Transcript Importance of History of Mathematics in Math Learning

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.
 x ?  ? # of ' yes' out of ' n'
n
n
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 33rd 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: 24.9 20.9 21.7 24.2 23.1
22.5 21.4 21.9 19.0 21.1
7-train:
16.5
36.1
21.1
20.1
10.4
15.6
23.7
32.2
13.2
32.1
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)
Positive test
result (+)
Have
prostate
cancer
Do not have
prostate
cancer
110
20
Negative test 20
result (-)
50
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