Motivation 

To summarize the research on the teaching of problem solving–how people apply their knowledge to new situations, reason about scenarios for which they have incomplete or uncertain information, and solve novel problems.

Problem Solving Definitions

Problem solving: a cognitive process that is used to transform a given state into a goal state when a problem does not have an obvious solution, often used interchangeably with thinking and reasoning. Problem solving can be academic, such as solving an unfamiliar arithmetic word problem, or non-academic, such as how get 3/4 of 2/3 of a cup of cottage cheese.

Types of problems (well-defined vs. ill-defined): Well-defined problems have clearly specified given (problem) states, goal (solution) states, and problem-solving spaces (i.e., the relevant information required to solve the problem and the rules/logic/operators that connection different bits of information). For example, an arithmetic problem, no matter how complex, is well-defined. In ill-defined problems, the given state, goal state, or problem-solving space might be unclear. For example, writing an essay or designing a sustainable building are ill-defined problems. The knowledge of the problem solver does not determine whether problems are well- or ill-defined.

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Motivation 

To address a problematic “imbalance between the number of quantitative and qualitative articles published in highly ranked research journals by providing guidelines for the design, implementation, and reporting of qualitative research.” They also discuss the risks and benefits of a highly ranked research journal (Computers & Education) recommending guidelines to be used, albeit flexibly, in qualitative research.

Qualitative or Quantitative Methodology and Data

The paper starts by addressing common misconceptions about when it is appropriate to mix-and-match qualitative and quantitative. They define qualitative methodology as hermeneutic or interpretivist and based on a belief in the validity of multiple culturally-defined interpretations of multiple realities. Therefore, qualitative methodology is incompatible with quantitative methodology, which they define as objectivist or empiricist and based on a belief in the validity of one true explanation of one objective reality. Within each of these methodologies, however, data collection methods, instruments, and analysis can be both qualitative (i.e., non-numeric) or quantitative (i.e., numeric) and mixed-and-matched at will. Much more detail about these concepts and their relationships can be found at Twining’s blog post that extends their very useful Table 1.

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