**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.