Paper presented at the annual meeting of the American Educational Research Association, April 30 – May 4.
Building on growing evidence that human reasoning simulates multi-modal dynamical imagery drawn from lived experience, we conjectured that some mathematical concepts are challenging because their images are difficult to simulate mentally and that this difficulty, in turn, is directly implicative of the difficulty to enact these concepts physically. For example, two linked equal-rate linear growths are easier to process than two linked different-rate linear growths, because miming the latter is by far more difficult to coordinate ambidextrously. To examine our conjecture, we built a computer-based servo-mechanical device, the Mathematical Imagery Trainer, designed to induce in students the physically challenging concept of proportionality and measured for reflective-learning gains. The full paper reports on a study with thirty 4th-grade students.