PROCEEDINGS OF THE 22ND ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2019
Oklahoma City, Oklahoma
“Zoom in infinitely”: Scaling-continuous covariational reasoning by calculus students
Page: 180
Recently, Ely & Ellis (2018) described a new mode of covariational reasoning—scaling-continuous reasoning—and conjectured that it might support productive student thinking in calculus. We investigate that hypothesis by analyzing how calculus students employed scaling-continuous covariational reasoning when discussing differential calculus ideas. The interviewed students who took a course based on a “local straightness” approach to calculus used scaling-continuous reasoning in their description of the derivative at a point, particularly in their imagery of zooming in on a function at a point to reveal its slope. The interviewed students who took a course based on an “informal infinitesimals” approach to calculus used scaling-continuous reasoning in their account of how zooming in on a neighborhood reveals the coordination between a bit of x (dx) and the corresponding bit of y (dy), a relationship that gives a differential equation for that curve.