Multiple Representations and the Understanding of Taylor Polynomials

Abstract

The study of Maclaurin and Taylor polynomials entails the comprehension of various new mathematical ideas. Those polynomials are initially discussed at the college level in a calculus class and then again in a course on numerical methods. This article investigates the understanding of these polynomials by students taking a numerical methods class at the Lebanese American University in Beirut. The class adopted a closed laboratory format where Mathematica was used extensively. Results show that the added graphical dimension due to the use of the software does not necessarily contribute to a further understanding of the topics under examination. In fact, each subject of the study exhibited a unique mode of understanding: For one, it was purely graphical, for another analytical/numerical, and for the third all three modes complemented each other.