Problem Solving�Module 2.2b: Solving Problems & Making Decisions�

• Explain the cognitive strategies that assist our problem solving and the obstacle that hinder it.

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Trial & Error

• Trying a variety of solutions and eliminating those that don’t work.

Algorithms

• A problem solving strategy that guarantees the solution to the problem
• Not always the most efficient method
• Would you want to use an Algorithm to solve a combination lock’s combo?
• 64,000 possibilities

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Using an Algorithm

• Pick any month of the year.
• Look at four dates that form a square in that month and add them together for a total.
• Given only this total, how can you determine the four dates the person chose using an algorithm?

Algorithm:

• To find the first date: divide the sum by 4 and then subtract 4.
• To find the second date: just add 1 to the date you got above.
• To find the third date: add 7 to the first date.
• To find the fourth date: add 8 to the first date.

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Heuristics

• A rule-of-thumb, simplier problem solving strategy
• makes a solution more likely and efficient but does not guarantee a solution
• Examples:
• What is 79 x 10?
• Need milk? Go to the dairy sections of store rather than search the entire store.
• “I” before “E” except after “C”
• They simplify the problem because they let you reduce the number of possible solutions.
• These can be handy shortcuts, but they can get us into trouble. (What about words like “weird”)

Insight

• The sudden realization of the solution to a problem – correct answer suddenly comes to us. An Aha! moment.
• “Unconscious Problem Solving” – You’re not aware of the thought process that led you to an insight.
• Incubation – Leave the problem for a time, allowing their minds to work on it without conscious effort. (Can led to Insight)

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Insight – Your Aha! Moment

Obstacles to Solving Problems

Confirmation Bias

• Confirmation bias—only search for information confirming one’s belief.
• Once a person forms a belief, they prefer belief-confirming information

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Mental Set

• A tendency to approach a problem in a particular way that has worked in the past
• At times it may make problem solving quicker and more efficient
• Not always helpful when a problem calls for a new approach

Problem: There are 6 eggs in a basket. Six people take one egg each. How is it that one egg can still be left in the basket?

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Answer: The 6^th person took the basket as well as the last egg!

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Was this hard? Your mental set probably kept you from thinking about the possibility someone could take the entire basket and not just an egg.

Nine dots problem

• Without lifting your pencil or re-tracing any line, draw four straight lines that connect all nine dots

Nine dots mental set

• Most people will not draw lines that extend from the square formed by the nine dots
• To solve the problem, �you have to break your mental set & the implicit assumption you have to stay within the dots.

Can you create a formula that will measure out the amount of water in the right-hand column, using any of the three jars (A, B, and C) with volumes as shown in the middle column?

Problems 1 through 7 can all be solved by filling Jar B, then pouring off enough water to fill Jar A once and Jar C twice

desired volume = B - A - 2C

Problem 6 can be solved with a simpler formula (A - C), and so can Problem 7 (A + C). Many people miss these easy solutions because the mental set from the first several problems becomes fixated. Did your thinking stay flexible?

Problems 1 through 7 can all be solved by filling Jar B, then pouring off enough water to fill Jar A once and Jar C twice

desired volume = B - A - 2C

Problem 6 can be solved with a simpler formula (A - C), and so can Problem 7 (A + C). Many people miss these easy solutions because the mental set from the first several problems becomes fixated. Did your thinking stay flexible?

Fixation:�Functional Fixedness

• Type of mental set
• Inability to see an object as having �a function other than its usual one
• Have to unlock the door?

• Use a paperclip.

• Tighten a screw without a screwdriver?

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• Use a coin!
• Check out this example of overcoming functional fixedness from Brain Games (2 min)

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Mounting candle problem

• Using only the objects present on the right, attach the candle to the bulletin board in such a way that the candle can be lit and will burn properly

Answer to candle problem

• Most people do not think of using the box for anything other than its normal use (to hold the tacks)
• To solve the problem, �you have to overcome functional fixedness

Decisions Involving Uncertainty�Module 2.2b�

• Explain the meaning of Intuition, and explain how the availability & representative heuristics influence our decisions and judgments.
• Explain how our decisions and judgments are affected by overconfidence, belief perseverance, and intuition.
• Explain how smart thinkers use intuition.

Intuition

• Our fast, automatic, unreasoned thoughts and feelings

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• Which van does your gut say you should accept a ride from?

The Power of Intuition

• Intuition is implicit (unconscious) knowledge that allows to act “without” thinking.
• Intuition is a learned association through experience that gives us our “gut” feelings about right & wrong.
• Unconscious automatic influences constantly affect our judgements.
• Give yourself time to NOT think about it and do something else and the solution may come to you later.

Representative Heuristic

• Judging a situation to how similar it is to the prototype or schema we already have in our mind. (form of stereotyping)

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Representative Heuristic

• How many Fish do you see?

If you said 4, you were forgetting that a Sea Horse is also a type of fish but since it isn’t representative of your prototype for fish, you didn’t count it.

Rep. Heuristic Can be False if…

• We fail to consider possible variations from the prototype.
• Fail to consider approximate number of prototypes that actually exist.

If it has webbed feet, a bill and lays eggs it meets my prototype for a duck so it must be a duck!

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BUT YOU FORGOT IT COULD BE A…

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Gambler’s Fallacy

• If you flipped a coin and it landed on heads 8 times in a row you might be tempted to think it will be tails next time.
• You are using representative heuristic when judging the likelihood that it will be something different this time around even though the chance is still 50/50.

Availability Heuristic

• Judge how common an event is by how easily you can recall previous occurrences of that event.
• Distorts our judgement of risk
• Rare events can cause us to overestimate the likelihood of reoccurrence (Fallacy of Positive Instances).
• After 9/11 there was a sharp decrease in the number of people using air travel while driving increased significantly.

• When we lack an available image of something in our memory we won’t think about the situation very much.

Availability �Heuristic

• Uses information from our memory to judge the likelihood of events
• When instances of an event are easily recalled we consider that event more likely to reoccur.
• If is vivid, recent or distinctive it will seem to be more commonplace

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See Why We Fear the Wrong Things (pg. 197)

Availability vs Representative�What’s the Difference?

Overconfidence

• The tendency to be more confident than correct when estimating the accuracy of one’s own beliefs and judgments
• How well do you know your info for this test?
• How long will it take you to do your homework?
• Do you tend to underestimate how long it takes? - Overconfidence is why! This is the Planning Fallacy
• Refuse to give up on an approach that is obviously not working because you’ve been doing it a while?
• Sunk-Cost Fallacy (click HERE for an example)

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Blind to One’s Incompetence

• Dunning-Kruger Effect
• “Illusory Superiority”
• People who are bad at something often think they are good at it.
• Ignorance of what they don’t know allows them to stay confident in their own abilities.

Belief Bias/Perseverance

• Clinging to one’s beliefs even in the face of contrary evidence.
• Using your already made belief to judge the evidence.
• Especially true if you have made your belief public to others.
• The best advice to give people who want to avoid belief perseverance is: “Consider the Opposite”

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The Lions will Win a Super Bowl!

The earth is flat!

Dude, Really?

Framing

• The way an issue is worded or presented can influence/trigger decisions and judgments.
• Are you in favor of a death tax?
• Are you in favor of an inheritance tax?

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Anchoring Bias

• When we rely too heavily pre-existing information or the first piece of information (the anchor) when making a decision.
• What is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1?
• What is 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8?
• Answer: 40,320 (we tend to overestimate the first one based on how it is written)
• Most likely you multiplied the first few numbers in the sequence and then estimated your final answer based on that.
• Most likely due to the Primacy Effect

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