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numbers that come to mind, but this can be time consuming and may not lead to a solution. Trial and error works best when choices are limited. After we have tried to solve a problem, we need to evaluate the results. How will we decide if we have solved the problem? Using critical thinking, we think reflectively and evaluate the evidence. We reason by transforming information to reach conclusions. Inductive reasoning involves reasoning from the specific to the general, forming concepts about all members of a category based on some members, which is often correct but may be wrong if the members we have chosen do not fairly represent all of the members. Deductive reasoning involves reasoning from the general to the specific. Deductions are logically correct and lead to good answers when the initial rules or assumptions are true. Have we attained our goal? Over time, we may profit from rethinking and redefining problems and solutions.

Obstacles to Problem Solving

Sometimes we are unsuccessful at solving a problem; we cannot attain our goal. What hinders our ability to solve the problem? Obstacles to problem solving and biases in reasoning can keep us from reaching a goal. Fixation is an inability to look at a problem from a fresh perspective, using a prior strategy that may not lead to success. If we’ve solved 10 problems in a 50-problem set using one rule, we tend to use the same rule to solve the 11th. This tendency to approach the problem in the same way that has been successful previously is a type of fixation called mental set. We may get stuck on the 11th problem because it requires a different rule from the first 10. Another type of fixation that can be an obstacle to problem solving is called functional fixedness, a failure to use an object in an unusual way. For example, if people are carrying plastic tablecloths to a picnic area when it starts to rain, and they get soaked because they aren’t wearing raincoats and don’t have umbrellas, they are evidencing functional fixedness. They could have used the tablecloths to protect them from the rain. Using decision-making heuristics when we problem solve can result in errors in our judgments. Amos Tversky and Nobel prize winner Daniel Kahneman studied how and why people make illogical choices. They looked at two types of research. Normative studies ask how we ought to make decisions, and do not actually reflect how people make decisions. Descriptive studies look at how decisions are actually being made. Tversky and Kahneman found we often make erroneous decisions based on intuition. Under conditions of uncertainty, we often use the availability heuristic, estimating the probability of certain events in terms of how readily they come to mind. For example, many people who think nothing of taking a ride in a car are afraid to ride in an airplane because they think it is so dangerous. In fact, riding in an airplane is much safer; we are far less likely to be injured or die as a result of riding in an airplane. Other errors in decision making result from using the representative heuristic, a mental shortcut by which a new situation is judged by how well it matches a stereotypical model or a particular prototype. Is someone who loves to solve math problems more likely to be a mathematics professor or a high school student? Although many people immediately reply that it must be the professor, the correct answer to the problem is the high school student. The total number of high school students is so much greater than the total number of mathematics professors that even if only a small fraction of high school students love to solve math problems, there will be many more of them than mathematics professors. Framing refers to the way a problem is posed. How an issue is framed can significantly affect people’s perceptions, decisions, and judgments. We are more likely to buy a product that says it is 90% fat-free, than if it says it contains 10% fat. A suggestion can have a powerful effect on how we respond to a problem. Kahneman and Tversky asked if the length of the Mississippi River