CAUSE Webinar
GAISEing into the Future of Statistics Education
Chris Franklin
University of Georgia
Jessica Utts
University of California, Davis
November 14, 2006
GAISE
• Guidelines for Assessment and Instruction in
Statistics Education
http://www.amstat.org/education/gaise/
• Strategic initiative of ASA. The GAISE
documents were endorsed by ASA in 2005.
• Provides a Framework for Teaching Statistics
– Within the PreK-12 Mathematics Curriculum and
– For the College Introductory Course
Guidelines for Teaching and Learning
Statistics within the PreK-12 Mathematics
Curriculum -- The Pre K-12 GAISE
Framework
Christine Franklin
University of Georgia
Department of Statistics
chris@stat.uga.edu
PreK-12 Writers and Advisors
Writers:
• Christine Franklin
• Gary Kader
• Denise Mewborn
• Jerry Moreno
• Roxy Peck
• Mike Perry
• Richard Scheaffer
Advisors:
Peter Holmes
Brad Hartlaub
Landy Godbold
Cliff Konold
Susan Friel
What’s Happening in Statistics
Education, PreK-12
• Everyone – students, teachers, parents,
employers – interested in data
• Data analysis has become a key component of
modern PreK-12 mathematics curriculum
• NCTM, NAEP, State guidelines -- GA has
become a model state with the integration of
data in the new GA Performance Standards for
mathematics
Current efforts
• Curriculum Standards (PSSM) of the
National Council of Teachers of
Mathematics (NCTM)
Data Analysis and Probability (one of the 5
strands) runs throughout the curriculum
Advanced Placement Statistics
• First exam in 1997 – 7500 exams
• In 2006 – 90,000 exams
What’s Needed for the Future
• Statistics is a relatively new science that is still
developing
• Many teachers have not had any opportunity to
develop sound knowledge of the principles and
practices of data analysis they are now called
upon to teach
• “Fleshing out” of the NCTM “Standards” is more
essential for the statistics strand than for others
GAISE
• The goals of the Pre K-12 document are to provide a basic
framework for informed Pre K-12 stakeholders that describes what is
meant by a statistically literate high school graduate and to provide
steps to achieve this goal.
• This framework provides a conceptual structure for statistics
education which gives a coherent picture of the overall curriculum.
This framework supports and complements the objectives of the
NCTM PSSM.
• A goal in the professional growth of our mathematics teachers
should be to give a big picture of statistics and allow implementation
of the NCTM Standards in an informed way.
Levels in PreK-12 GAISE
• The main content of the Pre K-12 Framework is
divided into three levels, A, B, and C that roughly
parallel the PreK-5, 6-8, and 9-12 grade bands
of the NCTM Standards.
• The framework levels are based on experience
not age.
Check out the ASA/NCTM Committee Statistics Teacher Network Newsletter,
Issue 68 (current issue)
• http://www.amstat.org/education/stn/
FRAMEWORK FOR STATISTICS
EDUCATION
Statistical analysis is an investigatory process that
turns often loosely formed ideas into scientific
studies by:
• refining a problem into one or more questions
that can be addressed with data
• designing a plan to collect appropriate data
• analyzing the collected data by graphical and
numerical methods,
• interpreting the analysis so as to reflect light on
the original question.
An understanding of variability is crucial for the
practice of this process
A Curriculum Framework for
Pre K-12 Statistics Education
Basic principles around which this Framework
revolves can be summarized as:
• Both conceptual understanding and procedural skill
should be developed deliberately, but conceptual
understanding should not be sacrificed for
procedural proficiency.
• Active learning is key to the development of
conceptual understanding.
• Real world data must be used wherever possible in
statistics education.
• Appropriate technology is essential in order to
emphasize concepts over calculations
These principles continue as the foundation of the College
GAISE recommendations.
GAISE College Group
Joan Garfield
Martha Aliaga
George Cobb
Carolyn Cuff
Rob Gould
Robin Lock
Tom Moore
Allan Rossman
Bob Stephenson
Jessica Utts
Paul Velleman
Jeff Witmer
Univ. of Minnesota (Chair)
ASA
Mt. Holyoke College
Westminster College
UCLA
St. Lawrence University
Grinnell College
Cal Poly San Luis Obispo
Iowa State
UC Davis
Cornell University
Oberlin College
The Goal
Produce a set of recommendations
and guidelines for instruction and
assessment in introductory statistics
courses at the undergraduate level.
Four Part Report
• Introduction and History
• Goals for Students in an Introductory
Course: What it Means to be Statistically
Educated
• Six Recommendations for helping
teachers achieve those goals
• Appendix of Examples and Suggestions
Six Recommendations
1. Emphasize statistical literacy and develop statistical
thinking
2. Use real data
3. Stress conceptual understanding rather than mere
knowledge of procedures
4. Foster active learning in the classroom
5. Use technology for developing conceptual
understanding and analyzing data
6. Integrate assessments that are aligned with course
goals to improve as well as evaluate student learning.
Expanding on Recommendations 1 and 2
Emphasize statistical literacy and develop
statistical thinking and Use real data
– Use scenarios that are familiar to students as
well as data of interest to them
– Don’t use data out of context of the problem
to be solved
– Start with a question and model the whole
process to arrive at the answer, even if it’s
throughout the course and not all in the same
day
Using Familiar Scenarios:
Wason Selection Task
Modified somewhat from this source:
http://coglab.wadsworth.com/experiments/WasonSelection.shtml
Cards have a letter on one side and a number on the other.
Consider the rule:
If a card has a B on one side, it has a 21 on the other side.
Question: Which card(s) do you need to turn over to verify
that the rule holds for all cards?
B
16
C
21
Using Familiar Scenarios:
Wason Selection Task
Cards have a letter on one side and a number on the other.
Consider the rule:
If a card has a B on one side, it has a 21 on the other side.
Question: Which card(s) do you need to turn over to verify
that the rule holds for all cards?
B
16
C
Answer: B and 16
21
New Example
Source: The Tipping Point; orig. Professor Leda Cosmides, UCSB
The Rule: No one under 21 is allowed to
drink alcohol in a bar.
There are 4 people drinking in a bar:
•
•
•
•
One is drinking beer.
One is 16 years old.
One is drinking coke.
One is 21 years old.
Question: For which person(s) do we need more
information to verify that the law is being upheld?
New Example
Source: The Tipping Point; orig. Professor Leda Cosmides, UCSB
The Rule: No one under 21 is allowed to
drink alcohol in a bar.
There are 4 people drinking in a bar:
•
•
•
•
One is drinking beer.
One is 16 years old.
One is drinking coke.
One is 21 years old.
Question: For which person(s) do we need more
information to verify that the law is being upheld?
The person drinking beer and the 16-year old .
The two tasks are the same, but one is a familiar
scenario! That makes it easier to understand.
Cards have a letter on one side and a number on the other.
Consider the rule:
If a card has a B on one side, it has a 21 on the other side.
Question: Which card(s) do you need to turn over to verify that
the rule holds for all cards?
Beer
Age 16
Coke
Answer: B and 16
Age 21
Example of Modeling Statistical Thinking
Model statistical thinking for students by presenting examples as questions that
need an answer, and showing the statistical process for finding the answer.
Work examples from the beginning (the question) to the end (the conclusion).
Question of interest:
Do men lose more weight by dieting or by exercising regularly?
Study done at Stanford, used overweight male volunteers, randomly
assigned to one year of diet or exercise. Lost more weight with diet.
Useful for illustrating these concepts and processes:
• Types of studies (randomized experiment versus observational study)
• Design of randomized experiments
• When cause and effect can be concluded (or not); it can for this experiment
• How to do hypothesis tests, from start to finish
• How to construct and interpret a confidence interval
GAISE Recommendations: Making It
Happen
Start with small steps, for example:
•
•
•
•
•
•
•
Add an activity to your course
Have your students do a small project
Integrate an applet into a lecture
Demonstrate the use of software to your students
Increase the use of real data sets
Add a case study (newspaper story <-> journal article)
Choose one topic to delete from the list you currently try to
cover and using the time saved to focus more on
understanding concepts.
QUESTIONS??
http://www.amstat.org/education/gaise
chris@stat.uga.edu
jmutts@ucdavis.edu