Example: A chocolate chip cookie recipe is an algorithm for baking chocolate chip cookies.

#### Deductive Reasoning

Deductive reasoning is the process by which a particular conclusion is drawn from a set of general premises or statements. The conclusion has to be true if the premises are true.

Example: If the premises “All birds have wings” and “A penguin is a bird” are true, then the conclusion “A penguin has wings” must also be true.

#### Inductive Reasoning

Inductive reasoning is the process by which a general conclusion is drawn from examples. In this case, the conclusion is likely, but not guaranteed, to be true.

Example: Given the premise “All the butterflies Fred has ever seen have wingspans of less than two inches,” Fred might conclude, “All butterflies have wingspans of less than two inches.”

#### Heuristics

A heuristic is a general rule of thumb that may lead to a correct solution but doesn’t guarantee one.

Example: A useful heuristic for finishing a timed exam might be “Do the easy questions first.”

#### Dialectical Reasoning

Dialectical reasoning is the process of going back and forth between opposing points of view in order to come up with a satisfactory solution.

Example: A student might use dialectical reasoning when she considers the pros and cons of choosing psychology as her college major.

#### Forming Subgoals

Forming subgoals involves coming up with intermediate steps to solve a problem. This is a way of simplifying a problem.

Example: Susan is asked to solve the analogy problem “Prison is to inmate as hospital is to ____.” Susan’s subgoal could be to figure out the relationship between “prison” and “inmate.” Once she achieves this subgoal, she can easily find the answer, “patient.”

#### Using Similar Problems

A problem is often easier to solve if it can be compared to a similar problem.

Example: Mike has to give his two-year-old daughter a bath, but she resists because she is afraid of the water. Mike remembers that he convinced her to get in the kiddie pool last week by letting her take her large plastic dinosaur toy with her for “protection.” He gives her the toy again, and she agrees to get in the tub.

#### Changing the Way a Problem Is Represented

A problem may be easier to solve if it is represented in a different form.

Example: If hundreds of guests at a banquet are trying to figure out where they are supposed to sit, written instructions might not be easy to follow. A seating chart, however, makes the seating arrangement easy to understand.

### Obstacles to Effective Problem-Solving

Researchers have described many obstacles that prevent people from solving problems effectively. These obstacles include irrelevant information, functional fixedness, mental set, and making assumptions.

#### Irrelevant Information

Focusing on irrelevant information hinders problem-solving.

Example: A familiar children’s riddle goes like this: As I was going to St. Ives, I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kits. How many were going to St. Ives? People may think of this as a complicated math problem, but in reality, only one person, the “I,” is headed to St. Ives. The seven wives and their respective entourages are headed the other way.

#### Functional Fixedness

Functional fixedness is the tendency to think only of an object’s most common use in solving a problem.

Example: Rachel’s car breaks down while she is driving through the desert. She is terribly thirsty. She finds several soda bottles in the trunk but no bottle opener. She doesn’t think of using the car key to open the bottles because of functional fixedness.

#### Mental Set

A mental set is a tendency to use only those solutions that have worked in the past.

Example: When Matt’s flashlight hasn’t worked in the past, he’s just shaken it to get it to work again. One day when it doesn’t come on, he shakes it, but it still doesn’t work. He would be subject to mental set if he keeps shaking it without checking whether it needs new batteries.

#### Making Assumptions

Making assumptions about constraints that don’t exist prevent people from solving problems effectively.

Example: Another familiar riddle goes as follows: A father and his son are driving on a highway and get into a terrible accident. The father dies, and the boy is rushed to the hospital with major injuries. When he gets to the hospital, a surgeon rushes in to help the boy but stops and exclaims, “I can’t operate on this boy—he’s my son!” How can this be? If people have a hard time answering, they may be making a false assumption. The surgeon is the boy’s mother.