  In this study, we examine introductory physics students' ability to perform
analogical reasoning between two isomorphic problems which employ the same
underlying physics principles but have different surface features. Three
hundred and eighty two students from a calculus-based and an algebra-based
introductory physics course were asked to learn from a solved problem provided
and take advantage of what they learned from it to solve another isomorphic
problem (which we call the quiz problem). The solved problem provided has two
sub-problems while the quiz problem has three sub-problems, which is known to
be challenging for introductory students from previous research. In addition to
the solved problem, students also received extra scaffolding supports that were
intended to help them discern and exploit the underlying similarities of the
isomorphic solved and quiz problems. The results suggest that students had
great difficulty in transferring what they learned from a 2-step problem to a
3-step problem. Although most students were able to learn from the solved
problem to some extent with the scaffolding provided and invoke the relevant
principles in the quiz problem, they were not necessarily able to apply the
principles correctly. We also conducted think-aloud interviews with 6
introductory students in order to understand in-depth the difficulties they had
and explore strategies to provide better scaffolding. The interviews suggest
that students often superficially mapped the principles employed in the solved
problem to the quiz problem without necessarily understanding the governing
conditions underlying each principle and examining the applicability of the
principle in the new situation in an in-depth manner. Findings suggest that
more scaffolding is needed to help students in transferring from a two-step
problem to a three step problem and applying the physics principles
appropriately.
