Teaching Critical Thinking in a Statistics Course

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Teaching Critical Thinking in a Statistics Course

• Prabha Betne
• LaGuardia Community College
• Mathematics Department
• November 18, 2006
• NYSMATYC Region IV Conference

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Why Critical Thinking?

• "Learning without thought is labor lost. Thought
  without learning is perilous."
• Confucius

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Some qualities of a critical thinker

• Think out of box
• Make decisions based on facts
• Connect to bigger picture
• Ask questions that lead to right answers
• View issues from many different perspectives
• Curiosity, etc.

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How to develop critical thinking?

• Regularly engage students in the process of
  thinking critically by means of
• Exercises
• Class discussions
• Reading assignments
• Writing assignments

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Assignments

• Example 1 (from the textbook)
• A newspaper report claims that bus stops cause
  crime because a study showed that crime rates are
  higher in cities with bus stops than in the rural
  areas that have no bus stops. What is wrong with
  that claim?

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Example 2 (from the textbook)

• A researcher was once criticized for falsifying
  data. Among his data were figures obtained from 6
  groups of mice, with 20 individual mice in each
  group.
• These values were given for the percentage of
  success in each group. 53, 58, 63, 46, 48,
  67.
• How can we say these data are made up numbers and
  not real values from the experiment? Explain.

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Example 3 (experimenting)

• Consider data values 0, 8, 10, 6, 4, 1, 0. Find
  the mean and median for the data.
• Now replace 10 with 100. Compute mean and median
  for the changed data.
• Write your comments explaining the effects on the
  values of mean and median.

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Example 4 (fundamentals)

• It possible to show that the formula for
  computing mean and computing proportion are the
  equivalent. Explain under what conditions this is
  true.

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Example 5 (expand on concepts)

• Exercise
• Replacement times for TV sets are normally
  distributed with a mean of 8.2 years and a
  standard deviation of 1.1 years.
• a. Find the probability that a randomly
  selected TV will have a replacement time less
  than 5.0 years.

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Example 5 (Continue)

• b. If you want to provide a warranty so that
  only 1 of the TV sets will be replaced before
  the warranty expires, what is the time length of
  the warranty?

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Example 5 (expand on concepts)

• As a quality control manager for a TV
  manufacturing company, you have to provide a
  warranty time for your TVs.
• a. Explain a procedure to obtain a warranty
  time? Write down the steps you will follow,
  various information you will need, and
  computations you will perform. Explain your
  reasons.

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Example 5 (Continue)

• b. Use a numerical example to illustrate your
  steps. You may use flow-chart to explain the
  steps. (Hint You may refer to exercise 13 on
  page 247 as an example to guide you. )
• c. Now solve the following exercise. Compare
  your flow-chart with part (b) of the following
  exercise and comment

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Assessment

• Pre Test and Post Test

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Pre-test

• Pre-test had four questions.
• 1. When you toss a regular coin, what is the
  chance that a head will show up? Explain the
  logic behind your answer.
• 2. When you toss two regular coins, what is
  the chance that both coins will land up head?
  Explain the logic used to answer the question.

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Pre - test (Continue)

• 3.     You go to work in Jackson heights from the
  college after finishing all the classes. You have
  choice of either taking E-train from Court Square
  station or taking 7 train from the 33rd street
  station. You want to decide which of the two
  choices is more sensible.

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Pre test (Continue)

• You collected data on your commute time (in
  minutes) for each choice on 10 different days.
• E-train 24.9 20.9 21.7 24.2 23.1
• 22.5 21.4 21.9 19.0 21.1
• 7-train 16.5 21.1 10.4 23.7 13.2
• 36.1 20.1 15.6 32.2 32.1

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Pre test (Continue)

• a.      Find the average commute times with
  E-train and with 7-train, separately.
• Considering the raw data and the averages
  obtained in part a, which choice makes more
  sense? Explain why.

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Pre test (Continue)

• 4.     Diagnostic tests of medical conditions can
  be positive ( indicates a patient has the
  condition) or negative (- indicates that a
  patient does not have the condition).
• Consider a random sample of 200
  patients, some of whom have Prostate Cancer and
  some of whom do not. Results of a diagnostic test
  called PSA (prostate specific antigen) blood test
  are shown in the table.

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Pre test (Continue)

Have prostate cancer Do not have prostate cancer
Positive test result () 110 20
Negative test result (-) 20 50
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Pre test (Continue)

• a. Study the table carefully and explain in
  your own words what information you obtain from
  the table.
• b. Based on the information from this table
  how someone who is tested positive for Prostate
  Cancer, will interpret the validity of his test
  result?

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Post test(Also had four questions)

• You have 10 letters and 10 addressed envelopes,
  one for each letter. What is the chance that one
  letter goes to the wrong envelope? Explain the
  logic behind your answer.
• 2. The following table lists the actual high
  and the one-day forecasted high temperatures (in
  degree Fahrenheit) for the month of January. What
  do the results from the table suggest about the
  accuracy of the forecasted temperatures? Explain
  the logic behind your answer using numerical
  results computed form the table.

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Outcomes pre vs. post

• Pre-test 3rd week of the classes
• The average score was 23.3 out of 50
• The scores ranged between 11 and 43.
• Post-test last week of the classes.
• The average score was 32.2 out of 50
• The scores ranged between 22 and 37.
• Post score is 8.9 points (38) above pre score.

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Questions ?

• Workload?
• Time?
• Class size?
• Other?

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Thank you