Problem solving, reasoning and decisions

Problem solving is thinking directed towards a specific goal. Every problem has two anchors: an initial state (where you are now: the problem) and a goal state (where you want to be: the solution). The two are joined by a series of steps or mental operations.

The usual steps are:

• Identify the problem and understand it clearly.
• Represent it: think about its parts and what is known.
• Plan possible solutions and choose one.
• Carry out the plan.
• Evaluate whether it worked; if not, try another.

Obstacles to problem solving:

• Mental set: the tendency to solve problems the way that has worked before. It helps with routine problems but can hide a simpler or better solution. Someone who always takes the same bus to college may never notice that walking a short cut would be faster.
• Functional fixedness: seeing an object only in its usual use. If you need to keep a door open and do not think of using your shoe as a doorstop because shoes are 'for wearing', that is functional fixedness.
• Lack of motivation: even a person with all the skills will not solve a problem they do not care to work at.

Reasoning is the process of gathering and analysing information to reach conclusions. Two kinds:

• Deductive reasoning goes from the general to the particular. It starts with a general rule assumed to be true and applies it to a case: 'All metals expand when heated; this rod is metal; so it will expand.' The conclusion is only as good as the starting assumption; if that is wrong, the conclusion is too.
• Inductive reasoning goes from the particular to the general. It builds a general conclusion from specific observations: after noticing that the plants on the sunny window grow faster every time, you conclude that sunlight helps them grow. Most scientific reasoning is inductive.
• Analogy is reasoning by comparing relationships: 'Wings are to a bird as fins are to a fish.' We often understand something new by seeing how it is like something we already know.

Judgment and decision-making are linked but different:

• In judgment we draw conclusions and form opinions from the information we have, such as deciding that a shop is good value after comparing prices.
• In decision-making we choose among alternatives, weighing the costs and benefits of each. Choosing which of three colleges to join, after thinking about fees, distance and courses, is a decision.
• Judgment comes first and decision follows it: we judge, then act on that judgment.

Different people make different decisions in the same situation, because they give different importance to the costs and benefits. For one student, a college's nearness to home matters most; for another, its sports facilities.