PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
On The Sensitivity Of Problem Phrasing - Exploring The Reliance Of Student Responses On Particular Representations Of Infinite Series
Page: 451
This study will demonstrate the ways in which students’ ideas about convergence of infinite series are deeply connected to the particular representation of the mathematical content, in ways that are often conflicting and self-contradictory. Specifically, this study explores the different limiting processes that students attend to when presented with five different phrasings of a particular mathematical task - ∑(1/2)n - and the ways in which each phrasing of the task brings to light different ideas that were not evident or salient in the other phrasings of the same task. This research suggests that when attempting to gain a more robust understanding of the ways that students extend the ideas of calculus – in this case, limit – one must take care to attend to not only students’ reasoning and explanation, but also the implications of the representations chosen to probe students’ conceptions, as these representations may mask or alter student responses.