  We have been investigating advanced students' learning of quantum mechanics
concepts and have developed interactive tutorials which strive to help students
learn these concepts. Two such tutorials, focused on the Mach-Zehnder
interferometer (MZI) and the double-slit experiment (DSE), help students learn
how to use the concept of "which-path" information to reason about the presence
or absence of interference in these two experiments in different situations.
After working on a pretest that asked students to predict interference in the
MZI with single photons and polarizers of various orientations placed in one or
both paths of the MZI, students worked on the MZI tutorial which, among other
things, guided them to reason in terms of which-path information in order to
predict interference in similar situations. We investigated the extent to which
students were able to use reasoning related to which-path information learned
in the MZI tutorial to answer analogous questions on the DSE (before working on
the DSE tutorial). After students worked on the DSE pretest they worked on a
DSE tutorial in which they learned to use the concept of which-path information
to answer questions about interference in the DSE with single particles with
mass sent through the two slits and a monochromatic lamp placed between the
slits and the screen. We investigated if this additional exposure to the
concept of which-path information promoted improved learning and performance in
the DSE questions with single photons and polarizers placed after one or both
slits. We find evidence that both tutorials promoted which-path information
reasoning and helped students use this reasoning appropriately in contexts
different from the ones in which they had learned it.
