Say the colors out loud!

People demand freedom of speech as a compensation for the freedom of thought which they seldom use. -- Soren Kierkegard

Thinking and Problem Solving

• We already know how the brain acquires, perceives, stores, and retrieves information.

• Thinking, or cognition, refers to all the mental activities that are involved in understanding, manipulating, and communicating about information.

How powerful is thought?

• Tristan Lundemo, a 19-year-old epilepsy patient sits in his hospital room playing a game similar to the game Pong. He’s not using a joystick, or a controller of any kind. Lundemo has 72 electrodes attached to his scalp, recording and monitoring his brain’s electrical activity.

• Lundemo just thinks “up, up, up, or over left, left, right, and it moves.”

• It may not move mountains, but pure thought can play a video game, and is being harnessed to help patients who are paralyzed or have lost limbs improve their lives.

So what is it?• At the neurological level,

researchers believe thought arises from the unified activity of different brain areas.

• The specific pattern varies from activity to activity as we experience different thoughts and respond to changing stimuli.

• At the psychological level, thinking is the internal language of the mind, which includes several activities that are part of our abilities to reason, solve problems, and engage in intelligent behavior.– Propositional thought: expresses a

proposition or statement. Ex. “I’m happy.”

– Imaginal thought: consists of images that we can see, hear, or feel in our mind.

– Motoric thought: relates to mental representations of motor movements, such as throwing an object.

Concepts and Propositions

• Concepts: basic units of semantic memory—mental categories into which we place objects, activities, abstractions, and events that have essential features in common.– Concepts can be acquired through explicit

instruction or our own observation of similarities and differences among objects and events.

– Defined by “prototypes” or the most typical and familiar member of a category or class. We often define which category something belongs to by its degree of resemblance to the prototype.

• Prototypes are heavily influenced by personal experience and cultural conditions. For example, one person’s “terrorist” is another person’s “freedom fighter.”

Bird

Bird

Bird

Not a Bird

Concepts and Propositions

• Propositions: statements that express ideas

• Propositions consist of concepts combined in a particular way.– Ex. “college students are intelligent people”

College Students Intelligent People

College Students Intelligent PeopleAre

Concepts:

Proposition:

Reasoning• Deductive Reasoning: “top

down” reasoning, from general principles to a conclusion about a specific case.

• Logic: the strongest and most valid form of reasoning because the conclusion cannot be false if the premises are true.– Known as a syllogism: if x

occurs, then you can infer Y.– Example: If all humans are

mortal (first premise), and if Socrates is a human (second premise), then Socrates must be mortal (conclusion).

• Inductive Reasoning: “bottom up” reasoning, starts with specific facts and tries to develop a general principle.

• Inductive reasoning leads to likelihood rather than certainty.– Example: Pavlov’s dogs. Pavlov

observes that dogs salivate when approached by the experimenter, begins to think in terms of a general governing principle that eventually became the foundation of classical conditioning.

– However, inductive reasoning also gives us this scenario: Every person named Jordan who you have ever met has blue eyes, but it would obviously be inaccurate to reason that, therefore, all people named Jordan have blue eyes.

Stumbling Blocks in Reasoning- we’re not always right, after all…

• Belief Bias: the tendency to abandon logical rules in favor of our own beliefs.– All things that are smoked are

good for one’s health.– Cigarettes are smoked.– Therefore cigarettes are good

for one’s health.– Logically, this is correct if we

accept it as a syllogism. However, it is not because the first premise is factually faulty, but not because the logic is faulty.

• Irrelevant Information: – Your drawer contains 19 black

socks and 13 blue socks. Without turning on the light, how many socks do you have to pull out of the drawer to have a matching pair?

• Emotions: we often throw logic completely out the window and rely on our emotions or “trust our gut”

• Framing: the influence of wording, or phrasing, or the context in which you present information can influence decision making.– Example: Do you ask your

parents if you can borrow the car the day after you volunteered to take out the trash, or the day after your report card showed a D?

Testing for Creativity

• Now, we are going to test your creativity.– One of the major barriers to creative problem

solving is being unwilling to step outside of the usual lines of thinking when approaching a problem.

• With your table, come up with ideas for how to use an eraser in a novel way.

Functional Fixedness

• We often develop “learning sets” which are developed early-on, and maintained by the reinforcing nature of our success in using them.

• To avoid functional fixedness, we have to train ourselves to be creative, or employ the creative faculties we have.– Ex: Does your typical studying strategy work

for this class? For Math? How about your CTE class?

Creativity- a brief word• The ability to generate novel solutions to problems• Creative people are typically:

– Willing to take chances– Unaccepting of limitations– Ready to use whatever is around to create something unique– Questioning of social ‘norms’– Willing to take unpopular stands– Inquisitive– Appreciative of art, music, and other creative activities

• Convergent thinking: narrowing down to single best solution• Divergent thinking: generating multiple solutions to problems

Note that intelligence and creativity are not necessarily inclusive!!

Problem Solving: The Crow and the Trains

Stage 1: Interpret and understand

the problem.

Stage 2:Generate hypotheses or possible solutions

Stage 3:Test the solutions or

hypotheses, seeking to disconfirm one or more of them.

Stage 4:Evaluate results and,

if necessary,Revise step 1, 2, or 3

Crows and Trains• Train A leaves Baltimore for its 50-mile trip to

Washington, DC, at a constant speed of 25 mph. At the same time, train B leaves Washington, bound for Baltimore at the same speed of 25 mph. The world’s fastest crow leaves Baltimore at the same time as train A, flying above the tracks toward Washington at a speed of 60 mph. When the crow encounters train B, it turns and flies back to train A, then instantly reverses its direction and flies back to train B. The supercharged bird continues this sequence until trains A and B meet midway between Baltimore and Washington.

• What is the total distance the bird will have traveled in its excursions between trains A and B?

Problem Solving: The Crow and the Trains

Stage 1: Interpret and understand

the problem.

Stage 2:Generate hypotheses or possible solutions

Stage 3:Test the solutions or

hypotheses, seeking to disconfirm one or more of them.

Stage 4:Evaluate results and,

if necessary,Revise step 1, 2, or 3

Heuristics“rules of thumb”

• Mary is a quiet individual, reserved and shy. She is very neat and orderly. Mary’s hobbies include reading, crafting, and listening to classical music.

• Which of the following is Mary more likely to be?– A: an airline pilot– B: a salesperson– C: a librarian

Problem Solving Techniques• Algorithms: a specific

procedure for solving a type of problem that works every time used correctly

• Heuristic: a “rule of thumb” that works most of the time– Representativeness heuristic:

snap judgements about samples according to the population they appear to represent (ex. Stereotypes)

– Availability heuristic: estimates of frequency/probability of events is based on the easy availability of examples

– Analogy heuristic: refer to an earlier problem that has partial similarity, and apply that solution to a new problem (try what worked before)

Meanwhile, in the real world…

• You’re in a grocery store trying to find the horseradish.– Algorithm approach: search

every shelf of every aisle.– Heuristic approach: check the

spices, vegetables, and condiments

Factors Affecting Problem Solving

• Expertise: practice and familiarity with the type of problem reduces solution time

• Mental Set: solving a problem with an approach that was successful with a similar problem– The approach becomes a

mental set of steps to solve the problem… but we can be fooled!

• Insight: Ah Ha! A seemingly sudden perception of relationships in a new perceptual field, when actually it is the result of mental trial and error.

• Cognitive Maps: mental representations or pictures of elements in a learning situation that allow:– Latent learning: learning which

lies dormant until called upon (we don’t know we know it until we need it to solve a problem)

– Incubation: putting a problem ‘on a back burner’ and later the solution suddenly appears

What am I doing?

• Around the room are several stations.

• You and a partner will visit several of these stations, solving the problems as you go. One person per exercise should primarily function as recorder.

• On a sheet of paper record the following for each station:– Station Name– Type of thought required

• Propositional• Imaginal• Motoric

– What kind of reasoning is used: deductive or inductive?

– Did you apply an algorithm, availability heuristic, analogy heuristic or representative heuristic?

– Describe the process used to solve the problem.

Sudoku

Arc and Line

• You have one quarter of a circle. Within this circle is rectangle ABCD, which touches the edge of the circle at point D.

• Assuming that point B is located at the center of the circle, how long is diagonal line AC?5

inches5

inches

A

BC

D

Cats and Mice

• Five cats can catch five mice in five minutes.

• With that in mind, how many cats does it take to catch 100 mice in 100 minutes?

Trees on a Road

• The road you see here is lined with trees, each planted at a different time, each a different distance from its neighbor.

• Of the five trees labeled A through E here, which two trees have the greatest distance between them?

A B

C

D

E

Did a light bulb go off in your head?

• Imagine two rooms, one with three switches, and the other with three light bulbs. Each switch controls one of the light bulbs. However, because the light bulbs are in a different room, you can’t see immediately which switch controls which light bulb.

• Your task is to figure out which switch controls which light bulb. You can spend as much time as you like in the room with the light switches, but eventually you must go into the room with the light bulbs. Once you enter the room with the light bulbs, you can’t return to the room with the light switches. What’s more, after entering the room with the light bulbs, you have only thirty seconds to figure out which switch controls which bulb.

• How do you do it?

A Doorway to Paradise• Imagine that when you die, you will

find yourself in a room with two doors, one leading to eternal paradise and the other leading to eternal damnation. You can choose which door to walk through, but the trouble is that the doors are unmarked.

• Each door has a guard, and you can ask each guard one “yes” or “no” question before you make your choice. One of the two guards will always answer truthfully and the other guard will always lie. Unfortunately, there’s no way of knowing which guard is which.

• What questions should you ask one of the guards to ensure that you wind up in paradise?

Get the Marble Out of the Cup

• Four toothpicks have been arranged in the shape of a cup, as in the diagram to the right. A marble has been placed inside the cup. By moving only two toothpicks, see if you can reposition the cup so that the marble is no longer in it. (yes, it should still look like a cup)

Counting on a Formula

• The numbers below are arranged according to a particular formula:1

11

21

1211

111221

312211

• Can you figure out the formula? What is the next term in the sequence?

Connect the Dots

• Nine dots are arranged in a grid, as in the diagram to the right.

• Draw four straight lines without lifting your pencil from the paper so that the lines pass through each dot.

Water Jugs: With a Vengeance

• In the film Die Hard: With a Vengeance, the characters played by Bruce Willis and Samuel L. Jackson have to defuse a bomb by pouring exactly four gallons of water into a jug. Their challenge is that they have only a three-gallon jug and a five-gallon jug to take their measurements with.

• How do they do it?

Wolves and Lambs

• There are three lambs and three wolves on the left bank of a river. There is a rowboat on the left bank that can carry up to two animals at a time. All six animals want to get to the right bank of the river. However, if there are ever more wolves than lambs on either bank of the river—even if the wolves remain in the boat—the wolves will eat the lambs. The boat cannot cross the river on its own: it needs at least one animal rowing it. How can all animals get across the river without anyone being eaten?

Discount river cruise… right…

Run That Race

• If you are in a race and you pass the person in second place, what place will you be in?

Follow the Sequence

• What is the next number in the sequence?

1,1,2,3,5,8,…

• Do you know the name of this type of sequence?

A Family Fishing Expedition

• Two fathers and their sons go fishing. Each person on the fishing trip catches a fish. In total they catch three fish. How is this possible?