Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus † Patrick W. Thompson Center for Research in Mathematics and Science Education San Diego State University Running Head: Rate and Calculus Thompson, P. W. (1994). Images of rate and operational understanding of the Fundamental Theorem of Calculus. Educational Studies in Mathematics, 26(2-3), 229–274. † Research reported in this paper was supported by National Science Foundation Grants No. MDR 89-50311 and 90-96275, and by a grant of equipment from Apple Computer, Inc., Office of External Research. Any conclusions or recommendations stated here are those of the author and do not necessarily reflect official positions of NSF or Apple Computer. Also, I wish to thank Paul Cobb and Guershon Harel for their helpful reactions to an earlier draft of this article.