Introduction
The Big Picture
Growth & Accountability
Growth & Accountability: The Colorado Growth Model
Student Growth Percentiles and Accountability
References
The Georgia Model of Student Growth
Damian W. Betebenner
National Center for the Improvement of Educational Assessment
Dover, NH
Atlanta, Georgia July 2019
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture
Growth & Accountability
Growth & Accountability: The Colorado Growth Model
Student Growth Percentiles and Accountability
References
About Me
Dr. Damian Betebenner, PhD
- Senior Associate at the Center for Assessment (NCIEA).
- Developed student growth percentiles and percentile growth
trajectories to help states and educational associations employ
student growth in decision making [Betebenner, 2008,
Betebenner, 2009, Betebenner, 2012].
- Since 2007 have been refining and sharing these techniques
with Georgia, Colorado, Massachusetts, Indiana, Nevada,
Hawaii and 25 other states in various stages of
investigation/adoption.
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture
Growth & Accountability
Growth & Accountability: The Colorado Growth Model
Student Growth Percentiles and Accountability
References
Student Growth Percentiles
2007 Began development of the Colorado Growth Model
(student growth percentiles/percentile growth trajectories).
2008 Successful application of Colorado Growth Model
(criterion-referenced/growth target component) as part of
USED Growth Model Pilot Program.
2010 Began working with Georgia Department of Education on
the development of the Georgia Model of Student Growth.
2010 Worked with states on incorporating growth into RttT
applications and with successful states on their use
(Massachusetts, Georgia, New York, Rhode Island).
2011 Worked with a number of states on incorporating student
growth percentiles into the ESEA waiver applications and
teacher evaluation systems.
2012 Worked with 5 states on co-developing interactive
visualizations to help better communicate student growth
percentile results.
2013 Extended SGP methodology to work with time-dependent
interim assessments.
2007-2019 Working to extend and refine the open-source
methodology with the assistance of state partners.
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture
Growth & Accountability The Data Revolution
Growth & Accountability: The Colorado Growth Model Lessons Learned
Student Growth Percentiles and Accountability
References
From a Paucity to a Plethora of Data
Data Data Everywhere (The Economist, 2010)
More and better organized data: mega, giga, tera, peta, exa,
zetta, yotta!
Historical records of student achievement.
Linkage of student achievement to student demographics,
teachers, schools, educational programs, . . .
Stakeholder interest in examining student achievement over
time (student growth) derives from data availability.
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture
Growth & Accountability The Data Revolution
Growth & Accountability: The Colorado Growth Model Lessons Learned
Student Growth Percentiles and Accountability
References
A Recurring Metaphor
Data as a window and a mirror
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture
Growth & Accountability The Data Revolution
Growth & Accountability: The Colorado Growth Model Lessons Learned
Student Growth Percentiles and Accountability
References
Lessons Learned
On Questions John Tukey
It is better to have an approximate answer to the right question than a precise answer to the
wrong question.
On Statistical Models George E. P. Box
All models are wrong but some are useful.
On Understanding Aristotle
We understand best those things we see emerge from their very beginnings.
On Accountability Sherlock Holmes
It is a capital mistake to theorize before you have all the evidence. It biases the judgment.
On Theories of Action Confucius
Tell me and I will forget, show me and I will remember, involve me and I will understand.
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Why Growth?
Growth & Accountability Different Models/Different Questions
Growth & Accountability: The Colorado Growth Model Relevant Questions/Concepts
Student Growth Percentiles and Accountability
References
The Attractiveness of Growth
What is growth and why measure it?
Student learning is a central goal of education.
Assessments of student achievement provide evidence of the
current status of student knowledge and understanding.
Learning is demonstrated by growth in student achievement
from one point in time to another point in time–not by status at
either point time alone.
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Why Growth?
Growth & Accountability Different Models/Different Questions
Growth & Accountability: The Colorado Growth Model Relevant Questions/Concepts
Student Growth Percentiles and Accountability
References
Guiding Questions
Growth models address specific questions
Different growth analysis techniques are good at answering
different questions.
It is critical to understand these different questions.
Different questions lead to different conversations which lead to
different uses and outcomes.
Changing conversations about education
Starting with the right questions simplifies development and
motivating the proper use of the growth model results.
The questions set the table for those conversations.
Yen (2007) for an excellent list of questions derived from a
survey of parent, teachers and administrators
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Why Growth?
Growth & Accountability Different Models/Different Questions
Growth & Accountability: The Colorado Growth Model Relevant Questions/Concepts
Student Growth Percentiles and Accountability
References
What are the relevant questions for parents?
Yen (2007), from a state survey of parents, teachers and administrators,
compiled a list of frequently voiced questions/concerns by stakeholder
group.
Parent Questions
Did my child make a year’s worth of progress in a year?
Is my child growing appropriately toward meeting state
standards?
Is my child growing as much in Math as Reading?
Did my child grow as much this year as last year?
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Why Growth?
Growth & Accountability Different Models/Different Questions
Growth & Accountability: The Colorado Growth Model Relevant Questions/Concepts
Student Growth Percentiles and Accountability
References
What are the relevant questions for teachers?
Yen (2007), from a state survey of parents, teachers and administrators,
compiled a list of frequently voiced questions/concerns by stakeholder
group.
Teacher Questions
Did my students make a year’s worth of progress in a year?
Did my students grow appropriately toward meeting state
standards?
How close are my students to becoming Proficient?
Are there students with unusually low growth who need special
attention?
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Why Growth?
Growth & Accountability Different Models/Different Questions
Growth & Accountability: The Colorado Growth Model Relevant Questions/Concepts
Student Growth Percentiles and Accountability
References
What are the relevant questions for administrators?
Yen (2007), from a state survey of parents, teachers and administrators,
compiled a list of frequently voiced questions/concerns by stakeholder
group.
Administrator Questions
Did the students in our district/school make a year’s worth of
progress in all content areas?
Are our students growing appropriately toward meeting state
standards?
Does this school/program show as much growth as that one?
Can I measure student growth even for students who do not
change proficiency categories?
Can I pool together results from different grades to draw
summary conclusions?
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Why Growth?
Growth & Accountability Different Models/Different Questions
Growth & Accountability: The Colorado Growth Model Relevant Questions/Concepts
Student Growth Percentiles and Accountability
References
What are the relevant questions for policy makers?
Policy Maker Questions
Can/how should student growth be used in judgments of
educator quality?
Can/how should student growth be used in judgments of
education (e.g., school) quality?
Are students on track for career and college readiness?
What adjustments for student demographics need to be
considered?
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Describing Student Growth
Growth & Accountability Student Growth Percentiles
Growth & Accountability: The Colorado Growth Model Criterion Referenced Growth
Student Growth Percentiles and Accountability
References
Growth & Accountability: The Colorado Growth Model
How much growth & is it enough?
Colorado begins conversations about education/educator
quality by answering two questions:
How much: How much growth did a student make?
Is is enough: Is it enough growth to reach or maintain proficiency?
Answering these two questions in a credible and clear manner
sets the stage for subsequent accountability discussions.
Colorado purposely separated the description (what is) from the
determination of responsibility (who/what is responsible).
This separation promoted greater ownership of results and
participation in finding root causes.
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Describing Student Growth
Growth & Accountability Student Growth Percentiles
Growth & Accountability: The Colorado Growth Model Criterion Referenced Growth
Student Growth Percentiles and Accountability
References
Describing Student Growth
Measuring student growth, even with a vertical scale, is not a simple
task.
Some believe a vertical scale simplifies the task of measuring
student growth.
Even with an interval (or ratio) scale, growth is not easy to interpret.
Consider, for example, height.
A child might grow 4 inches between ages 3 and 4.
4 inches is a well understood quantity.
The 4 inch increase becomes really meaningful only when understood
alongside the growth of other 3 to 4 year olds.
Student growth percentiles were developed to provide a normative
context for describing student growth.
Damian W. Betebenner The Georegia Model of Student Growth
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Introduction
The Big Picture Describing Student Growth
Growth & Accountability Student Growth Percentiles
Growth & Accountability: The Colorado Growth Model Criterion Referenced Growth
Student Growth Percentiles and Accountability
References
Student Growth Percentiles
Should we be surprised with a child’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 ).
As such, growth percentiles describe the rarity of a student’s current
achievement conditional upon their prior achievement.
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture Describing Student Growth
Growth & Accountability Student Growth Percentiles
Growth & Accountability: The Colorado Growth Model Criterion Referenced Growth
Student Growth Percentiles and Accountability
References
Student Growth Percentiles
Should we be surprised with a child’s current achievement given their
prior achievement?
Student growth percentiles answer this question.
Consider a low achieving student with 75th percentile growth and a
high achieving student with 25th percentile growth.
The low achieving student grew at a rate exceeding 75 percent of their
academic peers.
The high achieving student grew at a rate exceeding just 25 percent of
their academic peers.
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 Georegia Model of Student Growth
Introduction
The Big Picture Describing Student Growth
Growth & Accountability Student Growth Percentiles
Growth & Accountability: The Colorado Growth Model Criterion Referenced Growth
Student Growth Percentiles and Accountability
References
Establishing growth-standards based upon growth-norms
The most common adequacy criterion are judging growth toward an
achievement goal (i.e., growth-to-standard).
Results from student growth percentile analyses can be used to
calculate percentile growth trajectories for each student.
These trajectories indicate what future rates of growth will lead to
and are used to make adequacy judgments.
This growth-to-standard approach was approved as part of
Colorado’s successful application to the Growth Model Pilot
Program.
Damian W. Betebenner The Georegia Model of Student Growth
Mathematics
Advanced
Achievement
● Catch Up
Target
DEMO Mathematics
Catch Up ●● ●
Target ●● Scale Score
Growth
Proficient ● Level Percentiles
Very High 81st − 99th
High 61st − 80th
Part Proficient
Typical 40th − 60th
Low 20th − 39th
Unsatisfactory Very Low 1st − 19th
Grade 3 Grade 4 Grade 5 Grade 6 Grade 7
Scale Score 438 447 489 495
Achievement Level
Achievement Target
Proficient Part Proficient Part Proficient Part Proficient
Proficient (514) Proficient (547)
Achievement
Growth Percentile 18 64 44
Growth Level
Growth Target
Very Low High Typical
Catch Up (70) Catch Up (82)
Growth
Billy Gonzales North End Middle School
How to interpret this student
growth & achievement report Mathematics
Advanced
Achievement
● Catch
Target
Up
DEMO ● DEMO Mathematics
● Catch Up ●●
Target ●● Scale Score
Scale Score ● ●
Growth
Proficient ● Level Percentiles
DEMO Very High 81st − 99th
Achievement High 61st − 80th
Part Proficient
Levels Typical 40th − 60th
Low 20th − 39th
Unsatisfactory Very Low 1st − 19th
Student
Grade 3 Grade 4 Grade 5 Grade 6 Grade 7
Growth 2015−2016 2016−2017 2017−2018 2018−2019 2019−2020
Percentile Scale Score 438 447 489 495
Achievement Level
Achievement Target
Proficient Part Proficient Part Proficient Part Proficient
Proficient (514) Proficient (547)
Achievement
Growth Percentile 18 64 44
Catch Up/Keep Up Growth Level Very Low High Typical
Growth
Move Up/Stay Up Growth Target Catch Up (70) Catch Up (82)
Targets
Suggested Uses
Advanced Reading
Move Up
Achievement
● Target
DEMO Reading
● Scale Score
● Review past growth to assess ●
Keep Up
student academic progress toward ●
Catch Up ●● Target
Proficient Target ●● Growth
DEMO achievement goals. ●
Level Percentiles
● Develop remediation or enrich−
● Very High 81st − 99th
ment plans based on rate of
High 61st − 80th
growth needed to reach higher
DEMO achievement levels. Part Proficient Typical 40th − 60th
Low 20th − 39th
● Identify the rate of progress ●
Very Low 1st − 19th
needed in order to reach or Unsatisfactory
maintain proficient status
Grade 3 Grade 4 Grade 5 Grade 6 Grade 7
on the DEMO next year. 2015−2016 2016−2017 2017−2018 2018−2019 2019−2020
Scale Score 449 533 579 602
Achievement Level
Achievement Target
Unsatisfactory Part Proficient Part Proficient Proficient
Proficient (592) Proficient (620)/Advanced (661)
Achievement
Growth Percentile 69 85 74
Growth Level
Growth Target
High Very High High
Catch Up (60) Keep Up (76)/Move Up (99)
Growth
For more information please visit the Student Growth Percentiles Package (the SGP Package) at www.sgp.io or contact dbetebenner@nciea.org
Cooperatively developed by the SGP Package & the Center for Assessment, Inc. Distributed by the SGP Package.
Introduction
The Big Picture
Growth & Accountability Teacher & School Accountability
Growth & Accountability: The Colorado Growth Model
Student Growth Percentiles and Accountability
References
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 Georegia Model of Student Growth
District C: 2008 CSAP Math School Results
Student Growth versus Student Achievement by Percent Free/Reduced Lunch
School Percent
Higher Achievement Higher Achievement Free/Reduced Lunch
Lower Growth Higher Growth
Percent at/above Proficient in School
Less than 20 percent
● 20 to 40 percent
● 40 to 60 percent
● 60 to 80 percent
● More than 80 percent
School Size
50 Students
100 Students
200 Students
30 500 Students
1,000 Students
10 Lower Growth Higher Growth
Lower Achievement Lower Achievement
Median of Student Growth Percentiles in School
Introduction
The Big Picture
Growth & Accountability Teacher & School Accountability
Growth & Accountability: The Colorado Growth Model
Student Growth Percentiles and Accountability
References
Student Growth Percentile Model
The Student Growth Percentile (SGP) methodology is an open
source methodology [Betebenner, 2008, Betebenner, 2009,
Betebenner, 2012]
The model is a norm and criterion-referenced growth model that
allows states to answer How much? and Is it enough?.
The software used to calculate and visualize SGPs is free (open
source) [Betebenner et al., 2019].
Currently over two dozen states are investigating/utilizing the model.
Damian W. Betebenner The Georegia Model of Student Growth
Growth Model Types by State
Growth Norm Model
Value Added Model
Gain Based Model
Introduction
The Big Picture
Growth & Accountability Teacher & School Accountability
Growth & Accountability: The Colorado Growth Model
Student Growth Percentiles and Accountability
References
Descriptive Accountability
Accountability system results can have value without making
causal inferences about school quality, solely from the results
of student achievement measures and demographic characteris-
tics. Treating the results as descriptive information and for iden-
tification of schools that require more intensive investigation of
organizational and instructional process characteristics are po-
tentially of considerable value. Rather than using the results of
the accountability system as the sole determiner of sanctions for
schools, they could be used to flag schools that need more in-
tensive investigation to reach sound conclusions about needed
improvements or judgments about quality [Linn, 2008, p. 21].
Damian W. Betebenner The Georegia Model of Student Growth
Introduction
The Big Picture
Growth & Accountability
Growth & Accountability: The Colorado Growth Model
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.
Betebenner, D. W. (2009).
Norm- and criterion-referenced student growth.
Educational Measurement: Issues and Practice, 28(4):42–51.
Betebenner, D. W. (2012).
Growth, standards, and accountability.
In Cizek, G., editor, Setting Performance Standards: Foundations,
Methods, and Innovations, pages 439–450. Routledge, New York.
Betebenner, D. W., Iwaarden, A. V., Domingue, B., and Shang, Y.
SGP: Student growth percentiles & percentile growth trajectories.
Available online complete with source code from https://sgp.io.
Linn, R. L. (2008).
Educational accountability systems.
In The Future of Test-Based Educational Accountability, pages 3–24.
Taylor & Francis, New York.
The Economist and Cukier, K. (2010).
Data data everywhere.
Yen, W. M. (2007).
Vertical scaling and No Child Left Behind.
In Dorans, N. J., Pommerich, M., and Holland, P. W., editors, Linking
and Aligning Scores and Scales, pages 273–283. Springer, New
York.
Damian W. Betebenner The Georegia Model of Student Growth
About this copy
The Georgia Model of Student Growth — Georgia Department of Education, July 25, 2019.
This is an image-based copy of the original beamer slides; builds and animations are flattened.