# Notes Outline

• Definition
• Types of Problems
• Barriers to Problem Solving
• Approaches to Problem Solving

# Problem Solving

Problem Solving involves active efforts to discover what must be done to achieve a goal that is not readily attainable.

Two main types:

• Trial & Error
• Insight or "Aha!"

Find a word that make sense being put together with the other words:

PINE                        CRAB                         SAUCE

# Types of Problems

1. Inducing structure - Some problems involve finding relationships between elements (words, numbers, symbols, or ideas).

EX: “Pineapple is to fruit as cabbage is to ___.”

In this analogy problem, the answer, “vegetable,” requires people to figure out the relationship between “pineapple” and “fruit” and apply a similar relationship to “cabbage.”

2. Arranging - Other problems involve arranging elements in a way that fulfills certain criteria.

EX: Arrange the letters in LEPAP to make the name of a fruit

3. Transformation - involves making a series of changes to achieve a specific goal, a process called transformation.

EX: A familiar riddle describes a situation in which a man has to take his fox, his chicken, and his tub of grain across a river in a boat. The boat will hold only him and one of his possessions at any one time. He can’t leave the fox and the chicken on the riverbank by themselves because the fox will eat the chicken, and he can’t leave the chicken with the grain because the chicken will eat the grain. He also can’t take the fox and the chicken in the boat together because the fox will eat the chicken when he’s occupied with rowing the boat. The same goes for the chicken and the grain. How will he get all three across?

Answer: Take the chicken over first. Go back and bring the grain next, but instead of leaving the chicken with the grain, come back with the chicken. Leave the chicken on the first side and take the fox with you. Leave it on the other side with the grain. Finally, go back over and get the chicken and bring it over.

# Barriers of Problem Solving

1. Perceptual set/Confirmation Bias - tendency to search for information that supports our preconceptions and to ignore or distort contradictory evidence.

EX: Obama is a Muslim, 9/11 was an inside job, gun control does (or does not) save lives, etc.

2. Irrelevant Information - Information presented WITH a problem that is not integral to solving the problem and distracts us.

EX: A teacher has 23 pupils in their class. All but 7 of them went away for a field trip to the museum. While there they saw dinosaur fossils and had lunch at the museum cafeteria. The bus broke down on the way home and three of the students got lost in the woods. Five parents are threatening to sue the school district as a result of the trauma. How many students remained safely at the school that day?

3. Functional fixedness – an inability to see things from a new perspective once we have framed the problem in our minds

4. Mental set - our tendency to approach a problem with a mind-set of what has worked for us previously. Sometimes this can be an obstacle when our mental set from a previous experience stops us from seeing things in a new way.

• EX: Given the sequence “O-T-T-F-?-?-?” what are the next three letters?
• Once you solve that, try to solve the next one: Given the sequence “J-F-M-A-?-?-?” what are the next three letters?
• EX: Take six matchsticks and arrange them to form four equilateral triangles.

5.  Unnecessary constraint - This particular phenomenon occurs when you place boundaries on the problem and become fixated on only one way to solve their problem, and it becomes increasingly difficult to see anything else

EX: Without lifting your pencil from the paper, draw no more than four lines that will cross through all nine dots.

6. Forming bad judgments – This overlaps many of the other barriers, and can occur when we trust our INTUITION (fast, automatic, unreasoned thinking) instead of reasoned thinking

• Availability Heuristic – when we estimate the likelihood of events based on how mentally available they are based on vividness, recency, or distinctiveness – overfeel and underthink.
• EX: When Muslims attacked on 9/11 it made people more likely to assume Muslims were terrorists; Fearing flying in a plane even though it is the safest form of travel; Fearing shark attacks even though you are more likely to be killed by a vending machine; in ability to see the danger of climate change because you remember a recent cold day

7. Overconfidence – people overestimate their own performance, accuracy, and judgment.

8. Belief perseverance – people tend to cling to beliefs in the face of contradictory evidence. Asking people to be UNBIASED does not work. Solution is fairly straight forward, ask a person to consider the opposite belief.

9. Framing - how the problem is presented to us.

• EX: 10% of people die in this surgery vs 90% survive
• Ex: Organ donation. In many European countries the default is YES with the option to opt OUT. In America the default is NO with the option to opt IN. In countries where the default is YES the rate of organ donation is nearly 100%, in America it is only about 25%.

# 8 Approaches to Problem Solving

1. Algorithms – step-by-step procedures that guarantee a solution – can take a LONG time

• EX:  Rearrange these letters to make a word: SPLOYOCHYG
• If you tried each letter in each of the 10 positions then there would be 907,200 options

2. Heuristics - simpler thinking strategies, take less time but are more prone to errors. “Rule of thumb” or guiding principle.

• EX: reduce options for SPLYOCHYG by grouping together letters you know go together like “CH” and “PSY”

3. Reasoning through induction & Deduction

• Inductive reasoning makes broad generalizations from specific observations.
• Here’s an example: "Harold is a grandfather. Harold is bald. Therefore, all grandfathers are bald."
• In deductive reasoning, if something is true of a class of things in general, it is also true for all members of that class
• For example, "All men are mortal. Harold is a man. Therefore, Harold is mortal."

4. Forming Subgoals – intermediate step towards a solution

Working backwards

5. Search for analogies – If you can spot a similarity between problems then you may be able to use the solution for Problem A on Problem B.

6. Change the representation of the problem – change it verbally, mathematically, or spatially. Make a list, table, an equation, a graph, a matrix, hierarchical tree, sequential flowchart. Allows you to strip away irrelevant details.

7. TAKING A BREAK! (incubation) – letting your mind rest often lets it work without you being aware

# Want to Know MORE about Problem Solving?!?

Mrs. Rice - Thinking & Problem Solving Part 1 (7:00)

Mrs. Rice Thinking and Problem Solving Part 2 (12:36)

Crash Course - Start at 5:50 for Problem solving part: