Models of Curriculum Use

in the Context of Mathematics Education Reform

Miriam Gamoran Sherin Corey Drake

Northwestern University Northwestern University

msherin@northwestern.edu c-drake2@northwestern.edu

Abstract: This paper examines how elementary-school teachers use a reform-based mathematics curriculum. Our analysis identified four processes that together describe the teachers' use of the new materials: (a) reading the curriculum, (b) evaluating the curriculum, (c) adapting the curriculum, and (d) implementing the curriculum. All of the teachers studied engaged with each of the four processes. However, the teachers engaged with these processes in different ways resulting in a number of what we call models of curriculum use. We believe that understanding how and why teachers implement mathematics reform in the ways that they do is a key to promoting more effective curriculum implementation on a large scale.

A central part of teachers' work is to interpret curriculum materials and to decide how to use these materials in the classroom. This process is particularly critical in light of recent reform efforts in mathematics education. While there is a proliferation of reform documents and recommendations, the fact remains that reform often reaches teachers through new curricula that teachers are expected to implement. In addition, teachers' experiences using reform-based curricula can influence their beliefs about reform and their willingness and ability to make changes in their practices.

Despite the importance of curriculum in the reform process, relatively little attention has been paid to trying to understand the ways in which teachers interpret and implement new curricula. Instead, researchers studying the impact of reform-based curricula often focus on improvements in student learning of mathematics. Much less attention has been given to the teacher's role in the implementation process. In contrast, we argue that understanding the process through which teachers use new curricula is critical for the success of mathematics education reform and for designing curricula that support both teachers' and students' needs in this time of change.

In this paper, we explore this issue by examining the process through which elementary-school teachers use a reform-based mathematics curriculum. We investigate how teachers use these new materials and the patterns of use that appear. In addition, we consider the relationship between teachers' curriculum use and their instructional practices. We believe that understanding how and why teachers implement mathematics reform in the ways that they do is a key to promoting more effective curriculum implementation on a large scale.

Curriculum Materials and Teachers' Instructional Practices

Our research is framed by three perspectives concerning the relationship between curriculum materials and teachers' instructional practices. First, policy-makers' decisions about which mathematics curricula to adopt at the state or local level affect teachers' instructional practices (Spillane & Zeuli, 1999). That is, teachers tailor their instruction, to some extent, to the curricular choices of the district within which they teach. At the same time, prior research on teachers' use of curriculum materials supports the notion that there is no such thing as a "teacher-proof" curriculum. While most classroom teachers are guided by a set of published curriculum materials, these materials are not used blindly (Ben-Peretz, 1990).

A second, and more recent, perspective explores the ways in which teachers respond to curriculum materials specifically in the context of mathematics education reform. In particular, researchers find that teachers adapt and revise materials in light of their students, their school, and their own teaching style and goals (Ball & Cohen, 1996). In addition, teachers may transform a novel lesson into a lesson with which they are more familiar, even if in doing so they bypass the intended purpose of the new lesson (Brown & Campione, 1996; Sherin, 1996). However, in other cases, the process of implementing a new lesson or unit provides valuable learning opportunities for the teacher, particularly as students offer novel explanations (Hufferd-Ackles, 1998). One goal of our research is to extend prior studies by examining more closely the kinds of adaptations that teachers make as they implement reform-based curricula.

Third, most of the above work on the relationship between teachers' practices and their use of new curricula has been in the form of case studies of teachers implementing reform (e.g. Cohen, 1990; Wilson, 1990). As a result, teachers' use of reform-based curricula can seem individual and idiosyncratic. In our work, we attempt to move beyond such results by explicitly looking for patterns among teachers' use of reform curricula. We want to understand more fully what influences how teachers use new curricula as well as the process through which curriculum materials are translated into instructional practices.

Research Design

Our research is part of a larger project that is investigating the experiences of teachers piloting the research-based reform mathematics curriculum Children's Math Worlds (Fuson et al., 2000). This paper focuses on six teachers who used the curriculum during the 1998-99 school year. The teachers teach grades one through three and have between one and fifteen years of teaching experience.

The data for this study consist of between 15 and 30 videotaped observations of each teacher's classroom. In addition, post-observation interviews were conducted in which the teachers were asked about their interpretation of the day’s lesson. Half of the teachers also participated in "mathematics story interviews" in which they were asked to describe their previous experiences teaching and learning mathematics, as well as their future plans for mathematics teaching (Drake & Hufferd-Ackles, 1999).

The data were analyzed using an iterative and grounded approach. The interviews were coded in order to identify patterns of curriculum use. These patterns were then confirmed, revised, or disconfirmed based on fine-grained analysis of classroom videotapes. Where appropriate, the identified patterns were revised a second time using the mathematics story interviews.

Results and Conclusions

As expected, none of the teachers simply used the curriculum as written. Instead, the teachers interpreted and transformed the materials as they prepared to teach and then carried out the lesson. In examining how this occurred, we found that the teachers' curriculum use could be characterized by four processes: (a) reading the curriculum, (b) evaluating the curriculum, (c) adapting the curriculum, and (d) implementing the curriculum. Reading the curriculum consists of reviewing any of the materials provided for the teacher or the students. In evaluating the curriculum, teachers consider their own understanding of the activities, as well as their students' ability to engage with the activities provided. Adapting the curriculum is defined as making significant changes in a lesson such as inserting or deleting an activity. Lastly, implementing the curriculum involves using the materials during instruction.

All of the teachers engaged with each of the four processes. Nevertheless, the teachers engaged with these processes in several different ways resulting in a number of what we call models of curriculum use. For example, Jill's model indicates that she first read the description of the lesson, then implemented the lesson, and afterwards evaluated and adapted the lesson for future implementation. In contrast, Laura adapted the lesson as she read the materials. Laura then implemented the revised lesson and finally evaluated the lesson following instruction.

With these models in mind, we then set out to examine the relationship between teachers' curriculum use and their instructional practices. Here we describe three key results. First, the order of the four processes in teachers' models seems to influence their ability to implement the curriculum effectively. In particular, we found that several teachers evaluated and adapted lessons prior to teaching, while others evaluated and adapted either during instruction or following the lesson. Those teachers who evaluated and adapted lessons in the midst of instruction seemed better able to engage students in discussions of mathematical ideas than the teachers who evaluated and adapted lessons prior to or following instruction. This finding is in line with other research that emphasizes the need for teachers to be able to make adaptations of lessons during instruction in order to implement reform successfully (i.e. Hammer, 1997).

Second, the teachers had different meanings for the different processes in their models of curriculum use. These varied meanings impacted teachers' practices in different ways. For instance, while all six of the teachers adapted the curriculum lessons and activities, each teacher tended to adapt in a particular way. Marta's adaptations generally involved either eliminating an activity or transforming a reform lesson into a traditional lesson covering the same content. For Sandra, adapting a lesson involved selecting among the different ways that the curriculum suggested to engage students with a particular concept.

I'm thinking…[to] maybe do the blackboard structure at the beginning for a little while, then maybe do the routines and check-up…and then maybe go back to [the blackboard structure.]

Finally, for Carrie, adapting meant creating activities or materials to serve as transitions or linkages between curricular lessons.

Then the math stories…as I was doing it, I was thinking I should just have them put numbers on the story…three over here, four over here, and seven over here. I’m trying to transition them into a number sentence.

Each teacher was clearly adapting, but the resulting instructional practices in each of their classrooms were quite different.

At the same time, the relationship between teachers' models of curriculum use and their classroom practices was not unidirectional. As teachers learned through their instruction about their students and about the curriculum, the order and meaning of the processes in their models often changed. In two cases, the change in the teachers' models was particularly pronounced. As these teachers developed greater knowledge about and comfort with their students and the curriculum, they began to shift from evaluating and adapting after instruction to evaluating and adapting before and during instruction. As suggested above, this change in the timing of the evaluation and adaptation processes had significant effects on the instructional practices of these teachers, particularly on their ability to hear and respond to students. It is interesting to note that both of these teachers were first-year teachers. As a result, it is possible that some of the shift in their models of curriculum use was due to their gaining general pedagogical experience, in addition to their greater knowledge and understanding of the curriculum and of their students.

Implications

Understanding how teachers make use of reform-based curricula is a critical issue for mathematics educators and researchers today. First, such research will add to our understanding of teacher cognition by illuminating the knowledge that teachers bring to bear to the task of interpreting curriculum materials. In addition, understanding how teachers make sense of new materials will have important implications for the design of reform-based curricula. For example, curriculum designers might want to make explicit the expectation that teachers will evaluate and adapt the materials presented to them. Furthermore, continuing to examine the relationship between models of curriculum use and teachers' instruction should help us to better understand how to foster successful implementation of mathematics education reform. In particular, effective models of curriculum use could be used in the future as the basis for professional development programs.

References

Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is - or might be - the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6-8,14.

Ben-Peretz, M. (1990). The teacher-curriculum encounter: Freeing teachers from the tyranny of texts. Albany: SUNY Press.

Brown, A. L., & Campione, J. C. (1996). Psychological learning theory and the design of innovative environments: On procedures, principles, and systems. In L. Schauble & R. Glaser (Eds.), Contributions of instructional innovation to understanding learning. Hillsdale, NJ: Erlbaum.

Cohen, D. K. (1990). A revolution in one classroom: The case of Mrs. Oublier. Educational Evaluation and Policy Analysis, 12, 311-329.

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 F. Hitt and M. Santos (Eds.), Proceedings of the Twenty First Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education: 709-715.

Fuson, K. C., De La Cruz, Y., Lo Cicero, A. M., Smith, S. T., Hudson, K., Ron, P., & Steeby, R. (2000). Blending the best of the 20th century to achieve a mathematics equity pedagogy in the 21st century. In M. Burke (Ed.), Learning mathematics for a new century, 2000 Yearbook of the NCTM. Reston, VA: NCTM.

Hammer, D. (1997, March). Discovery learning and discovery teaching. Cognition and Instruction, 15, (4), 485-529.

Hufferd-Ackles, K. (1998). Student contributions correcting and strengthening teachers' conceptions of math. In S. Berenson, K. Dawkins, M. Blanton, W. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 541-548). Raleigh, NC: North Carolina State University.

Sherin, M. G. (1996, April). Novel student behavior as a trigger for change in teachers' content knowledge. Paper presented at the annual meeting of the American Educational Research Association, New York.

Spillane, J. P., Zeuli, J. S. (1999). Reform and mathematics teaching: Exploring patterns of practice in the context of national and state reforms. Educational Evaluation and Policy Analysis, 21(1), 1-21.

Wilson, S. M. (1990). A conflict of interests: The case of Mark Black. Educational Evaluation and Policy Analysis, 12, 293-310.