved effective in some classrooms, but not all. Perhaps a better route is a co-teaching or coaching model in which the teacher is forced to be an active participant in the planning, implementation, and evaluation of lessons (Stein, Smith, Henningsen, & Silver, 2000). Extended, effective professional development is necessary and important for the future of mathematics teaching and learning and models of teacher change are necessary to inform the planning and implementation of these professional development experiences.

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Janet B. Andreasen, Bonnie A. Swan, & Juli K. Dixon

University of Central Florida, Orlando, Florida

Table 1. Participant Years of Experience and Grade Level Taught
(2004-05)

Name Number of Years Experience Grade Level Taught

John 27 Third
Joan 14 Fifth
Beth 9 Fifth
Sue** 8 Fourth
Kim 7 Fourth
Jessica 7 Third
Rebecca 5 Third
Sarah 3 Third
Steve 2 Fifth

*All names in this study have been changed to preserve anonymity.
**This teacher was also participating in a master's degree program that
focused on reform-based teaching practices.