Teaching Critical Thinking in a Statistics Course Prabha Betne LaGuardia Community College Mathematics Department November 18, 2006 NYSMATYC Region IV Conference

Why Critical Thinking? "Learning without thought is labor lost. Thought without learning is perilous." Confucius

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.

How to develop critical thinking? Regularly engage students in the process of thinking critically by means of Exercises Class discussions Reading assignments Writing assignments

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?

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.

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.

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.

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.

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?

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.

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

Assessment Pre Test and Post Test

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.

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 33 rd street station. You want to decide which of the two choices is more sensible.

Pre – test: (Continue) You collected data on your commute time (in minutes) for each choice on 10 different days. E-train: train:

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.

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.

Pre – test: (Continue) Have prostate cancer Do not have prostate cancer Positive test result (+) Negative test result (-) 2050

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?

Post – test (Also had four questions) 1.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.

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.

Questions ? Workload? Time? Class size? Other?

Thank you