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May 2005

Part 4 of a Four-Part Series: Scaling Up Innovative Practices in Math and Science

Learning mathematics with understanding requires teachers to help students build on what they know and on how they think. Similarly, students’ reasoning should be placed at the center of effective instructional decision making and professional development.

In 8 years of research at WCER’s National Center for Improving Student Learning and Achievement in Mathematics and Science (NCISLA), UW-Madison education professor Thomas Carpenter and colleagues* worked with teachers and schools to create and study classrooms in which compelling new visions of mathematics and science became the norm.

To support teacher change and to enable these visions to “travel” to other classrooms, Carpenter and collegues sought to understand how these classrooms function, what it takes to construct them, and how this knowledge can be used to create similar classrooms in new settings.

Part 3 of this four-part series discussed requirements for school organization that support teaching for understanding. This article, which concludes the series, focuses on what travels and what conditions are necessary for travel to occur. To start at the beginning of the series, see part 1.

NCISLA found that the most critical things that teachers need to learn revolve around content knowledge and the student learning trajectories specific to that knowledge. Learning specific content and learning how students learn that content are central to professional development.

NCISLA also found that professional development must emphasize student reasoning rather than teachers’ scripted performance. NCISLA researchers documented regularities in what students do and how teachers respond to them. Regularities were found in student reasoning, in the types of tasks that elicited that reasoning and supported change, and in ways of interacting with students.

NCISLA developed a number of resources to support the emergence of successive levels of students’ mathematical or scientific reasoning. These resources include:

• Fine-grained analyses of specific content domains (for more information see the NCISLA Research Briefs)
• Analyses of hypothetical learning trajectories for these content domains
• Specific tasks or types of tasks that provide a window into student reasoning and that support the development of more advanced reasoning;\
• Examples of norms governing student participation and teacher-student interaction
• Strategies and activities that help teachers focus on students’ reasoning.

NCISLA found that these resources can support the development of professional teaching communities in new settings. The context in which the resources are used, however, affects how they are used. The ways resources are used in a new setting can differ significantly from the ways they were used in the setting in which they initially were studied. Thus, the resources themselves cannot simply travel to a new school or district with the expectation that the teacher professional development process will replicate what occurred at other sites. To facilitate effective travel, the resources must be transformed or adapted to the constraints and opportunities of new contexts.

New teaching communities in new contexts

Travel entails supporting the development of professional teaching communities in a new educational context, not merely transporting practices in the hope that professional community will emerge. The work in new sites must maintain fidelity to the guiding principles of the original work.

One critical feature for travel was the continuing involvement of teachers in design practices. Yet while it’s important to engage teachers in design practice, there is a danger that the further the practices are removed from the initial design experiments, the less teachers are inclined to engage in such practices. A low probability of success faces attempts to employ the resources and apply the conceptions of professional teaching communities developed in one site without direct connections to the people who were involved in developing the conceptions and resources. Professional communities in new sites thus must have access to human as well as pedagogical resources.

In the current era of high-stakes testing and accountability, district and school administrators frequently respond to the prevailing pressures by attempting to monitor and regulate teachers’ instructional practices. Carpenter and colleagues believe it would be better for administrators to become instructional leaders, to develop professional communities, and to improve their understanding of content, students, and instructional practices. Working to bring about change in the institutional setting must become part of the agenda of the professional teaching community.

This research found that what travels—and can be sustained—are patterns of reasoning and what teachers do with them, not the enactment of specific instructional activities.

This research was funded by a grant from the U.S. Department of Education’s Office of Educational Research and Improvement (R305A60007-01).

For more information:

Carpenter, T. P., Blanton, M. L., Cobb, P., Franke, M. L., Kaput, J., & McCain, K. (2004). Scaling up innovative practices in mathematics and science. Madison: University of Wisconsin–Madison, NCISLA. Retrieved February 7, 2005, from http://www.wcer.wisc.edu/ncisla/publications/ reports/NCISLAReport1.pdf

Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 19–32). Mahwah, NJ: Erlbaum.

Fennema, E., & Romberg, T. A. (Eds.). (1999). Mathematics classrooms that promote understanding. Mahwah, NJ: Erlbaum.

Gamoran, A., Anderson, C., Quiroz, P., Secada, W., Williams, T., & Ashmann, S. (2003). Transforming teaching in math and science: How schools and districts can support change. New York: Teachers College Press.

NCISLA. (n.d.). Powerful practices in mathematics and science: Research-based practices for teaching and learning [monograph, CD-ROMs]. Available from http://www.learningpt.org/msc/products/practices.htm

Romberg, T. A., Carpenter, T. P., & Dremock, F. (in press). Understanding mathematics and science matters. Mahwah, NJ: Erlbaum.

* Carpenter’s colleagues include Maria Blanton (University of Massachusetts–Dartmouth), Paul Cobb (Peabody College, Vanderbilt University), Megan Loef Franke (University of California, Los Angeles), Adam Gamoran (Universify of Wisconsin-Madison), James Kaput (University of Massachusetts–Dartmouth), and Kay McLain (Peabody College, Vanderbilt University