Qualitative Approach to Graphs of Functions in a Microworld

This paper deals with a teaching experiment of how 6th grade students understand the rate of change with covariational reasoning in a LOGO-based microworld JavaMAL. We introduce the function graphs using the traces of a turtle swimming in the JavaMAL microworld in which textual commands are used not only for controlling the turtle`s motion but also for modifications and reflections on students` thinking. We found that visual and symbolic representations for the rate of change can work together for a meaningful qualitative approach to the graphs of functions.