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Overview
Student Growth Percentiles and Accountability
References
The Colorado Growth Model:
A Technical Overview
Damian W. Betebenner
National Center for the Improvement of Educational AssessmentDover, NH
CCSSO Conference on Student Assessment
Los Angeles, CA June 23rd, 2009
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Overview
Student Growth Percentiles and Accountability
References
The Colorado Growth Model
Student Growth Percentiles: What Is
Student Growth Percentiles: What Should Be
The Colorado Growth Model
Student Growth for Multiple Purposes
Growth as the cornerstone of accountability: In Colorado student
progress to judge state, district, school and student performance.
The Colorado Growth Model addresses three related questions
using the same metric:
What is the level of growth for a student (i.e. Actual Growth)?
What should the level of growth for a student be (i.e. Aspirational
Growth)?
What could the level of growth for a student be (i.e., Realistic Growth)?
Student growth percentilesa normative description ofgrowthforms the basis of the Colorado Growth
Model [Betebenner, 2008]
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Overview
Student Growth Percentiles and Accountability
References
The Colorado Growth Model
Student Growth Percentiles: What Is
Student Growth Percentiles: What Should Be
Student Growth Percentiles
Normative Growth Question
Should we be surprised with a students current achievement given
their prior achievement?
Given a students prior scale scores and the associated conditional
density, their current scale score corresponds to a percentile of that
conditional distribution.
This percentile is the students growth percentile.
Growth percentiles are closely related to estimating the probability of
observing a students current achievement taking account of their
past achievement:
Pr(Current Achievement|Past Achievement).
Growth percentiles describe the rarity of a students current
achievement conditional upon their prior achievement.
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Overview The Colorado Growth Model
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Overview
Student Growth Percentiles and Accountability
References
The Colorado Growth Model
Student Growth Percentiles: What Is
Student Growth Percentiles: What Should Be
Student Growth Percentiles
Normative Growth Question
Should we be surprised with a students current achievement given
their prior achievement?
Student growth percentiles address this question.Consider a low achieving student with 90th percentile growth and a
high achieving student with 10th percentile growth.
The low achieving student grew at a rate exceeding 90 percent of
similar students.
The high achieving student grew at a rate exceeding just 10 percent of
similar students.
The low achievers growth is more exemplary(probabilistically) than thehigh achievers.
Judgments about the adequacy of student growth require external
criteria.
Damian W. Betebenner The Colorado Growth Model
Overview The Colorado Growth Model
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Overview
Student Growth Percentiles and Accountability
References
The Colorado Growth Model
Student Growth Percentiles: What Is
Student Growth Percentiles: What Should Be
Combining Actual and Aspirational Growth
What Is
Each student receives a growth percentile quantifying their growth in
each of three subject for the academic year.
What Should Be
Each student receives percentile growth projections/trajectories esti-
mating:
What level of growth is required to reach each of the 3
performance levels in 1, 2, 3, and 4 years.
What Could Be
The percentile metric establishes a normative foundation allowing
stakeholders to set challenging yet realistic goals.
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Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
73rd
95th
7thq q
Not On Track to Reach Proficient Not Catching Up
Colorado's Growth Model uses each student's growth percentile in two ways:
First, the growth percentile is used to describe how much a student has grown
during the last year. Second, the growth percentile is used to determine whether the
student is on track to reach/maintain proficiency. The following slides demonstrate,
for an individual student, how Colorado's Growth Model is used to determinewhether the student is On Track to Reach Proficient, that is "Catching Up".
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Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
73rd
95th
7thq q
Is the student's growth,from 2007 to 2008, sufficientto put them on track to reach
proficient within 3 years?
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Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
73rd
95th
7thq q
Is the student's growth,from 2007 to 2008, sufficientto put them on track to reach
proficient within 3 years?
After 1 year the studentremains partially proficient,
so their 1 year growth was notenough to get them to proficient.
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Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
92nd
73rd
95th
7thq q
Is the student's growth,from 2007 to 2008, sufficientto put them on track to reach
proficient within 3 years?
After 1 year the studentremains partially proficient,
so their 1 year growth was notenough to get them to proficient.
In 2007 CDE estimated that it would take92nd percentile growth, consecutively for two years, to reach proficient.
Their 73rd percentile growth puts them behind that 2 year target.
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Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
88th
92nd
73rd
95th
7thq q
Is the student's growth,from 2007 to 2008, sufficientto put them on track to reach
proficient within 3 years?
After 1 year the studentremains partially proficient,
so their 1 year growth was notenough to get them to proficient.
In 2007 CDE estimated that it would take92nd percentile growth, consecutively for two years, to reach proficient.
Their 73rd percentile growth puts them behind that 2 year target.
In 2007 CDE estimated that itwould take 88th percentile growth,
consecutively for three years, to reachproficient. Their 73rd percentile growth
puts them behind that 3 year target.
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Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
88th
92nd
73rd
95th
7thq q
Is the student's growth,from 2007 to 2008, sufficientto put them on track to reach
proficient within 3 years?
After 1 year the studentremains partially proficient,
so their 1 year growth was notenough to get them to proficient.
In 2007 CDE estimated that it would take92nd percentile growth, consecutively for two years, to reach proficient.
Their 73rd percentile growth puts them behind that 2 year target.
In 2007 CDE estimated that itwould take 88th percentile growth,
consecutively for three years, to reachproficient. Their 73rd percentile growth
puts them behind that 3 year target.
Conclusion: Because the student was not proficient in 2008 and their 200708
growth percentile of 73 was less than both the two and three year targets, thestudent's growth is considered to be insufficient to reach proficient within three years
In short, the student is not on track to be proficient and is not "catching up".
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Grade 5/2005 Grade 6/2006 Grade 7/2007 Grade 8/2008 Grade 9/2009 Grade 10/2010
63rd
26th66th
q
q q
q
On Track to Remain Proficient Keeping Up
Colorado's Growth Model uses each student's growth percentile in two ways:
First, the growth percentile is used to describe how much a student has grown
during the last year. Second, the growth percentile is used to determine whether the
student is on track to reach/maintain proficiency. The following slides demonstrate,
for an individual student, how Colorado's Growth Model is used to determine
whether the student is On Track to Remain Proficient, that is "Keeping Up".
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Grade 5/2005 Grade 6/2006 Grade 7/2007 Grade 8/2008 Grade 9/2009 Grade 10/2010
63rd
26th66th
q
q q
q
Is the student's growth,from 2007 to 2008, sufficient
to remain at or aboveproficient for the next 3 years?
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Grade 5/2005 Grade 6/2006 Grade 7/2007 Grade 8/2008 Grade 9/2009 Grade 10/2010
63rd
26th66th
q
q q
q
Is the student's growth,from 2007 to 2008, sufficient
to remain at or aboveproficient for the next 3 years?
After 1 year the studentremains proficient,
so their 1 year growth wasenough to remain at proficient.
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Grade 5/2005 Grade 6/2006 Grade 7/2007 Grade 8/2008 Grade 9/2009 Grade 10/2010
18th
63rd
26th66th
q
q q
q
Is the student's growth,from 2007 to 2008, sufficient
to remain at or aboveproficient for the next 3 years?
After 1 year the studentremains proficient,
so their 1 year growth wasenough to remain at proficient.
In 2007 CDE estimated that itwould take, at a minimum, 18th percentile growth,
consecutively for two years, to maintainat or above proficient. Their 63rd percentile
growth puts them above that 2 year minimal target.
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Grade 5/2005 Grade 6/2006 Grade 7/2007 Grade 8/2008 Grade 9/2009 Grade 10/2010
22nd
18th
63rd
26th66th
q
q q
q
Is the student's growth,from 2007 to 2008, sufficient
to remain at or aboveproficient for the next 3 years?
After 1 year the studentremains proficient,
so their 1 year growth wasenough to remain at proficient.
In 2007 CDE estimated that itwould take, at a minimum, 18th percentile growth,
consecutively for two years, to maintainat or above proficient. Their 63rd percentile
growth puts them above that 2 year minimal target.
In 2007 CDE estimated that itwould take, at a minimum, 22nd percentile
growth, consecutively for three years, tomaintain at or above proficient. Their 63rd
percentile growth puts them above that 3 yearminimal target.
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Grade 5/2005 Grade 6/2006 Grade 7/2007 Grade 8/2008 Grade 9/2009 Grade 10/2010
22nd
18th
63rd
26th66th
q
q q
q
Is the student's growth,from 2007 to 2008, sufficient
to remain at or aboveproficient for the next 3 years?
After 1 year the studentremains proficient,
so their 1 year growth wasenough to remain at proficient.
In 2007 CDE estimated that itwould take, at a minimum, 18th percentile growth,
consecutively for two years, to maintainat or above proficient. Their 63rd percentile
growth puts them above that 2 year minimal target.
In 2007 CDE estimated that itwould take, at a minimum, 22nd percentile
growth, consecutively for three years, tomaintain at or above proficient. Their 63rd
percentile growth puts them above that 3 yearminimal target.
Conclusion: Because the student was proficient in 2008 and their 200708
growth percentile of 63 was greater than both the two and three year minimum targets, thestudent's growth is considered to be sufficient to remain proficient during the next three years.
In short, the student is on track to remain proficient and is "keeping up".
OverviewStudent Growth Percentiles and Accountability School Accountability
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References
Going from Students to Schools
Its of interest to examine schools where students demonstrate, on
average, extraordinarily high and low student growth.
To summarize the student growth percentiles associated with a
school (or other grouping) calculate the median of the student
growth percentiles.
If students were randomly assigned to schools, expect to see a
median of 50.
Values greatly above or below 50 are of interest in identifying best
practices or providing extra support.
Examining growth with achievement sheds new light on school
performance.
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District C: 2008 CSAP Math School ResultsStudent Growth versus Student Achievement by Percent Free/Reduced Lunch
Median of Student Growth Percentiles in School
Percentat/above
Proficientin
School
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80 90 100
School Percent
Free/Reduced Lunch
q Less than 20 percentq 20 to 40 percentq 40 to 60 percentq 60 to 80 percentq More than 80 percentSchool Size
50 Students
100 Students200 Students
500 Students
1,000 Students
OverviewStudent Growth Percentiles and Accountability
R f
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References
References
Betebenner, D. W. (2008).
Toward a normative understanding of student growth.In Ryan, K. E. and Shepard, L. A., editors, The Future of Test-Based
Educational Accountability, pages 155170. Taylor & Francis, New
York.
Damian W. Betebenner The Colorado Growth Model