PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Virtual manipulatives, vertical number lines, and Taylor series convergence: The case of Cody
Page: 963
Evidence from recent Taylor series studies suggests that well-designed virtual manipulatives can support calculus students in developing an understanding of Taylor series convergence consistent with the formal pointwise convergence definition. In particular, virtual manipulatives depicting convergence along vertical number lines (VNLs) provide graphical representations of quantities necessary for pointwise convergence. We detail one student’s reasoning about Taylor series convergence before and after a VNL was revealed in a Taylor series graph. Prior to the VNL the student had produced very accurate Taylor polynomial graphs based on visually perceptual clues but had omitted notions of pointwise convergence. After a VNL was revealed, the student’s reasoning now included quantities along the vertical as he responded to approximation tasks. We believe that such reasoning can later support the student in developing an understanding of pointwise convergence.