TEACHING STATISTICS IN THE
ELEMENTARY GRADES: A
PRACTICAL- AND CONTENTBASED JUSTIFICATION
NCTM CHICAGO REGIONAL CONFERENCE FALL 2012
Derek Webb
Bemidji State University
Anna Bargagliotti
Loyola Marymount University
Statistics Education Today
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Over the past two decades, increasing importance
has been placed on data analysis in the US
Data-driven decision making and studies have
drawn interest from the general population,
policymakers, businesses, and schools
Prominent people and news outlets have
continuously touted the importance of understanding
and interpreting data
There is a Large Interest in Education Data
For example, Secretary of Education Arnie
Duncan recently commented on the use of data
in the evaluation of education:
 “…we believe [testing] it is important to
measure progress. We need to know who is
ahead and who is behind – who is succeeding
and who needs more support. In an ideal world,
that data should also drive instruction and
meaningful professional development.”
-Arnie Duncan, Speech August 22, 2012
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Media outlets note the importance of data in education:
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“Why is data so valuable in education? For one, it will
advance us beyond the primary aged-based system of
educational advancement that has been in place for much
of the past century. By generating and enabling access to
consistent streams of data from different parts of the
classroom, we are no longer limited to simply knowing what
students know at a point in time– we can now get a sense of
when and how they learned it and how likely they are to
retain and apply that knowledge”
- Vineet Madan, Huff Post Education, posted June 2012
How can we prepare a statistically
literate population?
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Statistical literacy refers to the ability to think and
reason in the presence of uncertainty as well as make
sense of statistical information
Statistics and probability have become an integral part
of mathematics K–12 education in the US
NCTM includes a strand dedicated to Data Analysis and
Probability throughout all grade levels
The Common Core State Standards (CCSS) have
deemphasized statistics in the elementary grades and
increased its emphasis in middle school and high school
http://www.corestandards.org/
Common Core State Standards
Does this mean that elementary teachers should
not know statistics?
Goal today is to:
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
Discuss practical-based reasons why it is important
for elementary teachers to be well-versed in
statistics
Discuss content-based reasons why it is important
for elementary teachers to be well-versed in
statistics
Audience Question 1

What grade level do you work with?
 A.
K-2
 B. 3-5
 C. 6-8
 D. 9-12
 E. 12-16
Audience Question 2

How many courses in statistics have you taken?
 A.
0
 B. I have not taken a course but I have taken a
professional development workshop or seminar
 C. 1
 D. 2
 E. More than 2
Audience Question 3

If you have taken one or more statistics courses, how
would you describe the course(s) based on what you
teach:
 A.
Very useful
 B. Somewhat useful
 C. Not useful
What are practical-based reasons why
teachers should be well-versed in statistics?
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Teacher performance and teacher pay is a hot-button
issue in current educational reform debates that heavily
relies on statistical methods
Complex statistical models that control for variables
such as the number of students in the class, student
disabilities, and teacher experience can be employed in
order to measure teacher performance though the
performance of their students
Teachers may be judged by administrators, in part,
through the use of such statistical methods
Teachers Need to Join the Conversation
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It is not be necessary for teachers to understand all
the statistics involved in value-added modeling
Teachers should understand the general statistical
ideas surrounding educational reform
Teachers at all grade levels need to have statistical
understanding in order to join important
conversations that effect the profession
No Child Left Behind Act Policies
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States produce an Annual Yearly Progress (AYP)
report
States, school systems, and schools are issued a
Report Card
The Report Card lists the subjects and the
assessments that are included in the evaluation for
the specific state
For example, in the state of Tennessee, the report
card includes the Tennessee Value Added
Assessment System (TVAAS)
The TVAAS
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The TVAAS provides each teacher confidential
information on each of their student’s standardized test
scores on the Tennessee Comprehensive Assessment
Program (TCAP) exam from grades 3 to 8
Using these performances, a teacher is presented with a
predicted score for each student’s achievement during
the year
The TVAAS also provides information open to the public
 E.g.,
the public can access the System Value Added Report
for a school district and school
Statistical Information in the Reports
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These AYP reports contain an enormous amount of
statistical information
Statistical vocabulary is everywhere on the report (e.g.,
standards error, growth standard, three-year average,
NCE)
For example: NCE
 NCE
is short for Normal Curve Equivalent
 The “Estimated System Mean NCE Scores” on the report shows
the average district test score for each grade as an NCE value
 The base year is stated at the top of the report as 2009, thus
all scores are equated to the 2009 scores
 Procedures to equate test scores are rich with statistical
concepts!
 These procedures are not presented in the report but a teacher
who has studied these procedures would have a much greater
sense of what these data mean
Practical Statistical Knowledge
Teachers Need
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Teachers should be able to give meaning to assessment
data
Teachers should be able to make valuable assessments
of their own students, classes, and schools
Teachers should understand the statistics surrounding
policy decisions being made in their profession
Audience Question 4

Do you feel like you have a good understanding of
the statistics presented in the AYP reports you
receive?
 A.
Yes
 B. Maybe
 C. No
Audience Question 5

Do you receive any training on how to read the
reports and the statistics involved in generating the
reports?
 A.
Yes
 B. Maybe
 C. No
Audience Question 6
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Do you receive any resources (including extra time)
to evaluate the reports and make changes in your
classroom based on the reports?
 A.
Yes
 B. No
 C. Some, but not enough
Audience Question 7

Would you find it valuable to receive more training
or more background on how to read and use the
reports?
 A.
Yes
 B. Maybe
 C. No
What are content-based reasons why
teachers should be well-versed in statistics?

Guidelines and standards exist that need to be
implemented in the classroom:
 The
Guidelines for Assessment in Statistics Education
(GAISE): A Pre-K-12 Curriculum Framework report
emerged from the statistics community in 2007 to
provide an outline for statistics education
http://www.amstat.org/education/gaise/
 The CCSS
Audience Question 8
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Have you heard of the GAISE report?
 A.
Yes
 B. No
The GAISE Report
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GAISE defines a statistically literate person as someone
who can Formulate Questions, Collect Data, Analyze
Data, and Interpret Results
GAISE presents a three-level (A, B, C) framework
corresponding to the depth of coverage
GAISE does not outline statistical learning by grade but
roughly suggest:
 students
in the elementary grades should acquire level A
depth,
 Students in middle school should be around level B, and
 Students in high school should achieve level C
Level A/Level B
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Level A is more teacher directed, Level B shifts
towards being student directed
Level A learning is typically contained within the
classroom environment, Level B begins to expand
past the student’s classroom to make assertions
about other classrooms or outside the school
Focus on data displays throughout
The CCSS
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CCSS offers grade-by-grade benchmarks for K-8
and a content outline for high school
CCSS contains a strand entitled “Measurement and
Data” for the elementary grades
CCSS focuses K-5 level statistics on three central
ideas
 generating
bar graphs
 taking measurements of objects and sorting
 drawing line plots
Teaching Under the CCSS
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To implement the CCSS we need effective resources
and examples as to what teachers should teach in the
classroom
It is important that the statistics being taught also be
connected to GAISE
CCSS covers a subset of concepts outline by GAISE
GAISE provides the spirit
 Think
Statistically! Pose a statistical question and investigate
the answer
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Teach for CCSS using GAISE – This can be done!
Bridging the Gap between Common Core State
Standards and Teaching Statistics
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Publication which offers 21 investigations for K-12 that
effectively illustrate how to present statistical material in
the classroom aligned with GAISE and CCSS
Website for information and purchasing publication
9 investigations are dedicated to level A understanding
 Investigation
2.4, “How can we sort our junk?”
Statistical Question: How can we sort
our junk?
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This lesson is aligned with 3 CCSS standards:
 K.MD.3
Classify objects into given categories; count the
numbers of objects in each category and sort the categories
by count.
 1.MD.4 Organize, represent, and interpret data with up to
three categories; ask and answer questions about the total
number of data points, how many in each category, and
how many more or fewer are in one category than in
another.
 2.MD.10 Draw a picture graph and a bar graph (with
single-unit scale) to represent a data set with up to four
categories. Solve simple put-together, take-apart, and
compare problems using information presented in a bar
graph.
Bag of Junk
How do we sort our junk?
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Each group has identical bags of junk
Look at the junk and together discuss:
 What
kinds of objects do you have?
 What type of attributes could you use as a sorting
factor?
 How will the choice of the attribute affect the outcome
of the sorting process?
Choose Clothes
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How many articles of clothing are there?
How could you sort the clothing?
Make a bar graph to display your results
Example Graphs
Example Graphs
Interpreting Results
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Why did your group choose the sorting attribute you
selected?
How did you determine the categories for your
attribute?
Are the graphical displays of the groups similar? How
are they similar? How are they different?
Provide an answer to the original question: “How can we
sort our junk?” by summarizing:
 how
you displayed your data
 what graphs you created
 what you learned about the type of junk you have through
the process of sorting
Could We Have Met the CCSS a
Different Way?
 Example:
Miss Smith’s students have 6 dogs, 4 cats, and 7
fish for pets. Please create a bar graph of this data.
Take-away
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There are both content and practical reasons for elementary
teachers to be prepared to think statistically
Although there in not a large emphasis on statistics in the CCSS
elementary grades, it is still very important that teachers be
well-versed in statistics
The introduction of statistical thinking begins in the elementary
grades thus elementary teachers play a key role
Using the GAISE spirit to teach the CCSS will ensure that
students have a good foundation in statistical thinking
The teaching profession is filled with statistics
The more teachers understand data, the more they can
contribute to policy discussions
Thank you! Questions?
Derek Webb
Bemidji State University
DWebb@bemidjistate.edu
http://faculty.bemidjistate.edu/dwebb/
Anna E. Bargagliotti
Loyola Marymount University
abargagl@lmu.edu
www.project-set.com