Laboratory / Mathematics
Change and accumulation
Move two points together on a parabola and watch the secant slope approach a tangent slope. Then accumulate rectangles under that slope curve and compare the total with the original change in position.
What changed
11 rectangles approximate the accumulated area. Narrower intervals expose the curve more faithfully.
Return to the route
Experiment after prediction.
Before changing a control, say which visible feature should move and which should remain invariant. That prediction is the useful part of the experiment; motion alone is not evidence.