PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
An evolving visual image of approximation with Taylor series – a case study
Page: 1-94
This paper will take a close look at the construction of a graphical image for reasoning with approximation in the context of Taylor series. In particular, it is a comprehensive case study of the genesis and evolution of an image created by one student, who draws extensively on other images and knowledge from calculus and physics to supplement gaps in his understanding of Taylor series and reason with Taylor series approximation tasks. His process resulted in a graphical image that was leveraged to build knowledge and reason with the situation, even while lacking key considerations that are central to an understanding of Taylor series. In this paper, we speak not only to considerations of a student’s understanding of this particular content. This work also provides a detailed examination of the processes of constructing a graphical image used for problem solving, for which it was necessary for the student to obtain and utilize evidence to amend that graphical image.