THE NATURE OF TEACHER CHANGE AND ITS LESSONS FOR THE EVAULATION OF INNOVATIVE EFFORTS IN THE TWENTY-FIRST CENTURY
Barbara S. Edwards
Oregon State University
Abstract: This paper reports the results of a five-year study of teacher change among calculus teachers at both the high school and college level and discusses the implications of these results on future evaluations of professional development efforts. The fact that change occurs in steps and over time implies that the evaluation of change should be longitudinal and employ a variety of assessment instruments.
The purpose of this paper is to report the results of a research project that began in 1993 as an evaluation of the National Science Foundation (NSF) sponsored Calculus Reform Workshops and grew into a longitudinal study of teacher change at the high school and college level. This paper reports the results of that study and the implications that those results and the methodology of the study have for evaluation of educational change in the twenty-first century.
Theoretical Framework and
Literature
This study is grounded in certain beliefs of the researcher in the relationship between teacher change and learning and in how change/learning occurs. In terms of learning, the researcher believes that the mathematical understanding an individual creates is dependent upon that individual’s point of view and his or her previous knowledge. Thus the creation of understanding has both social and cognitive aspects (Carlson, 1997). Teacher change involves a learning process – a development of each individual’s pedagogical understanding – with both social and cognitive aspects. Certain cognitive requisites for change are indicated (Shaw & Jakubowski, 1991); and social aspects exist since negotiating these cognitive steps may be enhanced by outside support (Wasley, Nonmoyer, & Maxwell, 1995). Although all change efforts seem to involve certain recognizable steps, the pedagogical results are not necessarily the same from one individual to the next. What reform looks like in any given classroom is dependent upon several personal factors among which are a teacher’s past experiences and beliefs (Cohen ,1990; Drake & Hufferd-Ackles, 1999), and his or her knowledge of mathematics and pedagogy (Lloyd & Wilson, 1998).
Cohen (1990) recounts the innovative efforts of Mrs. Oublier, a second grade teacher who had spent her early teaching career teaching mathematics in a very traditional way of memorized facts and procedures. Then she attended a workshop that, in her view, completely changed her ideas about the teaching of mathematics. From the researcher’s perspective, however, the change was much less profound. Cohen saw her teaching as a complicated blend of her traditional ways and the new ideas. One possible explanation for this might be in the research of Bright, Bowman, and Vacc (1998) who found that pedagogical changes, especially those of the magnitude that Mrs. Oublier was attempting, might require teachers to go through “phases” involving intermediate steps. “The jump from ‘teacher as teller’ to ‘teacher as active participant in a community of learners’ may be too great for many teachers to make directly. Rather, there are intermediate behaviors and beliefs that may have to serve as a bridge (p. 610).”
This paper concerns calculus instructors who were being encouraged to negotiate a “jump” in their pedagogical practice. The researcher’s theoretical beliefs about teacher change and evidence from previous research indicated the need for an investigation that would be longitudinal and primarily qualitative in nature.
Methods
The participants of this study were drawn from a pool of over 800 participants in the NSF sponsored Calculus Reform Workshops. A fundamental goal of that project was the dissemination of calculus reform through several six-day workshops held during the summer of 1993 through the summer of 1997. The workshops were facilitated by leaders in the development of calculus reform curricula and were attended by an even mix of calculus instructors from high schools, two-year colleges, four-year colleges and universities. Motivation for attending the workshops varied among participants from curiosity about the new approaches in calculus to a determination to learn how to teach in a reformed manner. All participants (except those in 1993) were asked to complete pre-workshop questionnaires. In February of the year following each summer’s workshops all participants were sent post-workshop questionnaires. The return of these post-workshop questionnaires over the life of the project was approximately 50%. In the post-workshop questionnaires volunteers were solicited for 30-60 minute telephone interviews which were conducted in May and June of 1994-1996. Twenty-five participants were interviewed in 1994; twenty participants were interviewed in 1995; and twenty were interviewed in 1996. In addition there were follow-up interviews of the 1993 participants in 1995 and 1996, and follow-up interviews of the 1994 participants in 1996.
The pre- and post-workshop questionnaires contained Likert-scale and short-answer questions about the participants’ use of technology, writing, small-group work, projects and alternative forms of assessment in the teaching of calculus both before and after the workshop, as well as questions about their goals for themselves and their students. The purpose of the initial telephone interviews was to investigate in some depth their answers on the questionnaires. The purpose of the follow-up telephone interviews was to investigate individual change over more than one academic year.
The researcher repeatedly listened to and partially transcribed each of the telephone interviews, and, with the information from the questionnaires, a story of each participant was created. The collection of stories was then analyzed to reveal certain dominant themes. The researcher then looked for any evidence in the data that would contradict these themes, and the results of the study emerged from this final analysis.
Results
Over 90 percent of the participants viewed the workshops as extremely successful in demonstrating calculus reform in action. Most of these participants left the workshops excited and determined to implement reform in their classrooms at some level. Each year, by the spring following the summer workshop, a smaller number, but over fifty percent, of the participants reported trying something new. Many reported decreasing the amount of time spent lecturing in class, or emphasizing the use of multiple representations of functions, or introducing the use of calculators, writing or projects to their students. However, there was evidence confirming earlier research findings, that a strong desire to change does not by itself ensure a successful innovative effort. Not all participants were able to implement some aspect of calculus reform in their classrooms and some of those who did not achieve success after one attempt abandoned the idea of reform all together.
Among those participants interviewed more than once, if an attempted change was viewed as successful in the first year that change continued or evolved into something else the next year. One two-year college teacher reported assigning a group writing project to her students during the first year and expanded it to a greater use of cooperative learning groups during the following year both inside and outside of class. The notion of intermediate steps or bridges is evident in one teacher’s story. He began by doing demonstrations on a graphing calculator during his lectures and evolved the next year into having his students work with the calculators on their own and even sometimes demonstrate their results before the class.
The tendency to make incremental small changes over time may be advisable. One four-year college instructor made monumental changes during the first year after attending a workshop – even in the eyes of this observer. However, in the telephone interview following his second year, he reported being tired and somewhat discouraged. Teaching in this new way was a lot of work – for instructor as well as students – and the number of students taking his calculus courses had decreased. On the day of the interview he said that he was questioning the new pedagogy and considering returning in large part to his “old ways.” Over the intervening summer, however, he reconsidered and although he made some alterations, he reported at the end of the third year that he was continuing as a “reformed” calculus instructor.
In all cases, participants who were most successful in their change efforts had some outside support. Often this was in the form of colleagues who were also involved in reform. Many of these participants went to other workshops on some aspect of reform or encouraged their colleagues to attend such workshops.
Less than ten percent of the participants claimed to have changed their goals for the teaching of calculus even in instances when the stated goals of the participant seemed to conflict with the innovations they were trying to implement. The discussion of goals and an invitation to reflect on this issue was an emphasis of the workshop organizers, yet few of the participants seemed to remember this or to have considered it. This result should be of interest to future authors of innovation because a conflict between an instructor’s goals and an innovator’s goals could lead to unfocused or paradoxical innovative efforts in the classroom.
Discussion
This study provides lessons for future evaluations of efforts designed to encourage teacher change. First, it seems advisable to collect data at several points during the change effort and over an extended period of time. Longitudinal data collection in this study demonstrated the on-going, non-monotonic nature of change. It takes time and is incremental, thus being able to observe the change at different stages is informative.
Not only the timing of data collection but the type of data collected is important. Relying on Likert scale or even short-answer questions to evaluate change may give a deceptive view of the success. Although this study was primarily qualitative in nature, the researcher did a quantitative comparison between participants’ answers on similar questions in the Likert scale format, the short answer format, and the interview format. There was a striking contrast in the degree to which change was reported depending upon the question format. In comparable areas, participants reported a much higher degree of change in the Likert scale questions than they did in the short-answer questions and the short-answer questions indicated more change than the telephone interviews.
This phenomenon may be related to the tendency reported by Cohen (1990) for the individual involved in the change effort to perceive a more profound degree of change than an observer perceives. This aspect of the analysis of teacher change by an outside observer/researcher leads to an important question. From whose point of view should change be analyzed – the teacher’s, the researcher’s, or a combination of the two? Although it is important to have a rubric of some kind from which to approach the evaluation of any change effort, it seems that something is lost if there must be a “right answer.” It seems that a much richer story can be told if the change is described in a way that comes from an analysis based on a combination of teacher and researcher viewpoints.
References
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Carlson, R. A. (1997). Experienced Cognition. Laurence Erlbaum.
Cohen, D.K. (1990). A revolution in one classroom: The case of Mrs. Oublier. Educational Evaluation and Policy Analysis, 12, 327-345.
Drake, C. & Hufferd-Ackles, K.. (1999). Living math histories: The influence of teachers’ prior math experiences on their implementation of a reform math curriculum. . In S. Berenson et al., Proceedings of the Twentieth annual Meeting of the Psychology of Mathematics Education-North American Chapter, Vol. 2 (pp. 709-715). Columbus, Ohio: ERIC.
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Yackel, E. (1995). Children's talk in inquiry mathematics classrooms. In Cobb, P. & Bauersfeld, H. (Eds.), The emergence of mathematical meaning (pp. 131-162). Hillsdale, NJ: Lawrence Erlbaum.
Wasley, P., Donmoyer, R. & Maxwell, L. (1995). Navigating change in high school science and mathematics: Lessons teachers taught us. Theory into Practice, 34(1), 51-59.