previously learned steps from memory (Bassok and Novick, 2012; Martinez, 2010). That is, during problem solving the path to the intended goal is uncertain. This characterization describes much of what people do on a daily basis, from (a) mundane activities like deciding what to cook for dinner given the ingredients at hand or how to get from work to home given certain street closures, to (b) student activities such as interpreting laboratory results, figuring out how to organize a term paper on evidence for speciation, or designing a roller coaster for an engineering class, to (c) professional work such as curing illnesses or determining the best way to structure a class so that students will understand a key concept. Clearly, problem solving is central to science and engineering as well to everyday life.

Researchers in numerous disciplines have drawn a distinction between well-defined and ill-defined problems (Hsu et al., 2004; Reitman, 1965). Most of the problems students encounter in their science and engineering classes are well-defined, such as a mechanics word problem. In these problems, the initial conditions, the goal, the means for generating and evaluating the solution, and the constraints on the solution are all clearly specified for students. For other types of problems, however, such as a more open-ended laboratory or an authentic design problem in engineering, students have to define one or more of the problem components on their own (Fay et al., 2007; Whitson, Bretz, and Towns, 2008). In a laboratory, the means of generating the solution may be ill-defined. For an engineering problem, the goal may be ill-defined; as a result, it may not be clear how to determine whether the goal has been accomplished. For example, what constitutes a better coffee cup, and how does one decide that a new cup design represents a big enough improvement over the status quo to declare the design finished?

Society’s most important problems are usually ill-defined in some way. Consider two examples: (1) How can the rapid regrowth of human skin be promoted so that life-threatening infections in burn patients are prevented? (2) How can affordable, alternative energy to power cars be generated, thereby limiting reliance on fossil fuels? These are the kinds of problems students will have to solve after they graduate. Students who have scant experience with ill-defined problems during their undergraduate education may be poorly prepared to grapple with the most significant problems in their fields.

This discussion of problem solving is structured around important findings from DBER that are consistent with prominent themes from the cognitive science literature, namely problem representation and the nature of the solution process. In the cases for which the findings apply to only a small number of problem domains or disciplines, their broader applicability to problem solving within the disciplines of interest here is an open question. For example, as the following discussion will show, research has shown that



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