Problem Solving

8.2

Algorithms and Heuristics

• Different problems must be approached in different ways – first we must identify the type of problem

Algorithms

• When used properly will always lead you to the answer– Formulas in math

• Figuring diameter of a circle

– Systematic Searches – Practicality

Heuristics

• Ha__ __ man– Around 300 possibilities!

• Phone numbers

• Heuristics – rules of thumb– Wheel of Fortune

• Likelihood of letters» Heuristics are faster but less reliable

Problem Solving Methods

• Trial and Error

• Difference Reduction– Problem A (Fig. 8-1) A Step Backward

• Means-End Analysis– Certain things we can do (means) will have

certain results (ends)– Break the problem into parts

PSM

• Working Backward– Identifying the goal first

• Analogies– Archimedes and the crown – “Eureka!”

1.) BIRD : NEST :: (A) dog : doghouse(B) squirrel : tree(C) beaver : dam(D) cat : litter box(E) book : library

2.) DALMATIAN : DOG :: (A) oriole : bird

(B) horse : pony(C) shark : great white

(D) ant : insect(E) stock : savings

3.) DOCTOR : HOSPITAL :: (A) sports fan : stadium

(B) cow : farm(C) professor : college

(D) criminal : jail(E) food : grocery store 4.) CUB : BEAR ::

(A) piano : orchestra(B) puppy : dog(C) cat : kitten

(D) eagle : predator(E) fork : utensil

5.) TENET : THEOLOGIAN ::(A) predecessor : heir

(B) hypothesis : biologist(C) recluse : rivalry

(D) arrogance : persecution(E) guitarist : rock band

Answers

• C

• A

• C

• B

• B

Insight and Incubators

• Insight – sudden understanding– Sometimes the answers reveal themselves to

us without much conscious awareness– Light bulb Effect

– Incubation Effect– Kohlers Chimps

• Boxes, sticks, and bananas

– Insight and jokes– Extreme problems and incubation

Obstacles

• Mental Set – our minds become fixed on a a solution process that has worked previously

• Functional Fixedness – Think of objects in the way they are usually used

Problem Solving and Creativity

• Convergent Thinking – Narrowing of the mind to find the single best solution

• Divergent Thinking – Associating freely to various elements, following “leads”

ABCDE’s of Problem Solving

• Assess

• Brainstorm

• Choose the approach

• Do it

• Evaluate

Reasoning

• Reasoning – using information to reach conclusions– Deductive Reasoning – The conclusion is true

if the premises are true• Premise – Idea or statement that provides

information that allows us to draw conclusions

– Inductive Reasoning – We reason from individual cases or particular facts to reach a conclusion

• Sometimes, said conclusion is wrong

Inductive Reasoning

• Confirmation Bias – we spend time trying to prove a hypotheses true, rather than false

» Things must be looked at from different angles and approaches to be proven

Decision Making

• Weighing the pluses and minuses– Balance sheets of pros and cons

• You must take your abilities into account

Shortcuts

• …just another word for heuristics, and I mean, seriously, who didn’t already know that?

• You didn’t? Really? Did you read the section? You did? Are you sure? Yeah, I kind of thought so…or…I’m sorry you didn’t remember that part.

Representativeness Heuristic

• T/F Quiz– What represents a random sequence?

• Making decisions about a sample based on the population that the sample appears to represent

Availability Heuristic

• Making decisions based on what is available to your immediate consciousness– Overestimations of the occurrence of events

Anchoring Heuristic

• Making decisions based on certain standards or ideas they hold– Common anchors – religion, politics – Making adjustments to anchors

Framing Effect

• How wording affects decision making– Lite v. Thin– Pro v. Anti

Overconfidence

• Why do people tend to be overconfident even when they are wrong?