Transcript MELT 2015 Wednesday - MELT-Institute

MATHEMATICS EDUCATION
LEADERSHIP TRAINING:
“MEASUREMENT & STATISTICS: 6-8”
Carmen Wilson, Ashe County HS
[email protected]
June 22-26, 2015
“SELECTING & CREATING
MATHEMATICAL TASKS”
In 1972, 48 male bank supervisors were each given the
same personnel file and asked to judge whether the
person should be promoted to a branch manager…The
files were identical except that half of them showed that
the file was that of a female and half showed that the
file was that of a male. Of the 24 “male” files, 21 were
recommended for promotion. Of the 24 “female” files,
14 were recommended for promotion.
(B. Rosen & T.Jerdee (1974). “Influence of sex role stereotypes on personnel
decisions”, Journal of Applied Psychology;59:9-14.)
What is Random?
Jelly Blubbers!
3 second glance:
Pick 10:
Number
Diameter (mm)
3 second glance:
Pick 10:
Simple Random Sample of 10:
Number
Diameter (mm)
3 second glance:
Pick 10:
SRS of 10:
Yesterday, we discussed
measurement bias.
Today, we see that there can also
Be sampling bias.
Let’s watch a clip from the past…
(Moore, D. Decisions Through Data (1993). COMAP)
Types of Samples:
•
•
•
•
•
•
•
Convenience Sample
Voluntary Response Sample
Systematic Random Sample
Simple Random Sample
Stratified Random Sample
Cluster Sample
Multi-Stage Sample
Can you identify any possible sources for bias here?
A marketing research company was asked to
Determine how much money teenagers
Spend on recorded music. The company
Randomly selected 80 malls around the
Country. A field researcher stood in a
Central location in the mall and asked
Passers-by who appeared to be teens to fill
Out a questionnaire. Based on 2050
Completed questionnaires, the company
Reported the average amount spent to be
$255 per teen per year.
Jelly Blubbers is like the
Random Rectangles activity…
Heads or Tails?
Some Simulation Sites:
http://www.shodor.org/interactivate/activities/Coin
/
https://www.random.org/coins/
http://mathforum.org/mathtools/cell/m4,6.14,ALL,A
LL/
Mystery Dice: What’s in the Bag?
How do we calculate theoretical
probabilities ?
Experiment 4 from Probability
Activities by Key Curriculum Press:
A more challenging problem…
(from AP Statistics 2009B Free Response #2, College
Board)
ARE YOU STILL THINKING ABOUT
WHETHER THOSE WOMEN WERE
VICTIMS OF DISCRIMINATION?
In 1972, 48 male bank supervisors were each given the
same personnel file and asked to judge whether the
person should be promoted to a branch manager…The
files were identical except that half of them showed that
the file was that of a female and half showed that the
file was that of a male. Of the 24 “male” files, 21 were
recommended for promotion. Of the 24 “female” files,
14 were recommended for promotion.
(B. Rosen & T.Jerdee (1974). “Influence of sex role stereotypes on personnel
decisions”, Journal of Applied Psychology;59:9-14.)
Let’s keep playing…
How about a game of Greedy Pig?
Round
1
2
3
4
5
TOTAL
Points
Chuck-A-Luck
A player chooses a number
from 1 to 6. Three dice are
rolled. If the player’s number
appears…
3 times – win $3
2 times – win $2
1 time – win $1
0 times – lose $1
What could you EXPECT to happen if
you played Chuck-A-Luck MANY
TIMES?
Justify your answer.
Some “classic” counting problems:
• The Birthday problem…
• Playing the Lottery…
Pick 6/49
In 1972, 48 male bank supervisors were each given the
same personnel file and asked to judge whether the
person should be promoted to a branch manager…The
files were identical except that half of them showed that
the file was that of a female and half showed that the
file was that of a male. Of the 24 “male” files, 21 were
recommended for promotion. Of the 24 “female” files,
14 were recommended for promotion.
(B. Rosen & T.Jerdee (1974). “Influence of sex role stereotypes on personnel
decisions”, Journal of Applied Psychology;59:9-14.)
Student Misconceptions…
“Both Answers Make Sense!”
Lockwood, E. (2014) Mathematics Teacher.
Vol. 108, No. 4, 297-299.
For a more in-depth explanation:
http://combinatorialthinking.com/
Time for Reflection…
Classwork/Homework
• EXIT Ticket
• For Tonight: Read “Orchestrating
Discussions”
• For Friday: Prepare to Share
Bibliography for Tuesday:
Burrill, G., Franklin, C., Godbold, L., Young, L. (2003).
Random Rectangles. Navigating through Data
Analysis in Grades 9-12. Reston: NCTM.
Crites, T. & St. Laurent, R. (2015). Putting
Essential Understanding of Statistics into
Practice in Grades 9-12. Reston: NCTM.
Foley, G. (2009). QUANT (Quantifying Uncertainty &
Analyzing Numerical Trends. Columbus: Ohio
Resource Center.
Lockwood, E. (2014) Mathematics Teacher.
Vol. 108, No. 4, 297-299.
Lovell, R. (1993). Probability Activities For Problem
Solving & Skills Reinforcement. Berkely: Key
Curriculum Press.
Moore, D. (1993). Decisions Through Data. DVD.
COMAP.
Moore, D. (2005). “Jelly Blubbers Activity”. Statistics,
Concepts and Controversies, 4th Edition. New York:
W. H. Freeman.
Scheaffer, R. (1996). Activity Based Statistics. New
York: Springer-Verlag.
Smith, M., Hughes, E., Engle, R. & Stein M. “Orchestrating Discussions”. (2009). Mathematics Teaching
in the Middle School, Vol. 14, No. 9, 548-556.
Smith, M. & Stein, M. “Selecting and Creating
Mathematical Tasks: From Research to Practice”.
(1998). Mathematics Teaching in the Middle School,
Vol. 3, No. 5, 344-349.