A Focus on Student Learning
An Introduction to Student Growth Percentiles and their use in New Mexico
Dr. Damian Betebenner
National Center for the Improvement of Educational Assessment
September 10th, 2024
Success is a journey, not a destination.
The doing is often more important
than the outcome.
Arthur Ashe
Know what you want to accomplish
and focus on the process rather
than the outcome.
Nick Saban
Know what you want to accomplish
and focus on the process rather
than the outcome.
Nick Saban
Education is not the filling of a pail,
but the lighting of a fire.
William Butler Yeats
Outcomes, outcomes, outcomes!
• I want to be successful.
• I want to be thin.
• I want to be admired.
We live in a society • I want to be powerful.
obsessed with ends • I want to be famous.
• I want to have a million followers.
• I want to be the best.
• I want to be liked.
• I want to have it all.
• I want to be the fastest.
• I want to have the perfect family.
• I want to win.
A Focus on Outcomes
(at the expense of a focus on process)
Process vs. Product
Means vs. Ends
Journey vs. Destination
Development vs. Result
Learning vs. Attainment
Growth Vs. Achievement
So what does all of this have to do
with student academic growth?
A Focus on Outcomes
(at the expense of a focus on process)
Process vs. Product
Means vs. Ends
Journey vs. Destination
Development vs. Result
Learning vs. Attainment
Growth Vs. Achievement
Accountability and Outcomes
• The central focus of educational accountability systems since NCLB has been academic outcomes,
largely derived from large scale, state administered summative assessments.
• Student academic proficiency has been the main determinant of education quality.
• NCLB mandated universal proficiency (100% proficient) by 2014
• ESSA mandates more modest proficiency targets.
• I am highly critical of the way that educational accountability has been conceived over the last two
decades, but not for the reasons you might think:
• I am a strong proponent of annual, large scale, summative assessments.
• I am a strong proponent of reporting achievement outcomes like student academic proficiency (I.e.,
percent proficient)
• Outcomes from large scale, standardized summative assessments like academic proficiency are
important, but there’s a rub.
The Problem
• Not all outcomes derived from state summative assessments are created equal.
• Distal outcomes: Achievement/attainment such as academic proficiency
• Proximal outcomes: Growth/learning such as student growth percentiles (SGP)
• Growth & Achievement (Learning & Attainment) are often treated as conceptually separate but they are
intricately related: Growth/Learning leads to Achievement/Attainment
• A desire for high achieving students is necessarily a desire for students who grow/learn a lot and vice-
versa.
• I often say Growth/Learning and Achievement/Attainment are opposite sides of the same coin.
• Current accountability systems ignore this relationship between growth and achievement and often
present growth and achievement as a value-laden choice (“Which do you prefer, growth or
achievement?”)
• Treating growth and achievement separately leads to system incoherence: Desired outcomes (proficiency)
are divorced from the efforts of teachers, schools, … to support and maximize the learning of students.
Remember:
Know what you want to accomplish
and focus on the process rather
than the outcome.
Nick Saban
Remember:
Know what you want to accomplish
and focus on the process rather
than the outcome.
Nick Saban
• Yes, we want all students to be proficient.
• That’s analogous to declaring that we want to win all
of our games.
• Accomplishing such goals requires a focus on process
(highly effective processes).
• The process by which students become proficient is
learning.
• Coherent accountability focuses on student learning
without losing sight of the end goal of student
proficiency.
Student Growth
• Student growth connects process with outcomes.
• Student growth is to learning as student attainment is to achievement.
• It is important to note that no single assessment measures student learning/growth.
• Assessments (plural), including MSSA, measure achievement/attainment: What a student knows
and can do at a given point in time.
• Learning is a process that happens over time.
• We use multiple assessments of achievement to infer whether or not learning has occurred.
Student Growth/Learning:
If you care about student achievement,
then you care about student growth.
• Where you are is a function of
where you started and how quickly
you’ve travelled since.
• Student growth and student
attainment/achievement are
related in this way.
• Distance=Rate x Time
• Those who start behind tend to stay
behind and those that start ahead
tend to stay ahead.
Student Growth - Calculations
• There is a common misconception that because student growth can be difficult to calculate it is difficult to
understand.
• Calculations may be complicated but knowing how to calculate student growth is not synonymous with
understanding student growth:
– The number π (pi=3.14159…) is difficult to calculate but is simple to understand conceptually.
– Height and weight percentiles associated with children are difficult to calculate but are simple to
understand conceptually.
– Credit scores are difficult to calculate but we all know what they mean practically.
• Computational details are important but often obscure a simple conceptual basis.
• Not knowing how something is calculated does not imply that one cannot understand the quantities.
A Math Story Problem
• Whose high jump changed more? Personal Bests in 2023 and 2024 for Two High Jumpers
Explain your answer. World Record: 6 feet, 10 1/2 inches
• Whose high jump change is more
remarkable? Explain your answer. 7
6 feet, 6 inches Judy
• Which hit jumper improved more?
Height (feet)
6 6 feet, 4 inches
Explain your answer.
4 feet, 0 inches
4 Anna
3 feet, 6 inches
Spring 2023 Spring 2024
Track Season
Student Growth
• Growth as an amount of change:
– What could be more simple?
– Like height or weight just calculate the amount of change.
– Requires a vertical scale (which New Mexico DOESN’T have).
– Growth = Score Time 2 - Score Time 1
• Not as simple as it seems:
– Comparisons between students often leads to wrong conclusions.
– Interpreting change requires context.
– Even if New Mexico MSSA had a vertical scale, you’ll see that it doesn’t give you want you
think.
Student Growth
Back to the story problem!
Personal Bests in 2023 and 2024 for Two High Jumpers
World Record: 6 feet, 10 1/2 inches
6 feet, 6 inches Judy
Height (feet)
6 6 feet, 4 inches
4 feet, 0 inches
4 Anna
3 feet, 6 inches
Spring 2023 Spring 2024
Track Season
Student Growth
• Which high jumper improved more:
– Judy improved 2 inches. Personal Bests in 2023 and 2024 for Two High Jumpers
World Record: 6 feet, 10 1/2 inches
– Anna improved 6 inches. 8
– An inch is an inch!!!
6 feet, 6 inches
– But is an inch really an inch??? Judy
Height (feet)
– 2 inches for an elite jumper is far more
6 6 feet, 4 inches
remarkable than 6 5
inches for a novice. 4 feet, 0 inches
4 Anna
3 feet, 6 inches
Spring 2023 Spring 2024
Track Season
Student Growth
• The same holds true for the vertically scaled tests (e.g., SBAC).
Average Scale Score Change 2022 to 2023
Top 10% ELA Grade 4 2023: -7.5
Bottom 10% ELA Grade 4 2023: +24.5
Top 10% Mathematic Grade 4 2023: -12.6
Bottom 10% Mathematics Grade 4 2023: +18.4
• Large increases for the lowest 10% of achievers, small (negative) increases for high achievers.
• Just as an inch isn’t necessarily an inch; a scale score point isn’t necessarily a scale score point.
• Moral of the story: There’s more to student growth than subtraction (and in New Mexico you
aren’t supposed to subtract student scores with the MSSA)
Student Growth
• This is analogous to height/weight measures for infants.
• Growth amounts are tricky to interpret and require context.
• Peer based comparisons used by growth analyses are a way to acquire
that context.
An infant male toddler is measured at 2 and 3 years of age
and is shown to have grown 4 inches. The magnitude of increase—4
inches—is a well understood quantity that any parent can grasp and
calculate at home using a simple yardstick. However, parents
leaving their pediatrician’s office knowing only how much their child
has grown would likely be wanting for more information: Parents are
not interested in an absolute magnitude of growth, but instead in a
norm-referenced quantity locating that 4 inch increase alongside the
height increases of similar children.
Student Growth
• Peer-based analyses are also called norm-referenced analyses.
• Like with infant height/weight charts, peers are children/student with
similar characteristics.
• For growth analyses using large scale assessments, peers are students with
(at least) the same scale score history on the same tests.
• Peer based norms are invaluable in providing context for stakeholders to
understand student growth.
• Peer based norms are possible even across test content areas or test
transitions.
• This is the mathematical basis of Student Growth Percentiles, as the
following slides illustrate.
Student Growth Percentiles - Academic Peers
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Student Growth Percentiles - Academic Peers
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Student Growth Percentiles - Academic Peers
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Student Growth
• Peer-based growth calculations are only as good as the assessments on which they are
based.
• With quality assessments, peer based analyses can allow for all students to
demonstrate growth.
• However, ceiling or floor effects on a test can impede the analysis of growth for students
at the extremes.
• The goal is to be able to allow various stakeholders groups to investigates student
growth/learning and answer questions relevant to them.
• What are some of these questions (Yen, 2007).
Relevant Questions for Parents
• Did my child make a year’s worth of learning 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?
Relevant Questions for Teachers
• Did my students make a year’s worth of progress in a year?
• Did my students grow appropriately toward mee ng state standards?
• How close are my students to becoming Pro cient?
• Are there students with unusually low growth who need special a en on?
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Relevant Questions for Administrators
• Did the students in our district/school make a year’s worth of progress in
all content areas?
• Are our students growing appropriately toward mee ng 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
pro ciency categories?
• Can I pool together results from di erent grades to draw summary
conclusions?
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Growth is achievement over time
Growth is achievement over time
• The figure depicts a student’s ELA
achievement in Grade 3/2022 and
Grade 4/2023.
• The student was Near Proficient in
both years but their growth (SGP =
72) was high (> 1 year of learning).
• Evidence suggests the student in on
fire in ELA (remember the Yeats
quote).
• Compare this with the student’s
mathematics performance.
Growth is achievement over time
Growth is achievement over time
• Like ELA, the student’s is Near
Proficient in both Grade 3/2022 and
Grade 4/2023.
• Yet their growth from 2022 to 2023 is
< 1 year.
• Why robust learning in ELA but not in
math?
• What strategies can 5th grade
teachers use to continue the ELA
trend and reverse the math trend?
Carina Roper Sample School
How to interpret this student
Advanced
English
growth & achievement report Language Arts
Achievement
Proficient MSSA
MSSA English
Language Arts
> 1 Year
Scale Score Scale Score
Growth
Level Percentiles
About 1 Year
MSSA Near Proficient > 1 Year 66th − 99th
Achievement
Levels < 1 Year
About 1 Year35th − 65th
< 1 Year 1st − 34th
Novice
Student
Growth Grade 3 Grade 4 Grade 5
Percentile Scale Score 341 453
Achievement Level Near Proficient Near Proficient Achievement
Growth Percentile 72
Growth Level > 1 Year Growth
Suggested Uses
Advanced
Review past growth to assess
student academic progress toward Math
MSSA achievement goals.
Achievement
Proficient
Develop remediation or enrich− MSSA Math
ment plans based on rate of Scale Score
> 1 Year
growth needed to reach higher
MSSA achievement levels. Growth
Level Percentiles
Identify the rate of progress
Near Proficient
needed in order to reach or About 1 Year > 1 Year 66th − 99th
maintain proficient status
on the MSSA next year. About 1 Year35th − 65th
< 1 Year
Novice < 1 Year 1st − 34th
Grade 3 Grade 4 Grade 5
Scale Score 352 448
Achievement Level Near Proficient Near Proficient Achievement
Growth Percentile 34
Growth Level < 1 Year Growth
For more information please visit the New Mexico Public Education Department (NMPED) at http://ped.state.nm.us or contact 505−827−5800
Cooperatively developed by NMPED & the Center for Assessment, Inc. Distributed by NMPED.
Changing conversations about education
• Accountability together with disconnected point in me assessments have
led to a focus on outcomes (achievement) at the expense of learning/
growth.
• This focus has led to incoherence in the way we understand the
performance of our educa on systems and the way in which we hold them
accountable.
• How much students grow/learn is directly connected to later levels of
achievement in the same way velocity is related to distance traveled.
• The purpose of New Mexico’s Growth Model/SGPs is to make these
connec ons apparent and change stakeholder conversa ons about
educa on and student performance.
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Thank you for
Inviting me
About this copy
A Focus on Student Learning — New Mexico Department of Education, September 10, 2024.
This is an image-based copy of the original Keynote slides; builds and animations are flattened.