Transcript GOLO: Analyzing the Probabilities of a Dice

Working with K-12 Students to
Create a Statistics Poster
John Gabrosek and Neal Rogness
Grand Valley State University
ASA Meeting Within a Meeting Webinar
December 3, 2007
A BRIEF HISTORY OF THE ASA - NCTM
STATISTICS POSTER COMPETITION
• The first national poster competition held in spring 1990 was a joint
effort between the ASA Center for Statistics Education and the ASA
Section on Statistical Graphics.
• In the mid-1990s the ASA and NCTM assumed responsibility for the
poster competition through the ASA/NCTM Joint Committee.
• The national competition spawned numerous regional and statewide
competitions.
• Statisticians at Grand Valley State University (GVSU) have
organized a competition open to all kindergarten through grade 12
students in the state of Michigan since 2000.
(background from Young 1998 and Rogness et. al 2003).
WHAT IS A STATISTICS POSTER
• A statistics poster is a visual display that uses one or
more related graphs to summarize data, discuss different
points of view, answer question(s) about and explore
data.
EDUCATIONAL GOALS OF A STATISTICS
POSTER COMPETITION –
ASA MISSION STATEMENT
The ASA Mission Statement states that ASA should
• “work for the improvement of statistical education at all
levels.”
• “promote the proper application of statistics.”
ASA members are encouraged to use their expertise for
• “the promotion and development of statistical education
for the public and the profession.”
(http://www.amstat.org/)
EDUCATIONAL GOALS OF A
STATISTICS POSTER COMPETITION
• The NCTM Standards set out a comprehensive vision for
mathematics instruction of students from prekindergarten (age 4) through grade 12 (age 18).
• Included in the NCTM standards are content area
expectations related to statistics and probability.
(http://standards.nctm.org/)
NCTM STANDARDS
• The Data Analysis and Probability Standard indicates
that students should be able to “formulate questions that
can be addressed with data and collect, organize, and
display relevant data to answer them.”
NCTM STANDARDS
• The Data Analysis and Probability Standard indicates
that students should be able to “formulate questions that
can be addressed with data and collect, organize, and
display relevant data to answer them.”
K-3: “Have the number of hurricanes that have hit the
United States increased or decreased in the past 154
years?”
“Data was collected from the United States National
Hurricane Center website…”
NCTM STANDARDS
• The Data Analysis and Probability Standard indicates
that students should be able to “formulate questions that
can be addressed with data and collect, organize, and
display relevant data to answer them.”
K-3: “What hand should you use if you have to put beans
in a cup?”
“We gathered data from a girls club at church… They
had 15 seconds to put beans in a cup… They did this
twice, first with the dominant hand, then with the other
hand.”
NCTM STANDARDS
• The Data Analysis and Probability Standard indicates
that students should be able to “formulate questions that
can be addressed with data and collect, organize, and
display relevant data to answer them.”
10-12: “Can people tell what type of water (bottled or
tap) they chose (as best tasting)?”
“We assigned 60 subjects...to two different groups. The
first group had sample 1 as tap water and sample 2 as
bottled water. The second group had sample 1 as bottled
water and sample 2 as tap water. ”
NCTM STANDARDS
• The Communication Standard specifies that students
should be able to (1) organize and consolidate their
mathematical thinking through communication, (2)
communicate their mathematical thinking coherently and
clearly to peers, teachers, and others, and (3) use the
language of mathematics to express mathematical ideas
precisely.
NCTM STANDARDS
• The Communication Standard specifies that students
should be able to (1) organize and consolidate their
mathematical thinking through communication, (2)
communicate their mathematical thinking coherently and
clearly to peers, teachers, and others, and (3) use the
language of mathematics to express mathematical ideas
precisely.
7-9: “This research is designed to explore what kinds of
stuffed animals children of different ages and sexes play
with.”
7-9: “The length and age histogram shows the
distribution of lengths of animals. If there was a
relationship between age and animal length, the
histogram would have shown more yellow toward the
longer (right side) animals and more red toward the
shorter (left side) animals. This was not the case.”
NCTM STANDARDS
• The Representation Standard requires that students be
able to “create and use representations to organize,
record, and to communicate mathematical ideas.”
NCTM STANDARDS
• The Representation Standard requires that students be
able to “create and use representations to organize,
record, and to communicate mathematical ideas.”
K-3: “What hand should you use if you have to put beans
in a cup?”
K-3: “The dominant hand DID put more beans in the cup,
on average just like WE guessed.”
NCTM STANDARDS
• The Measurement Standard involves gaining an
understanding of measurable attributes of objects.
NCTM STANDARDS
• The Measurement Standard involves gaining an
understanding of measurable attributes of objects.
K-3: “I wanted to know how to round and learn about
categories… In math I learned how to measure in
centimeters and wanted to practice it. I have just
learned how to round to 10 and chose that as my
category.”
K-3: “I am john and I am doing a study about the stuffed
animals of our family. We have lots of stuffed animals
and they are hard to put away. Mom thinks we don’t have
too many but I think we do.”
State Mathematics Standards
• Check the state mathematics standards
for your own state
• No doubt, participation in the Poster
Competition will allow you to meet some of
your own state standards as well as the
NCTM Standards
Utah State Mathematics Standards
•
Third Grade Mathematics Standard V
–
•
Fourth Grade Mathematics Standard V
–
•
Students will construct, analyze, and construct reasonable conclusions from data and apply
basic concepts of probability.
Sixth Grade Mathematics Standard V
–
•
Students will interpret and organize collected data to make predictions, answer questions,
and describe basic concepts of probability.
Fifth Grade Mathematics Standard V
–
•
Students will collect and organize data to make predictions and identify basic concepts of
probability.
Students will analyze, draw conclusions, and make predictions based upon data and apply
basic concepts of probability.
Math 7 Standard V
–
Students will understand concepts from probability and statistics and apply methods to solve
problems.
HOW-TO CREATE A
STATISTICS POSTER
• Selecting a topic
• Determining how to display data graphically
• Communicating your message
SELECTING A TOPIC
• Brainstorm a list of possible topics as a class or in
groups of up to 4 students
Be free-thinking
Do not rush to critique any ideas
Brainstorm sources for ideas – think about national,
state, regional, local, school issues
SELECTING A TOPIC
• Critique the ideas as a class or within groups
If an idea is too broad encourage students to narrow
it down
Discuss the interest of the topic to the students
and to others inside and outside the class
SELECTING A TOPIC
• Consider how to collect data on the chosen topic
Discuss the population of interest & sampling concerns
• When the study is done, who or what is it you want to be able to say
something about?
• If data are being collected from individuals, how will these persons be
selected fairly so they represent the population of interest?
Discuss whether data will be obtained from a survey, an
experiment, the Internet, from the library, etc.
Discuss challenges with data collection
• Survey questions must be clear – pilot survey
• Experiments must be doable and repeatable – keep them simple
• Data must be obtainable to answer the question of interest
DATA COLLECTION
Baseball - This broad category must be narrowed down.
For example, students could compare the number of
home runs hit by the home run champions over the past
40 years in the American and National Leagues.
Separate graphs for each league would allow
comparison between the two leagues.
Television - A student can take a poll of students at his
school. He can ask each student "What is your favorite
type of TV show – comedy, drama, sports, etc.” If the
student also records the student’s gender (or grade), the
student can give separate bar charts for comparison.
DISPLAYING DATA GRAPHICALLY
• Goal of graphs
The reader of your poster should be able to look at the
graphs and understand the story of the data. It may be
useful to think of graphs as photos that make it easy for
your reader to visualize all of the information that you
have collected.
DISPLAYING DATA GRAPHICALLY
• Data types
Qualitative – data fall into categories or labels, such as
the league a homerun champion plays in
Quantitative – data are meaningful numbers
discrete – generally counts, such as the number of
homeruns hit by the league champion
continuous – generally measurements, such as the
weight of the homerun hitting champion
DISPLAYING DATA GRAPHICALLY
• Graph Selection
Qualitative or Discrete – bar graphs, pie charts
DISPLAYING DATA GRAPHICALLY
• Graph Selection
Continuous – histogram, stem-leaf plot, boxplot
COMMUNICATING YOUR MESSAGE
• Make sure everything on the poster is correct
• There should be one unifying message
COMMUNICATING YOUR MESSAGE
• Place materials logically on poster
COMMUNICATING YOUR MESSAGE
• Be Creative
Common Pitfalls to Avoid
• Title, variable labels, and/or value labels are not clear
and user-friendly (e.g., no legend is provided)
• Graph is incorrect for the type of data
• 3-D items are not securely attached
• Irregular-shaped posters (weigh creativity against ease
of shipment/handling)
• Topic is of marginal interest (consistent with grade level
of students)
• It is not obvious how the graphs connect
• Graphs do not provide any new information (i.e., using a
bar chart and a pie chart to relay the same information)
• Spelling and/or grammar issues
2007 ASA
Poster Competition Winners K-3
S. Carson, A. DeVito, G. Hall, A. Sahadevan, L. Starkman, and
I. Weil - Has There Been Diversity in the U.S. Presidency?
Hathaway Brown Primary School, Shaker Heights, Ohio.
2007 ASA
Poster Competition Winners 4-6
B. Tilley - Are Hybrid Cars Really More Economical?
Pine-Richland Middle School, Gibsonia, Pennsylvania
2007 ASA
Poster Competition Winners 7-9
M. Bonner - Favorite Fizz
St. Aloysius Academy, Bryn Mawr, Pennsylvania
2007 ASA
Poster Competition Winners 10-12
C. Resnik, G. Burkhardt, and A. Pfrimmer - AFC vs NFC
Peters Township High School, McMurray, Pennsylvania
2007 ASA
Poster Competition Winners 10-12
D. Tamarkin and A. Simon - Kids Vs. Adults: What They Think of
the Drinking and Driving Ages
Beachwood High School, Beachwood, Ohio
RESOURCES
For further information on creating a
statistics poster visit:
www.gvsu.edu/stat/statposter
and scroll to: Articles describing poster
creation
TIMELINE
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Jan. 15, 2008 – topic selection done
Feb. 1, 2008 – data collection done
Feb. 15 2008 – graphs done
March 1, 2008 – layout of posters
March 15, 2008 - posters done
April 1, 2008 – posters received deadline
April 19, 2008 – judging of posters
SEND POSTERS TO:
Statistics Poster Competition
American Statistical Association
732 North Washington Street
Alexandria, VA 22314
WEBSITES TO VISIT
• American Statistical Association Poster Competition
http://www.amstat.org/education/index.cfm?fuseaction=poster1
• Michigan Statistics Poster Competition
http://www.gvsu.edu/stat/statposter
• Pennsylvania Poster Competition
http://www.math.iup.edu/paposters
• Nevada Poster Competition http://www.nevada.edu/~nvasa
• Connecticut Poster Competition
http://www.amstat.org/chapters/Connecticut/home/Poster/poster_ind
ex.htm
• Ohio Poster Competition
http://www.bio.ri.ccf.org/ASA/poster.html
• New York City Poster Competition
http://www.nycasa.org/2008postercompetition.html
www.gvsu.edu/stat/statposter
John Gabrosek and Neal
Rogness
Department of Statistics
Grand Valley State University
Allendale, Michigan USA
[email protected]
[email protected]