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April 2005

Part 3 of a Four-Part Series

Efforts to reform mathematics and science instruction in schools must address three key organizational challenges:

• Providing resources
• Aligning commitments, and
• Sustaining and generating reform

This knowledge results from 8 years of collaboration among teachers, schools, and researchers at WCER’s National Center for Improving Student Learning and Achievement in Mathematics and Science (NCISLA). NCISLA researchers worked to create and study classrooms in which compelling new visions of mathematics and science are becoming the norm.

This article is the third of four parts. Part 4 will focus on what travels, what conditions are necessary for travel to occur, and how similar classrooms can be created in new settings. You can read part 2 here.

Providing resources

Creating fundamental and sustained changes in teaching practices requires long-term commitments of material, human, and social resources for professional development. Teachers in the NCISLA study said that time was their most critical material resource and that the most important use of their time was for planning and learning with other teachers. Because their expertise and knowledge about student thinking in mathematics and science were limited, teachers also said that expertise from outside the schools was essential to stimulating their investigations and learning.

The study also found that self-sustaining change (i.e., change that would endure beyond the life of the research and development project) requires professional development that alters the nature and distribution of resources available in the school and district.

When schools and districts restrict teachers to conventional roles, they prevent the school as an organization from enhancing its capacity in human and social resources. On the other hand, schools and districts enhance their capacity for change if they promote leadership roles for teachers, recast the role of administrators as one of facilitating rather than managing, change the allocation of time during the school day, and provide materials and resources suitable to new teaching endeavors.

Schools and districts foster growth of new human and social resources when they allow new roles to emerge. By contrast, schools and districts that force new initiatives to conform to existing arrays of resources risk stifling potential change or marginalizing change agents.

Sustaining reform

Sustaining teaching for understanding depends on the emergence of leadership within professional communities, a commitment to professional interdependence (rather than independence), and a commitment of human and material resources. The infusion of human and material resources must accomplish two things:

• It must contribute to the development of social resources in ways that enable teachers to assume responsibility for leadership; and
• It must foster and maintain communities of inquiry aimed at understanding student thinking and designing instructional practices that build student understanding.

Change can be sustained when (a) school personnel routinely evaluate, invent, and implement new practices, (b) those practices are motivated by reform and are consistent with reform, and (c) schools support teachers’ professional communities and professional development. In contrast, when teachers haphazardly acquire new practices with little or no community support or professional development opportunities, new practices tend to become brittle and routine—and, at times, are abandoned altogether.

Creating similar classrooms in new settings

The teaching approach and related professional development described here are complex. Complex practices cannot, in principle, simply be codified and then handed over to others with the expectation that they will be enacted or replicated as intended.

Yet traditional views of professional development presume that teachers can be trained to faithfully enact instructional methods and strategies that have proven effective elsewhere. Carpenter and colleagues consider this an inappropriate conception of professional development—especially for teachers seeking to develop classroom practices that place students’ reasoning at the center of instructional decision making. This kind of teaching requires professional development that supports teachers in creating the knowledge to adjust instruction to their students’ needs and understandings.

Instructional strategies that build on student reasoning cannot simply be transferred to a new setting. By their very nature, such attuned instructional practices need to be refined by teachers who have the intellectual framework and support to analyze, evaluate, and appropriately adjust practices based on student understanding.

Instruction that revolves around student reasoning involves ambiguity and uncertainty, and teachers need support in dealing with this uncertainty. The ability to create and sustain classrooms that build on student reasoning depends on developing professional teaching communities in which teachers help each other deal with uncertainty and rely on each other as resources as they engage in ongoing discussion of teaching and learning.

From the perspective of teacher professional development, the long-term goal of reform can be framed as the creation of environments where teaching becomes a generative activity in which teachers routinely deepen their understanding of students’ reasoning in specific mathematics and science domains. The critical elements required to accomplish this goal are that teachers make their classrooms sites for their own learning and that they have opportunity to participate in professional teaching communities that support teaching for understanding.

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 October 5, 2004, 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.), Classrooms that promote mathematical 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), James Kaput (University of Massachusetts–Dartmouth), and Kay McLain (Peabody College, Vanderbilt University