  Most students struggle when faced with complex and ill-structured tasks
because the strategies taught in schools and universities simply require
finding and applying the correct formulae or strategy to answer
well-structured, algorithmic problems. For students to develop their ability to
solve ill-structured problems, they must first believe that standardized
procedural approaches will not always be sufficient for solving ill-structured
engineering and scientific challenges. In this paper we document the range of
beliefs university students have about problem-solving. Students enrolled in a
physics course submitted a written reflection both at the start and the end of
the course on how they solve problems. We coded approximately 500 of these
reflections for the presence of different problem-solving approaches. At the
start of the semester over 50% of the students mention in written reflections
that they use Rolodex equation matching, i.e. they solve problems by searching
for equations that have the same variables as the knowns and unknowns. We then
describe the extent to which students' beliefs about physics problem-solving
change due to their experience throughout a semester with context-rich,
multifaceted problems. The frequency of strategies such as the Rolodex method
reduces only slightly by the end of the semester. However, there is an increase
in students describing more expansive strategies within their reflections. In
particular there is a large increase in describing the use of diagrams, and
thinking about concepts first. Hence the use of context-rich, multi-faceted
problems positively impacts students' attitude towards problem-solving.
