Using an Isomorphic Problem Pair to Learn Introductory Physics:   Transferring from a Two-step Problem to a Three-step Problem
  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. 
Shih-Yin Lin and Chandralekha Singh
physics.ed-ph