Cognitive Reflection Test -- Math Competition

Daniel Kahneman, as a psychologist, who won an economics Nobel Prize. In Thinking, Fast and Slow, Kahneman wrestles with flawed ideas about decision making. He separates the way we make decisions into two systems.

 

System 1 “is the brain’s fast, automatic, intuitive approach, System 2 “the mind’s slower, analytical mode, where reason dominates.” Kahneman says “System 1 is...more influential…guiding…[and]...steering System 2 to a very large extent.” The measurable features of System 1 and System 2 cut across prior categories. Intuitive information-processing has typically been considered irrational, but System 1’s fast thinking is often logical and useful (“intuition is nothing more and nothing less than recognition”). Conversely, despite being conscious and deliberate System 2 can produce poor (sometimes irrational) results.

 

Math is a second nature skill, requiring much System 2 training (before becoming a System 1 skill). Also, we evolved to often act without System 2 consciously deciding (habits are triggered by System 1)

 

The following questions are known as the Cognitive Reflection Test. They come from the paper, "Cognitive Reflection and Decision Making by Shane Frederick” (2005).


Can you answer them correctly?

 

  1. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost? _____ cents

2. If it takes 5 machines 5 minutes to make 5 balls, how long would it take 100 machines to make 100 balls? _____ minutes

 

3. In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake? _____ days

Give it a try before reading the answers.

In a survey of 3,428 college students, an astonishing 33 percent missed all three questions. Most people–83 percent–missed at least one of the questions. Even very educated people made mistakes. Only 48 percent of MIT students sampled were able to answer all the questions correctly.

 

How do you compare?

How many did you get right? Compare your score to the below averages (# correct of 3 questions) for various colleges:

 

Massachusetts Institute of Technology: 2.18

Princeton University: 1.63

Harvard University: 1.43

Web-based studies: 1.10

Michigan State University: 0.79

 

The Solutions.

 

For question #1, one might intuitively say, “$1.00 plus $0.10 is $1.10, therefore a ball costs $0.10“. While this is quite intuitive, it is also incorrect. A person who is more thorough might respond that the ball actually costs $0.05 (.05+(1+.05)=1.1). The correct answer is the ball costs $0.05.

 

For question #2, an intuitive response would be that “5=5=5 so 100=100=100“. However, if it takes a single machine 5 minutes to make a single widget, even a million machines can make a million widgets in 5 minutes. The correct answer is therefore 5 minutes.

 

For question #3, the common intuitive response would be, “half the pond would be covered in half the time, so 48/2=24 days“. However, this ignores the exponential growth of the lily pads. Try working it backwards, if the pond is covered after 48 days, and they double in size every day, then day 47 would be half covered. The correct answer is 47 days.

 

Try these additional logic questions:

 

4. Thomas is ranked both the fifteenth highest and fifteenth lowest in his class? How many students are in the class? 

 

15, 25, 29, 30, 31, or 32

 

Solution: 29 = 14 + 14 + 1 

 

5. With the digits 1 2 3 4 5 6 7 8 and 9, make them add up to 100. They must stay in the same order. You can use addition, subtraction, multiplication, and division. Remember, they have to stay in the same order.

 

Solution: 1+2+3+4+5+6+7+ 8x9=100;  28 + 72 = 100

 

The intuitive brain is so powerful even though we do not get much positive feedback from making intuitive-based decisions. To develop your system one capabilities, you need to slow down and check your answers with facts, data, and calculation.

 

 

NOW, HAVE SOME FUN WITH THE NOETIC LEARNING MATH COMPETITION QUESTIONS. TAKE THE 2ND, 3RD, 4TH, OR 5TH GRADE CHALLENGE FOR SPRING 2017. DO NOT WORRY ABOUT TIME. AFTER YOU FINISH ALL 20 QUESTIONS, SELF-GRADE IN PEN AND ENTER YOUR SCORE ON THE FRONT (FOR EXAMPLE, IF YOU GOT 12 QUESTIONS CORRECT, ENTER 12/20).

 

I gave the children their appropriate grade level tests and some of them the next grade level test but they should feel free to try additional tests as they feel comfortable. Go system 2!!!


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Cognitive_Recognition_Tests_and_Noetic.pdf64.88 KB
Noetic_spring_2017_2nd_with_answers.pdf1.21 MB
Noetic_spring_2017_3rd_with_answers.pdf1.22 MB
Noetic_spring_2017_4th_with_answers.pdf1.28 MB
Noetic_spring_2017_5th_with_answers.pdf1.21 MB