Uncontrollable Mental Imagery: Graphical Connections Between A Function And Its Derivative

The view that imagery might be a disadvantage on certain tasks might surprise some mathematics educators who contend that a learner's conceptual understanding is increased whenever visual imagery is used. One of the limitations of imagery found in the literature comes to bear on a unique aspect of mathematics teaching and learning. This is the notion of an uncontrollable image, which may persist, thereby preventing the opening up of more fruitful avenues of thought, a difficulty which is particularly acute if the image is vivid. Although one calculus student's images supported high levels of mathematical functioning, occasionally his vivid images became uncontrollable, and the power of these images did more to obscure than to explain. This type of imagery can be a major hindrance in constructing meaning for mathematical concepts — contrary to the panacea view of imagery which is sometimes expressed.This revised version was published online in September 2005 with corrections to the Cover Date.