Thinking & Problem Solving

Thinking

Thought• Cognition—mental activities involved in

acquiring, retaining, and using knowledge• Thinking—manipulation of mental

representations to draw inferences and conclusions.

– Mental processes directed at a goal or purpose.– 2 kinds of mental representations:1. Mental image—representation of objects

or events that are not present2. Concepts – mental category we form to group

objects, events, or situations that share common characteristics or features.

Mental Image

• Mental Image – mental representation of an object or event not physically present.

• Mental imaging works similar to actual visual imaging.

• Mental images are constructed and therefore subject to error.

• Steven Kosslyn had people memorize a map of an island and then asked them to imagine specific areas.

• People took time to mentally scan their mental image and find the different locations.

• People took the same amount of time to mentally scan the image as they did to visually scan it.

Concepts

• Concept—mental category we form to group objects, events, or situations that share common characteristics or features.

• Three Types of Concepts:1. Formal concept

2. Natural concept

3. Prototype

Concept Hierarchy

• A means to keep mental information organized from basic concepts to specific ones

• Move from basic category to more specific subordinate categories.

Concept Hierarchy

Examples of Concepts• Formal concept— rigid rules or features that

define a particular concept. – All or nothing categorization process

• Categories for solid, liquid, or gas • A square is…

• Natural concept—Eleanor Rosch said these form from everyday experience and do not have boundaries that are sharply defined – Members of these share a kind of “family resemblance”

that helps us to recognize items that belong in the same category, even if they are not identical.

– Example: space shuttle & hot air balloon are both examples of the natural concept “aircraft”

Prototype

• A model

• A typical best example of a particular thing

• The closer a new object is to our concept prototype the easier it is to categorize it– If an object has four wheels and doors it

probably fits our prototype for…

Problem Solving•Thinking and behavior directed toward attaining a goal that is not readily available.

•Must understand the problem correctly to accurately solve it.

Kinds of Thinking

• Convergent Thinking – focused on finding a particular answer to a problem

• Divergent Thinking – Thinking Creatively to generate as many possible answers to a question or problem as you can. “Brainstorming”

• Incubation – Leave the problem for a time, allowing their minds to work on it without conscious effort. (Can led to Insight)

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

y + z = r2

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 this total, how can you determine the four

dates the person chose using an 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.

Heuristics

• A rule-of-thumb problem solving strategy that 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, or they can get us into trouble. (What about words like “weird”)

Two ways we use Heuristics

• Subgoals – divide the problem into to smaller more manageable parts– As you solve each subproblem you get closer to

solving the larger problem.

• Working Backward – determine the steps to reach your goal starting from the end point. (i.e. making a budget).

Insight• The sudden realization of the solution to a

problem – correct answer suddenly comes to us.

• “Unconscious Problem Solving” – You’re not aware of the thought process that led you to an insight.

The solutions to these problems are often characterized by sudden flashes of insight. Solutions are on page 288 in your textbook.

Intuition

• Intuition—coming to a conclusion without conscious awareness of thought processes involved

• Kenneth Bowers explains: New info is combined with existing info in the long-term memory in a two-stage process.

1. Guiding Stage – Unconsciously look for a pattern in the info. Based on your expertise and memories.

2. Integrative Stage – Pattern is now in the consciousness in the from of a hunch.

– You then try to prove or disprove your hunch/hypothesis.

Obstacles to Solving Problems

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 credit card.

•Tighten a screw without a screwdriver?

–Use a coin!

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

Mental Set

• A tendency to approach a problem in a particular way that has worked in the past

• A well-established habit of perception or thought

• The set may or may not be helpful in solving a new problem

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.

Fixation

• A mental set that hinders the solution of a problem

• One needs to think beyond the mental set to solve the new problem

Can you 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?

Decision Making

Decision Making

• Single feature model—make a decision by focusing on only one feature–Do you use this model in making decisions?

–Ever choose a date based on looks?

–Go see a movie because a friend told you it was good?

–Choose a restaurant based on price?

•Choose a class based on how easy you heard it was?

Additive Model

• Systematically evaluate the important features of each alternative.

• First create a list of factors that are important to you.

• Then rate each alternative on each factor.• What factors do you consider when

choosing a college? (See transparency chart)

TUITION COST

ACADEMIC RANKING

HOUSINGDEGREE/

PROGRAMS OFFERED

SOCIAL LIFE

TOTALS

U of M

WMU

1 = BEST 5 = WORST

Elimination-by-Aspects• Rate choices based on features. • Evaluate each alternative one characteristic at a time

staring with the one you think is most important.• Eliminate those that do not meet the desired criteria

even if they have other desirable characteristics.• Over time your alternatives will be narrowed down.• We often use this to get our options to a few and then

use the additive model to make the final decision.

Decisions Involving Uncertainty

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.

• Can be correct or incorrect

Availability Heuristic• Judge probability of an event by how easily you can

recall previous occurrences of that event• 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.

Representative Heuristic

• Estimate the likelihood of an event by comparing how similar its essential features are to our prototype or schema we already have in our mind.

• Example: Is the following person more likely to be an Ivy League psych professor or a truck driver?– A man, 5’7”, 155 pounds, who wears glasses, attends

poetry readings & enjoys classical music• Statistically, he is far more likely to be a truck driver

because there are hundreds of thousands of truck drivers and possibly only 100-200 Ivy League psych professors. – Even if 50% of professors fit the schema it still is

statistically more likely to be a truck driver.

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!

BUT YOU FORGOT IT COULD BE A…

Bias Effects

• Confirmation bias—only search for information confirming one’s belief.

• Belief bias/perseverance—accept only information that conforms to beliefs

• Self-Serving Bias – Take credit for good results and share the blame for failures.

• Self-Fulfilling Prophecy – Tendency to act in ways that will confirm your belief thereby making it come true.

Overconfidence

• The tendency to be more confident than correct when estimating the accuracy of one’s 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!

More Faulty Thinking

• Hindsight Bias• “Knew it all Along”• When we learn the

outcome of an event or solution to a problem, we are convinced the answer was quite obvious.

• Dunning-Kruger Effect• “Illusory Superiority”• People who are bad at

something often think they are good at it.

• Their incompetence keeps them from realizing they are incompetent.

Framing

• The way an issue is worded or presented can influence decisions and judgments– Do you think it is OK to kill unborn children?– Do you believe that abortion is an appropriate

option for those with unwanted pregnancies?– 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)

Belief Bias/Perseverance

• Clinging to one’s beliefs even after new information discredits the basis on which they were formed

• 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”

Self-Fulfilling Prophecy

• Rosenhan study (Famous Study #13)

• Teachers told they had “bright” students found ways to get them to excel.

1. Break mental sets – be creative! (see next slide)

2. Find useful analogy

3. Represent information efficiently

4. Find shortcuts

5. Establish sub-goals

6. Turn ill-defined problems into well-defined problems

Strategies for solving problems

Be Creative! (pg. 313-314)

• Choose the goal of creativity

• Reinforce creative behavior

• Engage in problem finding

• Acquire relevant knowledge

• Try different approaches

• Exert effort and expect setbacks