Becoming a Teacher of Statistics

Portfolio

by

Susan Sexton

 

Statistical Task

 

 

Probability and Statistics for Secondary Teachers

STAT 6070

University of Georgia

Fall 2007

Instructor: Christine Franklin

 

 

 

Telepathic Tasks

            Begin by telling the students you have noticed recently a unique telepathic ability that you have somehow acquired over time. Tell them you are going to demonstrate this ability. Let the students know that you are thinking of a two digit number 1 through 50 in which both digits are odd but different than each other. Provide an example such as 15 and a counter example such as 11. After a moment of apparent thinking, inform the students that you will write down the number on your notepad and will try to telepathically communicate the number to them. For dramatic emphasis, write down 37 then cross it out and write down 35 and state the second number would be a better choice (without telling them the numbers).

            Next ask the students to write down the first number that comes to their mind and have them quickly write their number on a sheet of paper to turn in. Now ask for students to identify themselves if they chose 37. Then ask if any chose 35, the real number written down. Verify this for the students by showing them the notepad.

            Next ask a couple of students to tally up the class results on the board. Once the tallies are displayed, ask the students if they think they can reason how you have been able to get in touch with your telepathic side over the years. Once the students are able to see that the sample space of the two digit numbers with the stated characteristics is very small (only 8) then the likelihood of correctly guessing two out of those eight would seem high. Furthermore, check to see if any students wrote 15, which probably would have been eliminated when provided as an example.

            Using the tallies on the board, ask whether or not the students think their responses are representative of a larger group of people, say all statistics students who engage in the same demonstration. Then have the students simulate the activity using a random number generator. They need to carefully identify their simulation procedure. How close were the simulated results to that of the class? Why is it different, why is it similar? What would happen for an even larger sample?

 

Source:

Bates, J. (1991). Teaching hypothesis testing by debunking a demonstration of telepathy. Teaching of Psychology, 18(2), 94–97.

            This motivator is adapted from Bates (1991) who describes a telepathic demonstration he did with his students to introduce hypothesis testing. He used three demonstrations including number guessing as discussed above, guessing two images, and inviting an informed colleague to help demonstrate supposedly telepathic abilities. He then required his students to hypothesize, in groups, how he was able to correctly guess many of the answers.

 

Follow-up Activity

A classic experiment to detect ESP (extrasensory perception) uses a shuffled deck of cards containing five suites (waves, stars, circles, squares, and crosses). As the experimenter turns over each card and concentrates on it, the subject guesses the suit of the card. Using, instead, a standard deck of playing cards, find the ace of hearts, the ace of clubs, the ace of diamonds, the ace of spades, and one joker.

a.     What is the probability that someone who lacks ESP will correctly guess the suit of the card? (1/5)

b.     How will this compare to someone who truly has ESP?

      (the person with ESP will have a greater probability)

c.     Have each person try their hand at ESP with the 5 cards 5-10 times with each member of your group. (note: If two group members, simulate 10 times, if 3 to 4 group members, simulate 5 times.)

1.     Tally up the individual and group results separately.

2.     Now have each person in your group simulate the activity 20 times using the random number generator on your calculator. Make your procedure clear so that someone can follow what you did.

d.     Do you think any of your group members have ESP? Explain why or why not.

 

Source:

Moore D. (1991). Statistics: Concepts and controversies (3rd ed.). New York: W. H. Freeman and Company.

This problem is adapted from Moore (1991). The intent of the original problem is to introduce hypothesis testing. However, as an extension to the telepathic number activity, this has been modified to reinforce ideas discussed in the motivation activity.

 

 

 

Concepts embedded within the task

Sample Space:

            By determining which two digit numbers from 1 through 50 have both digits odd and distinct from one another, the students can either be introduced to or reinforced with the idea of sample space.

 

Independence:

            By determining the probability that each two digit number have equal opportunity to occur one out of eight times, the teacher can discuss independence of the digits and how one studentsÕ decision to pick a number is independent of another (regardless of the ESP/telepathy involved!). Furthermore, the idea of dependence can be discussed since the number 15 was introduced as an example two digit number.

 

Probability:

            Students will also be able to reason about the probability of picking one of the eight two digit numbers.

 

Statistic and Parameter:

            Students can begin to understand how their probabilities will represent the class (a sample) in relation to the entire set of statistics students completing the activity.

 

Randomization:

            The idea of randomization can be discussed when students begin to simulate the activity, especially since 15 is not factored into the calculatorÕs Òmind.Ó

 

 

 

 

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