Critical Thinking

What do we learn?

• Data• information• Knowledge• Wisdom• Intelligence• Power (making right decisions)• Experiences of success• Boosted self-esteem and self-confidence

What’s involved in critical thinking?

• Logical operations • Reasoning• Problem-solving • Decision-making• Meeting challenges in new scenarios• Transfer knowledge and skills in different

social and cultural context.

Sense vs. sensibility• While at the funeral of her own mother, a

woman met a man who she did not know. She thought he was 'amazing'. She believed him to be her dream partner so much that she fell in love with him right there, but never asked for his number and could not find him. A few days later she killed her sister.

Question: What was her motive for killing her sister?

Sense and Sensibility• Answer:

She was hoping the guy would appear again at her sister's funeral.

If you answered this correctly, you think like a psychopath. This was a test developed by a famous American psychologist, used to test if one has the same mentality as a killer.

Many arrested serial killers took part in the test and answered the question correctly.

Which way is the bus below traveling, left or right?

Can you justify your answer?

How do you use unmarked 3-liter and 8 liter pails to produce 4-liter water?

For a 3 x 3 matrix, fill the cells with digits 1 through 9 so that each row, column, and

diagonal yields the sum of 15.

Can critical thinking be taught?

• Students should be given time to practice, instead of being spoon-fed or being engaged in rote learning. (Drill is different from practice.)

• Students should be challenged constantly with problems and new scenarios.

• Can IQ scores be used to assess critical thinking skills?

Inductive thinking/reasoningSay this Not this

Look at how those people are behaving. They must be mad. Those people are all mad.

All of your friends are good. You can be good, too. Be good.

The base costs is XXX. The extras are XXX, plus tax at XXX. Overall, it is great deal at YYY.

It will cost YYY. This includes XXX for base costs, XXX for extras and XXX for tax.

Heating was XXX, lighting was YYY, parts were ZZZ, which adds up to NNN. Yet revenue was RRR. This means we must cut costs!

We need to cut costs, as our expenditure is greater than our revenue.

 

 

Deductive Thinking/reasoning

Say this Not thisGravity makes things fall. The apple that hit my head was due to gravity.

The apple hit my head. Gravity works!

They are all like that -- just look at him!

Look at him. They are all like that.

Toyota make wonderful cars. Let me show you this one.

These cars are all wonderful. They are made by Toyota, it seems.

There is a law against smoking. Stop it now. Stop smoking, please.

 

 

Reasoning – Who is the liar?

Four friends – Andrew, Barbara, Cindy, and Daniel – were shown a number. Here is what they had to say about that number:

Andrew: It has two digits.Barbara: It goes evenly into 150.Cindy: It is not 150.Daniel: It is divisible by 25.

It turns out that one (and only one) of them is lying. Which one is it?

• Reasoning: Daniel is the liar.• If Andrew were lying, the number would have three digits. (It

couldn’t have just one digit, because then it couldn’t be divisible by 25, and Daniel would also be lying.) But if the number had three digits, either Barbara or Cindy would have to be lying, because 150 is the only three digit number that goes evenly into 150. Therefore Andrew must be telling the truth, because there can only be one liar.

• If Barbara were lying, then the number does not go into 150. But then either Andrew or Daniel must be lying, because the only two-digit numbers that are divisible by 25 (25, 50, or 75) all go evenly into 150. So Barbara must be telling the truth.

• If Cindy were lying, then the number would be 150. But then Andrew would also have to be lying because 150 has three digits, not two. And we know Andrew is telling the truth.

• So the only possibility left is that Daniel is the liar, and this works out. If the number were 10, for example, Daniel would be lying, but the other three statements would all be true.

Learn to be observant

• Can problems be solved by observations? The fact that the Earth moves around the sun cannot be observed without other measurement.

• Learn to be observant• The Texas Vet school• Wizards page: http://www.wennberg.net/mathias/fun/cave_of_magic/

What is the square root of 12345678987654321?

• 11^2 = 121• 111^2 = 12321• 1111^2 = 1234321• • • • • 111111111^2 = 12345678987654321

Three jars of marbles

• Three jars of marbles being mislabeled as “Black,” “White,” and “Mixed”, how can you tell which is which by taking out one marble from these jars?

W M B

Microsoft question:

• 3 switches in one room to control 3 bulbs in the next room. You are allowed to visit each room only once. How can you decide which switch controls which bulb? You are not restricted to how much time you can linger in the room.

How long does it take you to become a billionaire?

• If you are given a penny on the first day and your allowance is doubled in the following days, cumulatively how many days does it take you to have over $1 billion?

Bunnies and chickens

• Bunnies and chickens are placed in the same yard. There are 50 heads, but there are 160 legs. How many chickens are in the yard?

The PowerPoint Timer challenge

• Can you create a timer in PowerPoint that will alert you with a sound after five minutes?

How many months are there in a year that have 28 days?

• A. One• B. Five• C. Depends• D. Twelve

Common SenseThe most salient common sense knowledge concerns situations

that change in time as a result of events. The most important events are actions, and for a program to plan intelligently, it must be able to determine the effects of its own actions.

• When you encounter a con man, what do you do?

• When someone points a gun at your head, what do you do?

• When you have a car accident, what do you do?

Street Smartness

• When you are lost in the wild to survive on your own, you need to drink water. You find a stream but you feel the water is not good for drinking. What would you do?

Scramble State Names

• Can you scramble two states’ names and come up with the names of two other states?

• South Carolina and North Dakota• South Dakota and North Carolina

Recover the stained invoice

• An invoice was stained by dark ink and pieces of information became messed up.

Product: Vacuum Cleaner – Model 1300ATotal units: 253Unit price: $?Total price: $?52

• The unit price should be between $50 and $100.

• Can you solve the problem with MS Excel?

Magic Pyramid• Place the numbers 1,

2, 3, 4, 5, and 6 in the circle shown left.

• Only one number may be placed in a circle and all the numbers must be used.

• The sum of each side’s three numbers must be equal.

Reasoning and Steps – Magic PyramidA B C A+B+C1 2 3 61 2 4 71 2 5 81 2 6 91 3 4 81 3 5 91 3 6 101 4 5 101 4 6 111 5 6 122 3 4 92 3 5 102 3 6 113 4 5 123 4 6 134 5 6 15

The missing square puzzle

The missing square puzzle

The missing square puzzle

Explanations to the missing square:

• The red triangle has a ratio of 8:3 while the blue triangle has a ratio of 5:2. This means these two hypotenuse lines do not have the same gradient. So the apparent combined hypotenuse in both Triangle 1 and Triangle 2 are actually bent. In other words, the hypotenuse in the red triangle is not parallel (in the same straight line) as the hypotenuse in the blue triangle for both Triangle 1 and Triangle 2.

• Note the grid point where the red and blue hypotenuses meet in Triangle 1, and compare it to the same point in Triangle 2; the edge is slightly over or under the mark. Overlaying the hypotenuses from Triangle 1 and Triangle 2 results in a very thin parallelogram with the area of exactly one square, the same area “missing” from Triangle 2.

Which of the following designs cannot be folded into a cube?A B

C

DE

Draw VENN Diagrams for the following:

A. All ice creams are dairy products and all dairy products are food.

B. Some rockets use liquid fuel, some rockets use solid fuel, and the space shuttle uses both liquid and solid fuel.

C. All whales and all dogs have hair. All snake do not have hair.

D. Flies are insects and beetles are insects.E. Some mammals can fly and some insects can fly.

Insects

FliesBeetles

mammals Can fly Insects

Dairy products

Ice Cream

Food

LiquidFueled rockets

Snakes

Space Shuttle

SolidFueled rockets

Has hair

DogsWhales

Has no hair

A B

C

D

E

Resources

• Crystal ball Web site: www.mysticalball.com• Wizards page: http://www.wennberg.net/mathias/fun/cave_of_magic/

• http://thiscoolpage.blogspot.com/2007/11/missing-square-puzzle.html

• How to teach critical thinking (Dan Willingham)• EducationalLearningGames.com