intuitions that guide our work in order to connect it with the work of others in meaningful ways.
Research that links teaching and learning has great potential for helping us understand the most fundamental relationship in the classroom. But, such research is always limited in important ways. To overcome the limitations, to move toward the goal of increased understanding, we must be clear about the limitations and must continue building theories that can be used to make connections among individual projects.
I would like to thank D. Ball, T. Carpenter, N. Mack, and L. Streefland for their comments on an earlier draft of this paper. I also would like to thank the National Science Foundation for supporting the research on decimal fractions summarized in this paper (Grant No. MDR 8651552) and for their partial support while writing it (Grant No. MDR 8855627). The opinions and interpretations, however, are those of the author and not the reviewers or the National Science Foundation. Some of the observations contained in the chapter were presented at the 1989 annual meeting of the American Educational Research Association, San Francisco.
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