AERA Annual Meeting, March 28, 2008
Center for Assessment
Boston College
It seems simple enough: Establish what constitutes a year’s growth in a year’s time for each student.
This simplicity belies a subtle complexity.
To adequately address the notion of a year’s growth, actual growth must be distinguished from aspirational growth.
What is a current year’s growth?
What should a current year’s growth be?
Answering the second question establishes a threshold distinguishing adequate from inadequate growth.
To make such a distinction requires an answer to the first question which defines a norm: What is the range of growth currently observed?
Aspirational growth should be possible—This is Linn’s existence proof applied at the individual level (Linn 2003).
Measuring student growth, even with a vertical scale, is not a simple task.
Numerous States believe that placing their tests on a vertical scale will simplify 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.
However, the 4 inch increase becomes fully understandable only when placed in context of growth of other children between ages 3 and 4.
In the following discussion student growth percentiles are introduced that provide a normative context to interpret student growth.
A quantity of fundamental interest to norming student progress (i.e., conditional achievement) is:
A student’s growth percentile is the conversion of Equation 1 to a percentile.
Estimation of the conditional density used to calculate student growth percentiles is performed using quantile regression (Betebenner & Shang, 2007; Koenker, 2005).
Consider a low achieving student demonstrating 90th percentile growth and a high achieving student demonstrating 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.
In this sense, the low achiever’s growth is more exemplary than the high achiever’s.
Growth percentiles allow for easy understanding and comparison of student growth.
However, judgment of whether the student’s growth was adequate requires external criteria.
Performance standards are the most obvious external criteria needed to define a year’s worth of growth.
If proficiency within 3 years is the achievement goal, then one can examine prior growth to estimate what growth percentile is sufficient to reach the desired outcome.
For high achieving students, modest growth percentiles are required to maintain their position above proficiency whereas for some low achieving student sustained high growth percentiles are necessary.
The process of defining a year’s growth is a standard setting procedure.
Clearly, defining a year’s worth of growth for some students as 80th percentile or better sets a very high standard.
And defining a year’s growth for some students as 25th percentile or better sets a low standard.
Growth standards should be equitable, reasonable, and desirable.
If the goal is high achievement for all students, then reaching that goal requires low achieving students to have higher growth percentiles than high achieving students.
As a consequence, accountability systems built toward high achievement demand more of schools serving predominantly low achieving students.
“Growth analyses” do not circumvent this reality.
Only by considering what is, what should be, and what is possible simultaneously, can growth models and their associated standards be equitable, just and truly informed.
And only within this context can an ambiguous term like “a year’s growth” be used intelligently in discussions about student progress.