Zen Master:
Let’s Get Centered
Learning Team and
Math Teacher Leader Seminar
February 12, 13, 22, & 23, 2008
Henry Kepner
Kevin McLeod
DeAnn Huinker
Connie Laughlin
Karen Corlyn
Lee Ann Pruske
Paige Richards
Mary Mooney
Session Goals
- Examine Part III – Analyze Data
of the GAISE Framework for Statistical Problem Solving.
- Examine the center, spread,
and shape of data. - Explore measures of central tendency.
A Framework for
Statistical Problem Solving
GAISE Report (2007)
- Formulate Questions
- Collect Data
- Analyze Data
- Interpret Results
GAISE: Guidelines for Assessment and Instruction in Statistics Education
MTL Survey Question
How many years of experience do the Math Teacher Leaders (MTL) have teaching as licensed teachers in MPS?
MTL Results:
Years Teaching in MPS
What does and what doesn’t each number tell you about the MPS teaching experience of MTLs?
Mode 6 years
Median 10 years
Mean 12.3 years
(January 2008, n = 109)
Are You Typical?
In MPS there are:
4,793 teachers
(job class 5105)
58,414 combined years of teaching experience
Mode 5 years
Median 10 years
Mean 12.19 years
“Appropriate Centers”
Directions
1.Remove a card from the envelope and read it to the table group.
2.Decide on the most appropriate measure of central tendency: mean, median, or mode.
Why do you consider it to be
the most appropriate measure?
3.Pass the envelope, repeat with a new card.
How’s Berty Doing?
At a parent-teacher conference, Bertrand’s parents ask how he is doing in math. As part of her answer, his teacher looks in her grade book and finds 5 of his quiz scores so far that semester. How could she best use this data to inform Betrand's parents?
Food Survey
Ms. Mercedes’ class took a survey of the students’ favorite foods in their classroom. They wondered what kind of food was most popular among the class.
This is what they found:
7 pizza
3 shrimp
10 chicken
6 tacos
1 hamburger
4 spaghetti
Shoe Sale
Stella’s Shoe Shoppe is having a winter blow out sale on all remaining shoe inventory. What is the most typical shoe size for sale?
size 510 pairs
size 616 pairs
size 79 pairs
size 84 pairs
size 98 pairs
size 103 pairs
size 1114 pairs
Moon River Tax Rates
As an assessor for the town of Moon River, what measure of center would you use to determine a fair property tax rate?
House Values
You are thinking of buying a house in Moon River and you would like to know the typical price of a house.
Walk Away:
Mathematical Ideas
Key Understanding:
The best descriptor of the center of a numerical data set (i.e., mean, median, mode) is determined by the nature of the data and the question to be answered.
Same Median, Different Mean
Nine teachers reported their
years of experience as follows:
7, 5, 5, 4, 6, 8, 7, 6, 6
Arrange cubes to represent this data set. What is the median? the mean?
Rearrange cubes to represent possible data sets for the following samples. You may add or remove cubes. Record each data set and its mean.
Another sample of 9 teachers also had a median of 6 years experience, but the mean was less than 6.
Yet another sample of 9 teachers had a median of 6 years experience, but the mean was greater than 6.
Record each data set and its mean.
Consolidate ideas…
What changes occurred in the data set that allowed you to keep the median but change the mean?
To lower the mean…
To increase the mean…
Milwaukee Public Schools
Mathematics Framework
Big “Statistical” Ideas
- When analyzing data, key features of the data are measures of center, spread, and shape.
- The question affects the choice of measure of central tendency.
- The median is a more robust measure of central tendency.
- The mean is more influenced by outliers.
Developed by the Milwaukee Mathematics Partnership (MMP) 1
with support by the National Science Foundation under Grant No. 0314898.