K.Eisenhardt summarizes the difference between theory-building and hypothesis-testing research:

As Pettigrew (1988) noted, given the limited number of cases which can usually be studied, it makes sense to choose cases such as extreme situations and polar types in which the process of interest is "transparently observable." Thus, the goal of theoretical sampling is to choose cases which are likely to replicate or extend the emergent theory. In contrast, traditional, within-experiment hypothesis-testing studies rely on statistical sampling, in which researchers randomly select the sample from the population. In this type of study, the goal of the sampling process is to obtain accurate statistical evidence on the distributions of variables within the population.

 We can draw a similar contrast between the processes of invention and implementation. First, to make a problem "transparently observable" inventor has to "go wide", i.e. stretch out the parameters of the situation(s) in which the problem occurs. Second, s/he has to create a theory of operation or a model (this is especially important for complex problems). E.g., s/he can identify a key dilemma, draw up a 5-element or a 10X diagram, etc.  Then, when the problem is clearly identified, explored, and relatively abstract solutions are found, the inventor needs to develop "hypothesis-testing" implementation strategy and eliminate the noise.
Unfortunately, the education system traditionaly emphasizes the last stage of the process, as being more "scientific". Though, it doesn't have to be that way. For example, brainstorming as a method was proactively taught with good results in many schools in the 1960s and 1970s.

References:

Title: Building Theories from Case Study Research

Author(s): Kathleen M. Eisenhardt

Source: The Academy of Management Review, Vol. 14, No. 4 (Oct., 1989), pp. 532-550

Publisher(s): Academy of Management

Stable URL: http://www.jstor.org/stable/258557