Talks archive, 2005–2009 – Toward a Normative Understanding of Student Growth

bg=White Defining a Year’s Growth References Toward a Normative Understanding of Student Growth Damian W. Betebenner National Center for the Improvement of Educational Assessment Dover, NH NECAP Meeting December 12th, 2007 D. W. Betebenner Normative Student Growth

bg=White Defining a Year’s Growth Actual versus Aspirational Student Growth References Describing Actual Student Growth Actual versus Aspirational Student Growth 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. Describe What is a current year’s growth? Prescribe 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]. D. W. Betebenner Normative Student Growth

bg=White Defining a Year’s Growth Actual versus Aspirational Student Growth References Describing Actual Student Growth Describing Actual Student Growth 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 similar children. In the following discussion student growth percentiles are introduced that provide a normative context in which to interpret student growth. D. W. Betebenner Normative Student Growth

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bg=White Defining a Year’s Growth Actual versus Aspirational Student Growth References Describing Actual Student Growth Student Growth Percentiles As the figures indicate, there is a distribution of 2006 scale scores associated with each 2005 scale score. The average (or median) of the conditional density could be used as a point estimate of the 2006 scale score given the student’s 2005 performance. This point estimate could be used to define “expected”, “average”, or “typical” growth. Similarly, the middle 50% of each density gives a range of scores where one would expect such a student’s score to reside 50% of the time. Using quantile regression techniques, conditional densities using more than a single prior score can be estimated. 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. For example, a student growth percentile of 60 indicates the student’s latest scale score exceeded 60 percent of his/her counterparts with equal prior scores. D. W. Betebenner Normative Student Growth

bg=White Defining a Year’s Growth Actual versus Aspirational Student Growth References Describing Actual Student Growth Student Growth Percentiles Student growth percentiles norm each student’s progress relative to similarly performing students. The growth percentiles are estimated using quantile regression techniques (Betebenner & Shang, 2007; Koenker, 2005). The percentile scale on which the growth percentiles lie allows for easy comparison of all students. For example, 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 their academic peers.1 The high achieving student grew at a rate exceeding just 10 percent of their academic peers. In this sense, the low achiever’s growth is more extraordinary than the high achiever’s. Judgment of whether the student’s growth is adequate requires external criteria specifying adequate for what?. The term academic peers is used to describe those students with equal prior achievement. D. W. Betebenner Normative Student Growth

bg=White Defining a Year’s Growth References References Betebenner, D. W. and Shang, Y. (2007). Reference growth charts for educational outcomes. Paper presented at the 2007 AERA Annual Conference, Chicago, IL. Retrieved May 12th, 2007 from http://monticello.bc.edu/Betebenner. Koenker, R. (2005). Quantile Regression. Cambridge University Press, Cambridge. Linn, R. L. (2003). Accountability: Responsibility and reasonable expectations. Technical report, Center for the Study of Evaluation, CRESST, Los Angeles, CA. D. W. Betebenner Normative Student Growth

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Toward a Normative Understanding of Student Growth — NECAPPresentation, December 2007.

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