Teacher
Change in a Reform Calculus Curriculum: Influences on Change
Thomas B. Fox
University of Houston-Clear Lake
Fox@cl.uh.edu
Abstract: One high school calculus teacher was studied
as she first implemented a reform calculus curriculum. Over the course of the year, the teacher
modified her instruction in important ways.
Influences on her change process included internal, external, and
‘first-year challenges’. These influences
included the teacher’s openness to change, her students’ attitudes and beliefs,
the newness of the curriculum to the teacher, and the reform nature of the
calculus curriculum.
In the 1990’s, implementation of reform calculus curricula began on a large-scale basis at many universities. Today many secondary schools are using them. The changes called for in the reform calculus movement parallel those advocated for secondary mathematics in general (National Council of Teachers of Mathematics [NCTM], 2000). Reforms such as these are not easily accomplished, and teachers are the ones who ultimately confront the complex prospect of change in their classrooms. If reform is to take place, more knowledge about the process and psychology of teacher change is needed in order to facilitate it better. The purpose of this research is to describe the influences on one high school calculus teacher’s change process during her first-year implementation of Calculus (Hughes-Hallett et al., 1994) [to be referred to as HC]. Formerly, the teacher used a curriculum authored before the current reform movement (Larson & Hostetler, 1987) [to be referred as LH]. The specific research question addressed here: What factors influenced the change process of one high school teacher as she implemented the HC?
Teacher change often does not take place despite the best efforts of teachers and others involved. Impeding factors can include a curriculum opposed to desired changes, student attitudes and beliefs, teacher reliance on prior modes of instruction, established classroom routines, and the school and its organization (Duffy & Roehler, 1986). This study refers to teacher beliefs as a “teacher’s view or conception of the nature of mathematics, model or view of the nature of mathematics teaching, [and] model or view of the process of learning mathematics” (Ernest, 1989, p. 249). Other factors found to impede teacher change include a lack of teacher knowledge of how to initiate change (Wasley, Donmoyer, & Maxwell, 1995), a lack of teacher familiarity with a new curriculum, and time constraints (Edwards, 1995). Among the factors having been found to positively influence teacher change are a teacher’s sense of self-efficacy, a school atmosphere open to change, and a teacher’s reflection upon the change process as it occurs (Smylie, 1988).
Curricular
materials are also believed to facilitate change: “Because many teachers rely
on textbooks as a core for their teaching, a textbook is a reasonable candidate
for communicating and providing guidance for change” (Ball, 1990, p. 257). The curriculum used by the teacher in this
study aspires to this goal. It is one
of many reform calculus texts commercially available and is often considered a
moderate attempt at reform. For certain
teachers, the use of reform orientated curricular materials has promoted change
(Edwards, 1995). For others, their lack
has been found to impede change (Wasley et al., 1995).
Research Design and
Methodology
This is part of a larger study that examined changes in practice and beliefs of a high school mathematics teacher as she implemented HC. At the time of this study, the teacher had taught mathematics for 13 years during 7 of which she had taught one section of a non-Advanced Placement [AP] calculus course. She was the only calculus teacher in her small, rural, Midwestern high school. The teacher was the main influence on the choice of the HC and expressed a desire to change her instruction. Her first year implementing the HC her class consisted of 10 students. The teacher described these students as “atypical” relative to those she had taught in the past; she believed that they complained more and seemed less studious.
The data were collected as follows. In the summer before implementing the HC, baseline interviews with the teacher were conducted. These interviews focused on teacher beliefs, instructional practices, and on reconstructing her lessons taught from LH. The following school year, data collection included observations of the teacher’s instruction in HC. A total of 52 lessons were observed and videotaped. Detailed narratives of the lessons were constructed. Teacher interviews were also conducted after all observations, before and after each chapter in the HC, and at the end of both semesters. These interviews were audio recorded and transcribed. Artifact collection included teacher lesson notes, student notebooks, and handouts from both curricula.
Qualitative methods were used to analyze the data. Data were analyzed using grounded theory (Strauss & Corbin, 1990). The particular manner in which the data were used is as follows. Field notes, interviews, and written documents were coded. Coding the data helped the researcher find commonalties. Initially, data were Open Coded for rough categorization. During this process, the focus was on mathematics content, teacher actions and beliefs, assessment, technology use, and representations used in instruction. Axial Coding techniques were then used to relate categories and subcategories discovered during Open Coding. Relationships between the different categories were then examined to determine the presence of more abstract concepts that might link less abstract categories (Strauss & Corbin, 1990). Direct comparison of instruction in both curricula was also made. Multiple data sources were used to validate trends in the data.
Results and Conclusions
When compared to her practice in the LH, the teacher, on the surface, maintained a similar mode of instruction in the HC. Her practice consisted of demonstrating prototype examples. However, the teacher was able to change her practice in important ways: (a) an increased focus on conceptual knowledge, (b) the use of graphing calculators to learn calculus, and (c) changes in evaluation that included testing concepts in addition to procedures.
Three
major types of intervening conditions were noted in this teacher’s process of
change: internal, external, and first-year challenges. Among the internal conditions were teacher
beliefs, the teacher’s desire to make students feel comfortable, her open
attitude toward change, and teacher concerns.
External conditions included the HC curriculum, a reform calculus
workshop, her students’ beliefs, and school factors. The first-year challenges primarily related to the newness of the
HC to the teacher and the challenges that this brought to her planning and
classroom teaching.
The teacher’s beliefs were found to influence the ways in which she
planned her lessons and subsequently her instruction. Among the beliefs that influenced her practice were those
regarding how students learn, the importance of reading the text, the role of
the teacher and students, and her beliefs about calculus and its teaching and
learning.
The teacher tended to hold what many would consider ‘traditional’ views of how students learn mathematics: “I think that students learn calculus by coming to class prepared every day, by listening in class to the presentation, by going home and trying their homework on their own." These beliefs, in part, influenced her to plan instruction that consisted primarily of presenting ideas found in the reading and showing students how to solve sample problems.
Another influential belief in this teacher’s change process was a desire to make her students feel more comfortable. This resulted in practices of rarely assigning students homework problems beyond the sample problems solved in class, giving students ‘homework hints’, telling students what types of problems would be found on tests, and carefully guiding students to the solutions of problems covered in class.
The teacher’s open attitude toward change was another internal factor that influenced her change process. This was characterized by her desire to modify her instruction, her choice of the HC text, and the fact that she liked it both during and after her first year using it. Finally, the teacher’s concerns and frustrations were also intervening internal factors. These concerns centered around pacing, students dropping out of the course, and students who were cheating.
Among the external factors that influenced this teacher’s change
process were the HC, a reform calculus workshop, her students, and school
factors. The HC materials were very
influential in the teacher’s change process.
It’s conceptual and technology foci helped the teacher center on them to
a greater degree. The HC’s ancillary
materials were also a very important aid to her in her planning. They influenced not only the sample problems
that she solved in class, but also her homework assignments and the tests she
constructed.
The final type of intervening condition can be best described as
‘first-year challenges’. The most
influential of these related to teacher planning. The newness of the HC to this teacher forced her to spend an
increased amount of time on planning.
She believed that in the first year using a new text, it was more
difficult to know what to focus on in instruction and where students would have
difficulties. This was significant
because it made it difficult for her to determine how long and difficult
student assignments would be and how long it would take to teach the
content. This appeared to influence her
to focus more on day‑to‑day operations and less on long-term goals
for change, such as implementing student projects.
The influences
on this teacher’s change process were diverse and came from various
sources. They impacted it in both
positive and negative ways. When
confronted with the complex environment that is a mathematics classroom,
teachers construct their own ways of creating a learning environment that will
result in student learning. For this
teacher, the three primary influences on her construction were the internal,
external, and ‘first year challenges’ discussed here. The HC was an especially strong influence, and its role in this
teacher’s change process reinforces Ball’s (1990) belief in the positive role
that reform curricula can play in influencing change. The role of this teacher’s students in her change process was
also strong.
Note
This work is part of a doctoral dissertation completed by the author at Illinois State University under the direction of Beverly S. Rich.
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