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Tom Carpenter

June 2004

Recommendations for reforming math and science education in the U.S. call for fundamental changes in the math and science content taught in schools and in the approaches to teaching that content.

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

To support teacher change and enable these visions to "travel" to other classrooms, NCISLA researchers sought to understand how the transformed classrooms function, what it takes to create them, and how this knowledge can be used to launch similar classrooms in new settings.

NCISLA Director Thomas Carpenter and colleagues* found that fundamental reforms in mathematics and science learning and teaching are most likely to be achieved through professional development grounded in teacher inquiry and student conceptual understanding. How successfully an innovation travels across diverse conditions and geographical areas depends on the extent to which a teachers' professional community is established.

From 1995 to 2003, NCISLA conducted an integrated program of research that connected (a) the development of students' understanding of core mathematics and science content and practices, (b) classroom instruction and assessment that supports learning with understanding, (c) professional development that fosters teaching for understanding, and (d) the organizational capacity required to support professional development and the emerging instructional practices.

Since 2000, NCISLA has focused on how to use this research to develop successful instructional practices in new settings.

Given the ambitious vision of learning and instruction that Carpenter and colleagues embrace, these efforts present challenges, yet hold promise for student and teacher growth.

This article focuses on NCISLA's findings about learning with understanding, which provide the foundation for all of the center's research.

Learning with understanding

The foundation for NCISLA's work with students and teachers was its conception of learning with understanding. Understanding is seen as continuous mental activity rather than as a static attribute of an individual's knowledge.

NCISLA research (citations below) found that mathematical and scientific understanding emerges from four related forms of mental activity:

1. constructing relationships;
2. extending and applying mathematical and scientific knowledge;
3. justifying and explaining generalizations and procedures; and
4. taking responsibility for making sense of mathematical and scientific knowledge.