The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II
Student Growth Percentiles and Accountability
Future Directions
References
Fostering Productive Conversations with Growth Data to
Improve Educator Effectiveness
Damian W. Betebenner
National Center for the Improvement of Educational Assessment
Dover, NH
The Role of Short Cycle Assessment in Educator Evaluation, Denver,
CO June 2nd & 3rd, 2011
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II The Data Revolution
Student Growth Percentiles and Accountability Lessons Learned
Future Directions
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 Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II The Data Revolution
Student Growth Percentiles and Accountability Lessons Learned
Future Directions
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 Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Questions & Models
Student Growth Percentiles and Accountability Relevant Questions/Concepts
Future Directions
References
On Questions & Models
Growth models address specific questions
Different growth analysis techniques often answer different, but
related, 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 –
motivating the proper use of the growth model results.
The questions set the table for those conversations.
Yen (2007) provides an excellent list of questions derived from a
survey of parent, teachers and administrators
Different stakeholders have different questions.
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Questions & Models
Student Growth Percentiles and Accountability Relevant Questions/Concepts
Future Directions
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 Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Questions & Models
Student Growth Percentiles and Accountability Relevant Questions/Concepts
Future Directions
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 Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Questions & Models
Student Growth Percentiles and Accountability Relevant Questions/Concepts
Future Directions
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 Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Questions & Models
Student Growth Percentiles and Accountability Relevant Questions/Concepts
Future Directions
References
What are the relevant questions for policy makers?
Administrator Questions
Can/how should growth be used in judgments of educator
quality?
Can/how should 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 Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
References
Growth & Accountability
Growth versus Status
Enthusiasm for growth in accountability stems from the belief
that growth and teacher/school quality are more closely related
than status.
Enthusiasm for growth also stems from its potential diagnostic
uses.
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
References
Growth & Accountability
Fundamental Premise
“Good” schools/teachers bring about growth in student achievement
in excess of that found at “bad” schools/teachers.
The inherent believability of this premise is at the heart of current
enthusiasm to incorporate growth models into accountability
systems.
Note that current NCLB accountability invokes the same premise
(with achievement substituted for growth).
“Good schools/teachers” are commonly referred to as highly
effective schools/teachers.
Race to the Top has pushed teacher effectiveness
It is critical to understand the distinction between growth and
effectiveness.
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
References
Value-added Analyses/Inferences
Who/What is responsible for student growth?
Often, analyses of student growth attempt to determine the amount
of student progress/growth that can be attributed to the school or
teacher.
Called Value-added analyses, these techniques attempt to estimate
the teacher/school contribution to student achievement.
Value-added models quantify effectiveness—purporting to measure
the impact on achievement that this school or teacher would have,
on average, upon similar students assigned to them.
These models and their effectiveness claims are controversial for a
number of reasons (EPI (2010), NRC/NAE (2010), Braun (2005),
Rubin and Stuart (2004)) .
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
References
Value-added Analyses/Inferences
Who/What is responsible for student growth?
Value-added models are better described as effectiveness models
than as growth models.
Value-added is an inference – a causal conclusion drawn from the
data.
Value-added isn’t a type of statistical model or type of assessment.
All growth models can be used for value-added purposes but not
vice-versa.
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
References
Descriptive Questions
Note that the questions from Yen’s (2007) survey are primarily
descriptive.
The questions are only peripherally associated with causality.
High stakes accountability has transformed questions about student
growth into questions about responsibility/cause: Teacher and
School Effectiveness.
Beginning with description of growth doesn’t prevent subsequent
discussions about responsibility/cause.
Beginning with responsibility/cause (i.e., rendering a verdict) often
prevents discussions about the data.
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
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
characteristics. Treating the results as descriptive information
and for identification of schools that require more intensive
investigation of organizational and instructional process
characteristics are potentially 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 intensive investigation to reach sound
conclusions about needed improvements or judgments about
quality [Linn, 2008, p. 21].
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
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 Fostering Productive Conversations with Growth Data
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The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
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 Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
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 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 Fostering Productive Conversations with Growth Data
The Big Picture
Value-Added
Growth & Accountability: Part I
Description, Inference, and Causality
Growth & Accountability: Part II
Describing Student Growth
Student Growth Percentiles and Accountability
Student Growth Percentiles
Future Directions
Criterion Referenced Growth
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 Fostering Productive Conversations with Growth Data
Advanced Reading
High
Achievement
CSAP Reading
● Typical
Scale Score
Proficient Growth
Low
● Level Percentiles
High 66th − 99th
Typical 35th − 65th
Part Proficient
● Low 1st − 34th
Unsatisfactory
Grade 3 Grade 4 Grade 5 Grade 6 Next Year
Scale Score 462 539 563 609
Achievement Level Unsatisfactory Part Proficient Part Proficient Proficient Achievement
Growth Percentile 66 66 90
Growth Level High High High Growth
Example Student 12 (1234567812) Sample Middle School
Advanced
Math
Achievement
High
CSAP Math
● Scale Score
Typical
● Growth
Proficient
● Level Percentiles
Low
High 66th − 99th
● Typical 35th − 65th
Part Proficient
Low 1st − 34th
Unsatisfactory
Grade 3 Grade 4 Grade 5 Grade 6 Next Year
Scale Score 379 388 444 462
Achievement Level Part Proficient Part Proficient Part Proficient Part Proficient Achievement
Growth Percentile 16 69 51
Growth Level Low High Typical Growth
Advanced Reading
High
Achievement
CSAP Reading
● Typical
Scale Score
Proficient Growth
Low
● Level Percentiles
High 66th − 99th
Typical 35th − 65th
Part Proficient
● Low 1st − 34th
Unsatisfactory
Grade 3 Grade 4 Grade 5 Grade 6 Next Year
Scale Score 462 539 563 609
Achievement Level Unsatisfactory Part Proficient Part Proficient Proficient Achievement
Growth Percentile 66 66 90
Growth Level High High High Growth
Advanced
Writing
Achievement
High
CSAP Writing
● Scale Score
Typical
● Growth
Proficient
Level Percentiles
● Low
High 66th − 99th
Part Proficient ● Typical 35th − 65th
Low 1st − 34th
Unsatisfactory
Grade 3 Grade 4 Grade 5 Grade 6 Next Year
Scale Score 425 449 469 504
Achievement Level Part Proficient Part Proficient Part Proficient Part Proficient Achievement
Growth Percentile 55 53 79
Growth Level Typical Typical High Growth
Copyright 2009, Colorado Department of Education/Center for Assessment, Inc.
2008 CSAP Mathematics
Growth and Achievement Chart
2008 Achievement Percentile Percentile Growth Trajectory
Scale Score
Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II School Accountability
Student Growth Percentiles and Accountability Growth & Effectiveness
Future Directions
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 Fostering Productive Conversations with Growth Data
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
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II School Accountability
Student Growth Percentiles and Accountability Growth & Effectiveness
Future Directions
References
Growth, Effectiveness, and Value-Added
“Good teachers/schools” are often called highly effective
teachers/schools.
What’s the relationship between growth and effectiveness?
Effectiveness indicates who/what is responsible for the growth
(value-added models).
RttT has placed teacher responsibility for student progress as a
primary issue.
In teacher performance evaluations, even when large scale
assessment results are available, depending upon the state they
constitute, on average, about a third of the overall teacher rating.
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Descriptive Accountability
Student Growth Percentiles and Accountability Web 2.0 Technologies
Future Directions
References
Descriptive Accountability
“This is the difference between a retrospective question of identifying
fault as opposed to a prospective strategy to engineer some corrective
measure, almost independent of considering whether there was
blame-worthiness. And to move away from the blame-worthiness
paradigm toward something that is more regulatory in nature where one
might seize upon disparities or circumstances that are for some reason
deemed unacceptable and engineer the interventions needed to bring
about the necessary change. . . . It’s the no-fault gap closing strategy in
which the effort is to build a consensus about a vision of an improved
society rather than figure out where’s the person we want to pillory.”
C. Edley (2006)
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Descriptive Accountability
Student Growth Percentiles and Accountability Web 2.0 Technologies
Future Directions
References
Web 2.0: Data Visualization and Social Networking
The Colorado Department of Education and the Center for
Assessment have been working for the last two years on developing
next generation data visualization to accompany growth model data.
The goal: Transform conversations about education through active
engagement with data (i.e., evidence).
Our efforts have received tremendous interest and recognition:
Recognized by Adobe for innovative uses of their technology as an
Adobe Max Award finalist in October, 2009.
2010 NCME Award for Outstanding Dissemination of Educational
Measurement Concepts to the Public.
14 states signing MOUs to co-develop a cloud-based reporting
platform in a non-proprietary fashion.
Colorado recently devoted $2.5 million of stimulus funds to the
development efforts
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Descriptive Accountability
Student Growth Percentiles and Accountability Web 2.0 Technologies
Future Directions
References
The Decade of Data Visualization
Chart Wars http://infosthetics.com/archives/2010/01/
chart_wars_the_political_power_of_data_
visualization.html
Hans Rosling/Gapminder
http://www.youtube.com/watch?v=jbkSRLYSojo
Journalism in the Age of Data
http://datajournalism.stanford.edu/
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II Descriptive Accountability
Student Growth Percentiles and Accountability Web 2.0 Technologies
Future Directions
References
Web 2.0: Data Visualization and Social Networking
With a collaborative spirit, with a collaborative platform where people can
upload data, explore data, compare solutions, discuss the results, build
consensus, we can engage passionate people, local communities, media
and this will raise–incredibly–the amount of people who can understand
what is going on.
And this would have fantastic outcomes: the engagement of people,
especially new generations; it would increase knowledge, unlock
statistics, improve transparency and accountability of public policies,
change culture, increase numeracy, and in the end, improve democracy
and welfare.
E. Giovannini, Chief Statistician, OECD. June 2007
Damian W. Betebenner Fostering Productive Conversations with Growth Data
The Colorado Growth Model
Adopted Model
Near Model Adoption
Interested in Model
The Big Picture
Growth & Accountability: Part I
Growth & Accountability: Part II
Student Growth Percentiles and Accountability
Future Directions
References
References
Braun, H. I. (2005).
Using student progress to evaluate teachers: A primer on
value-added models.
Technical report, Educational Testing Service, Princeton, New
Jersey.
Economic Policy Institute (2010).
Problems with the use of student test scores to evaluate teachers.
Technical report, Washington, D.C.
Downloaded August 30th, 2010 from
http://epi.3cdn.net/724cd9a1eb91c40ff0_hwm6iij90.pdf.
Edley, C. (2006).
Educational “Opportunity" is the highest civil rights priority. So what
should researchers and lawyers do about it?
Retrieved June 22, 2006 from the World Wide Web:
http://www.softconference.com/MEDIA/WMP/260407/#43.010.
Linn, R. L. (2008).
Educational accountability systems.
In The Future of Test-Based Educational Accountability, pages 3–24.
Taylor & Francis, New York.
National Research Council and National Academy of Education
Getting value of out value-added: Report of a workshop.
Technical report, Washington, D.C.
Commitee on Value-Added Methodology for Instructional
Improvement.
Rubin, D. B., Stuart, E. A., and Zanutto, E. L. (2004).
A potential outcomes view of value-added assessment in education.
Journal of Educational and Behavioral Statistics, 29(1):103–116.
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 Fostering Productive Conversations with Growth Data
About this copy
Fostering Productive Conversations with Growth Data to Improve Educator Effectiveness — Renaissance Short Cycle, June 3, 2011.
This is an image-based copy of the original beamer slides; builds and animations are flattened.