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Rafael Martinez-Planell & Maria Trigueros


Multivariable Calculus Results in Different Countries

Keywords: Multivariable calculus; functions of two variables; differential calculus; integral calculus

Abstract: This study presents the result of a survey of research studies on the understanding and teaching of multivariable calculus. The goal of this study is to put the results obtained by the authors in studies that took place in Mexico and Puerto Rico in a wider international context. Studies included a wide geographic spectrum including countries in North and South America, Europe, the Middle- East and Eastern Asia. In spite of the diversity of cultures and diversity in theoretical approaches results obtained are similar and include common difficulties and common suggestions in order to design teaching methodologies that can help students deeply understand two-variables functions and calculus. Most studies point out the need of students' reflection on three- dimensional space, the importance of the use of graphic and geometrical representations and a thorough work on functions before introducing other calculus topics. Research deals in different ways with the idea of generalization as it considers how students' knowledge of one-variable calculus provides affordances and constraints to their understanding of multivariable calculus. Some research- based strategies which have been experimentally tested with good results are included. Topics considered include: basic aspects of functions of two variables, differential calculus, integral calculus, and limits and continuity. (Click here for article)