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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 Assessment Dover, NH
CCSSO Conference on Student Assessment Los Angeles, CA — June 23rd, 2009
Damian W. Betebenner
The Colorado Growth Model
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 percentiles—a normative description of growth—forms the basis of the Colorado Growth Model [Betebenner, 2008]
Damian W. Betebenner
The Colorado Growth Model
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 student’s current achievement given their prior achievement? Given a student’s prior scale scores and the associated conditional density, their current scale score corresponds to a percentile of that conditional distribution. This percentile is the student’s growth percentile. Growth percentiles are closely related to estimating the probability of observing a student’s current achievement taking account of their past achievement: Pr(Current Achievement |Past Achievement ). Growth percentiles describe the rarity of a student’s current achievement conditional upon their prior achievement.
Damian W. Betebenner
The Colorado Growth Model
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
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 student’s 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 achiever’s growth is more exemplary (probabilistically) than the high achiever’s.
Judgments about the adequacy of student growth require external criteria.
Damian W. Betebenner
The Colorado Growth Model
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 estimating: 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.
Damian W. Betebenner
The Colorado Growth Model
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 determine whether the student is On Track to Reach Proficient, that is "Catching Up". 73rd
95th
●
Grade 3/2005
7th
●
Grade 4/2006
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
In 2007 CDE estimated that it would take 92nd percentile growth, consecutively for two years, to reach proficient. Their 73rd percentile growth puts them behind that 2 year target.
92nd
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
In 2007 CDE estimated that it would take 92nd percentile growth, consecutively for two years, to reach proficient. Their 73rd percentile growth puts them behind that 2 year target.
88th 92nd
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
In 2007 CDE estimated that it would take 88th percentile growth, consecutively for three years, to reach proficient. Their 73rd percentile growth puts them behind that 3 year target.
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
In 2007 CDE estimated that it would take 92nd percentile growth, consecutively for two years, to reach proficient. Their 73rd percentile growth puts them behind that 2 year target.
Conclusion: Because the student was not proficient in 2008 and their 2007−08 growth percentile of 73 was less than both the two and three year targets, the student's growth is considered to be insufficient to reach proficient within three years 92nd In short, the student is not on track to be proficient and is not "catching up".
88th
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
In 2007 CDE estimated that it would take 88th percentile growth, consecutively for three years, to reach proficient. Their 73rd percentile growth puts them behind that 3 year target.
Grade 7/2009
Grade 8/2010
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". 63rd
66th
26th
●
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
63rd ●
66th ●
26th ●
●
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
63rd ●
66th ●
26th ●
●
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
63rd ●
66th ●
18th
26th ●
●
In 2007 CDE estimated that it would take, at a minimum, 18th percentile growth, consecutively for two years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 2 year minimal target.
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
63rd ●
66th ●
22nd
18th
26th ●
●
In 2007 CDE estimated that it would take, at a minimum, 18th percentile growth, consecutively for two years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 2 year minimal target.
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
In 2007 CDE estimated that it would take, at a minimum, 22nd percentile growth, consecutively for three years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 3 year minimal target.
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
Conclusion: Because the student was proficient in 2008 and their 2007−08 growth percentile of 63 was greater than both the two and three year minimum targets, the student'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". ● 18th 63rd
66th
22nd
26th ●
●
In 2007 CDE estimated that it would take, at a minimum, 18th percentile growth, consecutively for two years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 2 year minimal target.
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
In 2007 CDE estimated that it would take, at a minimum, 22nd percentile growth, consecutively for three years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 3 year minimal target.
Grade 9/2009
Grade 10/2010
Overview Student Growth Percentiles and Accountability References
School Accountability
Going from Students to Schools
It’s 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.
Damian W. Betebenner
The Colorado Growth Model
District C: 2008 CSAP Math School Results Student Growth versus Student Achievement by Percent Free/Reduced Lunch 100
Higher Achievement Lower Growth
Percent at/above Proficient in School
90
School Percent Free/Reduced Lunch
Higher Achievement Higher Growth
● ● ● ● ●
80 70
Less than 20 percent 20 to 40 percent 40 to 60 percent 60 to 80 percent More than 80 percent
60
School Size 50
50 Students 100 Students
40
200 Students 500 Students
30
1,000 Students 20
Higher Growth Lower Achievement
Lower Growth Lower Achievement
10 0
0
10
20
30
40
50
60
70
Median of Student Growth Percentiles in School
80
90
100
Overview Student Growth Percentiles and Accountability 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 155–170. Taylor & Francis, New York.
Damian W. Betebenner
The Colorado Growth Model
The Colorado Growth Model: A Technical Overview Damian W. Betebenner National Center for the Improvement of Educational Assessment Dover, NH
CCSSO Conference on Student Assessment Los Angeles, CA — June 23rd, 2009
Damian W. Betebenner
The Colorado Growth Model
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 percentiles—a normative description of growth—forms the basis of the Colorado Growth Model [Betebenner, 2008]
Damian W. Betebenner
The Colorado Growth Model
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 student’s current achievement given their prior achievement? Given a student’s prior scale scores and the associated conditional density, their current scale score corresponds to a percentile of that conditional distribution. This percentile is the student’s growth percentile. Growth percentiles are closely related to estimating the probability of observing a student’s current achievement taking account of their past achievement: Pr(Current Achievement |Past Achievement ). Growth percentiles describe the rarity of a student’s current achievement conditional upon their prior achievement.
Damian W. Betebenner
The Colorado Growth Model
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
200
800 400
le
S le S
ca
ca
S
S re co
800
200
06
05
400
20
20
600
co re
600
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 student’s 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 achiever’s growth is more exemplary (probabilistically) than the high achiever’s.
Judgments about the adequacy of student growth require external criteria.
Damian W. Betebenner
The Colorado Growth Model
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 estimating: 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.
Damian W. Betebenner
The Colorado Growth Model
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 determine whether the student is On Track to Reach Proficient, that is "Catching Up". 73rd
95th
●
Grade 3/2005
7th
●
Grade 4/2006
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
In 2007 CDE estimated that it would take 92nd percentile growth, consecutively for two years, to reach proficient. Their 73rd percentile growth puts them behind that 2 year target.
92nd
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
In 2007 CDE estimated that it would take 92nd percentile growth, consecutively for two years, to reach proficient. Their 73rd percentile growth puts them behind that 2 year target.
88th 92nd
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
In 2007 CDE estimated that it would take 88th percentile growth, consecutively for three years, to reach proficient. Their 73rd percentile growth puts them behind that 3 year target.
Grade 7/2009
Grade 8/2010
Is the student's growth, from 2007 to 2008, sufficient to put them on track to reach proficient within 3 years?
In 2007 CDE estimated that it would take 92nd percentile growth, consecutively for two years, to reach proficient. Their 73rd percentile growth puts them behind that 2 year target.
Conclusion: Because the student was not proficient in 2008 and their 2007−08 growth percentile of 73 was less than both the two and three year targets, the student's growth is considered to be insufficient to reach proficient within three years 92nd In short, the student is not on track to be proficient and is not "catching up".
88th
73rd ● 95th ●
●
Grade 3/2005
7th
●
Grade 4/2006
After 1 year the student remains partially proficient, so their 1 year growth was not enough to get them to proficient.
Grade 5/2007
Grade 6/2008
In 2007 CDE estimated that it would take 88th percentile growth, consecutively for three years, to reach proficient. Their 73rd percentile growth puts them behind that 3 year target.
Grade 7/2009
Grade 8/2010
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". 63rd
66th
26th
●
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
63rd ●
66th ●
26th ●
●
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
63rd ●
66th ●
26th ●
●
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
63rd ●
66th ●
18th
26th ●
●
In 2007 CDE estimated that it would take, at a minimum, 18th percentile growth, consecutively for two years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 2 year minimal target.
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
63rd ●
66th ●
22nd
18th
26th ●
●
In 2007 CDE estimated that it would take, at a minimum, 18th percentile growth, consecutively for two years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 2 year minimal target.
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
In 2007 CDE estimated that it would take, at a minimum, 22nd percentile growth, consecutively for three years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 3 year minimal target.
Grade 9/2009
Grade 10/2010
Is the student's growth, from 2007 to 2008, sufficient to remain at or above proficient for the next 3 years?
After 1 year the student remains proficient, so their 1 year growth was enough to remain at proficient.
Conclusion: Because the student was proficient in 2008 and their 2007−08 growth percentile of 63 was greater than both the two and three year minimum targets, the student'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". ● 18th 63rd
66th
22nd
26th ●
●
In 2007 CDE estimated that it would take, at a minimum, 18th percentile growth, consecutively for two years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 2 year minimal target.
Grade 5/2005
Grade 6/2006
Grade 7/2007
Grade 8/2008
In 2007 CDE estimated that it would take, at a minimum, 22nd percentile growth, consecutively for three years, to maintain at or above proficient. Their 63rd percentile growth puts them above that 3 year minimal target.
Grade 9/2009
Grade 10/2010
Overview Student Growth Percentiles and Accountability References
School Accountability
Going from Students to Schools
It’s 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.
Damian W. Betebenner
The Colorado Growth Model
District C: 2008 CSAP Math School Results Student Growth versus Student Achievement by Percent Free/Reduced Lunch 100
Higher Achievement Lower Growth
Percent at/above Proficient in School
90
School Percent Free/Reduced Lunch
Higher Achievement Higher Growth
● ● ● ● ●
80 70
Less than 20 percent 20 to 40 percent 40 to 60 percent 60 to 80 percent More than 80 percent
60
School Size 50
50 Students 100 Students
40
200 Students 500 Students
30
1,000 Students 20
Higher Growth Lower Achievement
Lower Growth Lower Achievement
10 0
0
10
20
30
40
50
60
70
Median of Student Growth Percentiles in School
80
90
100
Overview Student Growth Percentiles and Accountability 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 155–170. Taylor & Francis, New York.
Damian W. Betebenner
The Colorado Growth Model
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