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Scaling Up Innovative Practices in Math and Science

This kind of teaching requires that teachers have a coherent vision of

1. The structure of the mathematical or scientific ideas and practices they are teaching
2. The conceptions, misconceptions, and problem-solving strategies students are likely to bring to the classroom and the areas in which students are likely to have difficulty
3. The learning trajectories students are likely to follow
4. The tasks and tools that can provide windows into students' thinking and support their learning and problem solving
5. The kinds of scaffolding that can support students' efforts to engage in sense making and problem solving, and
6. The class norms and activity structures that support learning.

The NCISLA researchers found that this kind of knowledge cannot be embedded in curriculum materials or scripted into instructional routines. Teachers need flexible knowledge that they can adapt to their students and the demands of situations that arise in their classes. Acquiring this kind of knowledge requires new conceptions of professional development.

Designing professional development

Instruction that supports learning with understanding requires teachers to make ambitious and complex changes. Teachers must engage in experimentation, take on the role of the teacher as intellectual, and reinvent their practice in such a way as to reflect the interdependence of teaching and learning.

Achieving this vision requires educators to grapple with what it means for teachers to engage in ongoing, generative learning and to determine how professional development can contribute to that end. Building a basis for ongoing learning is one of the defining features of learning with understanding. NCISLA's work provides a needed framework for teacher professional development, addressing both student learning and teachers' growth as learners and professionals.

In a 7-year longitudinal study of a teacher professional development program, Franke, Carpenter, Linda Levi and Elizabeth Fennema found that teachers whose learning became generative perceived themselves as creators and elaborators of their own knowledge about children's mathematical  thinking. They perceived knowledge acquired through professional development as something on which they could build, and they recognized that they also learned from classroom engagement with their students. Teachers whose knowledge did not become generative, on the other hand, tended to see what they gained from the professional development program as a fixed body of knowledge acquired from experts.

Generative learning imposed structure on teachers' knowledge, allowing them to attend to and remember details of their students' mathematical thinking and thereby refine their general understanding of children's mathematical thinking. All of the teachers demonstrating generative learning reflected on their own understanding of mathematics and on changes in their instructional practices that might help their students better learn mathematics. These teachers were articulate in expressing their ideas about their conceptions and practices and the relations between them.

Professional development can sow the seeds for ongoing inquiry, helping teachers strengthen their own mathematical and scientific understanding, deepen their understanding of how students' mathematical and scientific understanding develops, and devise instructional practices to foster that development.

* Carpenter's colleagues include Maria Blanton (University of Massachusetts-Dartmouth), Paul Cobb (Vanderbilt University, Peabody College), Megan Loef Franke (University of California-Los Angeles), James Kaput (University of Massachusetts-Dartmouth), and Kay McLain (Vanderbilt University, Peabody College).

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 July 15, 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.

Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001) Capturing teachers' generative growth: A follow-up study of professional development in mathematics.  American Educational Research Journal, 38, 653-689.

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