Design is problem solving, and problem solving has two major aspects, optimization and innovation.
Here, we can also identify overlaps between cognitive processes involved in mathematical problem solving and problem solving in general: Structuring, mathematizing, processing, interpreting, and validating (Baumert et al. [2009]; Hiebert et al. [1996]; Kuo et al. [2013]; Polya [1945]).
An alternative to starting with complete and distinct notions of design is to treat design problem solving as problem solving in general, and focus individually on the reasoning processes that are involved.
"All I've ever done is problem solving, creative problem solving," he says.
PISA defines problem solving as: "Problem solving is an individual's capacity to use cognitive processes to confront and resolve real, cross-disciplinary situations in which the solution path is not immediately obvious and the literacy domains or curricular areas that might be applicable are not within a single domain of mathematics, science or reading" (OECD, 2004).
In particular, the objectification of control information is shown to provide a better paradigm for problem solving and for talking about problem solving.
I think of transformational change as fundmentally altering the way we think about something, and therefore how we approach problem solving and implementing our ideas for solving the problem.
This chapter explores common descriptions of design that design involves abductive reasoning, construction, ill-defined problem solving skills, or wicked problem solving skills and argues that they are not always sharp enough to both distinguish design from other types of problem solving and unite design across different design-related disciplines.
Similarly, work on heuristics for discovery and theory construction by scholars such as Darden (1991) and Bechtel & Richardson (1993) present science as problem solving and investigate scientific problem solving as a special case of problem-solving in general.
aThe differences between students' achievement in mathematics and problem solving, and science and problem solving have to be interpreted relative to the OECD average, since the achievement scales were scaled with a mean of 500 and a standard deviation of 100 for the OECD countries (OECD [2004], p. 55).
Understanding the cognitive processes, which are involved in problem solving, and analyzing the structure of the problem solving construct have been a challenge in psychology and science education (Greiff et al. 2013; Kind 2013).
