Remembering and imagining: Moving back and forth between motion and its representation

This paper considers the activity of 13th grade students who work in group to track a 3D uniform circular motion. A device called Motion Visualizer 3D is used to display in real time the trajectory of motion on a computer screen. The students are asked to draw the 2D temporal representations of motion along the three directions (width, height, depth). The analysis of their speech and gestures shows moments in which they make present past knowledge or actions (remembering), and moments when they anticipate features of the not yet known graphs (imagining). In so doing, the research points out that understanding motion in mathematical terms grows out of a complex dynamics between recollections and expectations.