At its roots, problem solving is exactly what it sounds like, the process of solving problems. However, problem solving methods permeate the studies of mathematics, science, and technology. The human processes involved in problem solving are often studied by cognitive scientists. One of the most important things to remember as a problem solver is to always read the question CAREFULLY!!! This is more than a math teacher cliche. I cannot tell you how many times I've screwed up a problem becuase I did not read the question carefully (i.e. I gave the whole fraction when the question only asked for the denominator).