U.S.-Mexico Cooperative Research: Expert/Novice Conceptual Approaches to Calculus

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This U.S.-Mexico award will support a research in science education collaboration between Dr. Ricardo Nemirovsky of the Technical Education Research Center (TERC) in Cambridge, Massachussetts, and Dr. Ricardo Cantoral of the Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional (CINVESTAV) in Mexico City. The purpose of the proposed research is to explore how students' intuitive calculus concepts as well as knowledge of their conceptual difficulties could help in developing an enhanced approach to the teaching of calculus. Calculus concepts are essential for understanding both the physical sciences and many events in daily life. Preliminary results indicate that calculus experts may retain intuitive conceptions of calculus operations not identical with those of the formal calculus in which they are trained. Researchers at CINVESTAV have found historically early conceptions of calculus shared many commonalities with approaches of novice students to calculus-based problems. By teaming up to explore both novice and expert conceptions of calculus, the collaborators hope to better understand how calculus is conceptualized and learned in order to develop a new model of calculus instruction that recognizes and seeks to develop students' alternative intuitive conceptions. The proposed cross-national collaboration will provide an efficient coordination of research resources aimed at supporting a new approach to calculus education.