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

这项美国-墨西哥奖将支持马萨诸塞州剑桥市技术教育研究中心(TERC)的里卡多·内米罗夫斯基博士在科学教育方面的合作研究，以及墨西哥城国家理工学院研究中心(CINVESTAV)的里卡多·坎托尔博士。这项研究的目的是探索学生直观的微积分概念以及他们对概念困难的认识如何有助于发展一种更好的微积分教学方法。微积分概念对于理解物理科学和日常生活中的许多事件都是必不可少的。初步结果表明，微积分专家可能会对微积分运算保持与他们所接受的正规微积分运算不同的直觉概念。CINVESTAV的研究人员发现，历史上早期的微积分概念与初学者处理基于微积分的问题的方法有许多共同点。通过合作探索微积分的新手和专家的概念，合作者希望更好地理解微积分是如何概念化和学习的，以便开发一种新的微积分教学模式，识别并寻求发展学生的另类直觉概念。拟议的跨国合作将提供有效的研究资源协调，旨在支持微积分教育的新方法。

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.