Department of Mathematics
Kansas State University
Friday, March 1, 2013
*Chunky and smooth images of change
Abstract: Students have well documented difficulties with graphs. In their review of literature, Leinhardt et. al (1990). identified learning problems in three general areas: a desire for regularity, a pointwise focus, and difficulties with abstractions of the graphical world. These first two areas of difficulties are closely related: Students with difficulties graphing tend to believe that graphs are made up of a finite number of discrete points connected by straight lines that are not made up of points.
In this talk, I discuss recent and current research that investigates connections between these difficulties and student difficulties in modeling dynamical systems and forming images of change, the impact that these student difficulties have on more advanced mathematical reasoning at the secondary and undergraduate level, the damage that developing these difficulties can do to the preparation of teachers (perpetuating the cycle), and the potential role of technology in developing solutions to these systemic and persistent problems.