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 concept2. Natural concept3. Prototype

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 polygon is…

• Natural concept—Eleanor Rosch said these form from everyday experience and do not have boundaries that are sharply defined – Name some mammals…

Concept Hierarchy

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

Concept Hierarchy

Prototype

• A typical best example incorporating the major features of a concept

• 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.

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

• Example: “I” before “E” except after “C”• They simplify the problem because they let you

reduce the number of possible solutions. (Use the index to find a topic)

• These can be handy shortcuts, or they can get us into trouble. (What if topic not in the index?)

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• “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 – perceive a pattern in the info but not consciously. Perception formed from your areas of expertise.

2. Integrative Stage – the pattern is now in the consciousness and you try to prove or disprove your 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 scissors

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

Problem Solving and ComputersMode Confusion

• Play “Cockpit Confusion” (11:14) Segment #11 from Scientific American Frontiers

• Mode Confusion for pilots.• When we rely too much on computers

Mental Set

• A tendency to approach a problem in a particular way

• 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

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)

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•Rare events can cause us to overestimate the likelihood of reoccurrence. (i.e plane crashes)

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

can recall previous occurrences of that event

• Most will overestimate deaths from natural disasters because disasters are frequently on TV

• Most will underestimate deaths from asthma because they don’t make the local news

Representative Heuristic• Estimate the likelihood of an event by comparing how similar its

essential features are to our prototype of the event. • Example: Because Ken is 6‘6“, people often mistakenly assume

that he must be a member of his college's basketball team• Can be false if…

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

• Most will overuse this strategy

Bias Effects

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

• Belief bias—accept only information that conforms to beliefs

• Fallacy of positive instances—remember uncommon events that confirm our beliefs

• Overestimation—tendency to overestimate rarity of events

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?

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?

Belief Perseverance

• The tendency for our preexisting opinions to distort our sense of whether a particular conclusion is logically valid

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

• the best advice to give people who want to avoid belief perseverance is: “Consider the Opposite”

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

2. Find useful analogy3. Represent information efficiently4. Find shortcuts5. Establish sub-goals6. 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