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GAISE
Guidelines for Assessment and Instruction
in Statistics Education
Pre-K -- 12 Report
Christine Franklin
University of Georgia
Department of Statistics
[email protected]
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
Current efforts
• Curriculum Standards (PSSM) of the
National Council of Teachers of
Mathematics (NCTM)
• One of the 5 strands, Data Analysis and
Probability, which runs throughout the
curriculum
Data Analysis and Probability
Strand
Instructional programs from Pre-K through grade 12
should enable all students to—
• formulate questions that can be addressed with data
and
• collect, organize, and display relevant data to answer
them;
• select and use appropriate statistical methods to
analyze data;
• develop and evaluate inferences and predictions that
are based on data;
• understand and apply basic concepts of probability.
Current efforts
Advanced Placement Statistics
• First exam in 1997 – 7500 exams
• In 2003 – 60,000 exams
Science Education and Quantitative Literacy
(SEAQL)
Series of workshops for science teachers
and materials on how to improve science
instruction by using QL techniques
What’s needed for the future
• Taken together, these programs and efforts, and
many others such as NAEP and state
guidelines, have produced an enormous need
for better statistics education among the
mathematics teachers of the country
• Mathematics Education of Teachers (MET)
Report
• Sees statistics as the topic in which current and
prospective teachers need the most help with
content and pedagogy
• Quotes from the report:
Quotes from MET Report
• Statistics is the science of data, and the daily display of data by
the media notwithstanding, most elementary teachers have
little or no experience in this vitally important field.”
• “Of all the mathematical topics now appearing in the middle
grades curricula, teachers are least prepared to teach statistics
and probability.”
• “Statistics is now widely acknowledged to be an extremely
valuable set of tools for problem solving and decision making.
But, despite the production of interesting statistics materials
for the schools, it has been hard to find room for the subject in
(high school) curricula dominated by preparation for calculus.”
What’s Needed for the Future
• It is this goal – helping teachers to teach
statistics – that must dominate the interest,
energy, and resources of the statistics
education community in the years ahead if
the information age is to reach its full
potential of informed decision-making
based on rational thought and quantitative
evidence
ASA Response to the MET Report:
TEAMS
• A leadership conference entitled
“Stat/Math TEAMS (Teacher Education:
Assessment, Methods, and Strategies)
• Held at University of Georgia, October 30
– November 2, 2003
• Major support from ASA and NSF
TEAMS
Goals of the conference
•
To create awareness among teacher educators of what’s needed to
better prepare K-12 teachers to give instruction in probability and
statistics
•
To build a team of statistics and math educators that can examine
issues and provide guidance in methods to improve teacher
preparation
•
To draft guidelines for the statistics education of teachers and
formulate a plan to have these adopted by the lead organizations
involved with teacher education and statistics education
•
To develop mechanisms for materials review and development,
pedagogical improvements, and the implementation of research
findings related to how students learn statistics and probability
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 “Standards” is more
essential for the statistics strand than for
others
GAISE
• A Framework for Teaching Statistic Within
the PreK-12 Mathematics Curriculum and
for the College Introductory Course
• Guidelines for Assessment and Instruction
in Statistics Education
• Strategic initiative of ASA
• What is this document and why is it
needed?
GAISE
• The goals of the K-12 document are to
provide a basic framework for informed K12 stakeholders that describes what is
meant by a statistically literate high school
graduate and to provide steps to achieve
this goal.
PreK-12 Writers and Advisors
Writers:
• Christine Franklin
• Richard Scheaffer
• Roxy Peck
• Denise Mewborn
• Gary Kader
• Jerry Moreno
Advisors:
Peter Holmes
Cliff Konold
Mike Perry
Susan Friel
Brad Hartlaub
Landy Godbold
GAISE
The foundation for the K-12 Framework rests on the
NCTM Standards.
• This Framework fleshes out the NCTM Data Analysis
and Probability strand with guidance and clarity on
the content that NCTM is recommending at the
elementary, middle and high school grades, focusing
on a connected curriculum that will allow a high
school graduate to have a working knowledge of an
appreciation for the basic ideas of statistics.
• It also provides guidance on methods that are
accepted as effective in teaching statistical concepts
to students with wide varieties of learning styles.
Levels in PreK-12 GAISE
• The main content of the 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.
Distinction of Levels
• At Level A the learning is more teacher
driven, but transitions toward student
centered work at Level B and becomes
highly student driven at Level C. Handson, active learning is a predominant
feature throughout.
GAISE
Statistical analysis is an investigatory process that
turns often loosely formed ideas into scientific
studies by:
• refining the question to one (or more) that can
be answered 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.
Distinction of Levels
• All four steps of this process are used at all three
levels, but the depth of understanding and
sophistication of methods used increases across
the levels.
• For example, an elementary class may collect
data to answer questions about their classroom,
a middle school class may collect data to answer
questions about the school, and a high school
class may collect data to answer questions
about the community and model the relationship
between, say, housing prices and geographic
variables such as the location of schools.
Distinction of Levels
Example of clarity of concepts at each level:
Use of probability:
•
Level A: Chance/uncertainty;
impossible----certain; equally likely
concept; compare experimental and theoretical
probability for coins and spinners
•
Level B: concept of not equally likely; simple
binomial distribution
•
Level C: use simulation for sampling
distributions to examine simulated p-values
Distinction of Levels
Example of clarity of concepts at each level:
Mean:
•
Level A: Idea of fair share – foreshadow the
balance point
•
Level B: Mean as a balancing point
•
Level C: Mean as an estimate from a sample
that will be used to make an inference about a
population – understanding the concept of using
a sampling distribution to take a sample mean to
estimate the population mean.
Distinction of Levels
Example of clarity of concepts at each level:
• What type of music is most popular among their
peers in school? (rock, country, rap)
• Level A: Summarize frequencies in table or bar
graph
• Level B: Transition to relative frequencies – leap to
proportional reasoning
• Level C: Transition to sampling distributions for a
sample proportion and role of probability in finding a
margin of error which provides information about
max. likely distance between sample proportion and
population proportion being estimated.
GAISE
Basic principles around which the 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
Conclusion
• Ultimate goal of the framework is to lay out
a foundation for educational programs
designed to help students achieve the
noble goal of being a sound statistically
literate citizen.
• Principles and goals of the PreK-12
GAISE document parallel the goals and
guidelines of the college report.