In studies of analogical transfer, subjects sometimes fail to
recognize that problems are structurally isomorphic
because of differences in the problems' content. One
potential explanation for this finding is that differences in
content lead subjects to infer that the problems have
different structures. This interpretation would be supported
by evidence that subjects construct differing mental models
for structurally isomorphic problems. In this study, we
show that subjects' gestures reveal their mental models of
problems that involve discrete and continuous change.
Four subjects talked out loud as they solved a set of four
problems that involved constant change. All subjects
produced gestures as they spoke, and their gestures revealed
both continuous and discrete mental models of the manner
of constant change. O n problems constructed to evoke
mental models of continuous change, subjects tended to
produce gestures that incorporated smooth, continuous
motions. O n problems constructed to evoke mental models
of discrete, incremental change, subjects tended to produce
gestures that incorporated repeated, sequential, discrete
motions. Subjects' gestures sometimes provided more
explicit cues to their mental models than did their speech.
The results indicate that subjects sometimes constructed
differing mental models for structurally analogous
problems.