Student Growth Percentiles: Toward a Normative Understanding of Student Growth

Kansas Department of Education · May 2008

Student Growth Percentiles: Toward a Normative Understanding of Student Growth — Kansas Department of Education, May 2008.
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May 13, 2008

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State agency
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  1. Overview Normative Student Growth Descriptive/Prescriptive Growth References Student Growth Percentiles: Toward a Normative Understanding of Student Growth Damian W. Betebenner National Center for the Improvement of Educational Assessment Dover, NH Growth Models – A Joint Exploration Lawrence, Kansas May 20th, 2008 Damian W. Betebenner Normative Student Growth
  2. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models References Statistics Wisdom (an oxymoron?) John Tukey It is better to have an approximate answer to the right question than a precise answer to the wrong question. George E. P. Box All models are wrong but some are useful. Recommendation: Start at the end What are the questions and uses Kansas would like student growth analyses to address? Damian W. Betebenner Normative Student Growth
  3. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models References What are the relevant questions? Statistical models address specific questions Different growth analysis techniques answer (or fail to answer) different, but often related, questions It is critical to understanding these different questions. Answers to different questions often lead to different uses and outcomes. Questions form the vocabulary of later discussions Starting with the right questions simplifies both the development of appropriate analyses and motivating the proper use of the results. Clearly articulating the questions to be answered (which often differ by stakeholder group) sets the stage for subsequent conversations that will take place. Damian W. Betebenner Normative Student Growth
  4. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models 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 Normative Student Growth
  5. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models 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 Normative Student Growth
  6. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models 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 Normative Student Growth
  7. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models References Why Growth in Accountability? Fundamental Premise “Good” schools bring about student growth in excess of that found at “bad” schools. The inherent believability of this premise is at the heart of current enthusiasm to incorporate growth models into state accountability systems. Note that current NCLB accountability invokes the same premise with achievement substituted for growth. In light of this premise, “good schools” are commonly referred to as highly effective schools. However, it is critical to understand the distinction between growth and effectiveness. Damian W. Betebenner Normative Student Growth
  8. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models References Value-added Models/Inferences Who/What is responsible for student growth? Currently, the most common 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 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. The foremost example being the value-added models developed by Dr. William Sanders and used in many school districts nationwide to infer teacher or school effectiveness. These models and their effectiveness claims are controversial for a number of reasons [Braun, 2005, Rubin et al., 2004]. Value-added models are better described as effectiveness models than as growth models. Damian W. Betebenner Normative Student Growth
  9. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models References Descriptive Growth Models Describing Growth versus Ascribing Responsibility Yen’s questions make no mention of effectiveness. The questions point toward a description of student growth. An important first step in the development of Colorado’s Growth Model was to separate the description of growth from the assignment of responsibility (i.e., accountability) Incorporation of growth into the accountability system followed from the viable description of growth. What follows is an introduction to student growth percentiles—a normative description of growth that forms the basis of Colorado’s Growth Model. Damian W. Betebenner Normative Student Growth
  10. Overview Normative Student Growth Describing Actual Student Growth Descriptive/Prescriptive Growth References 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 other children between ages 3 and 4. In the following discussion student growth percentiles are introduced to provide a normative context for interpreting student growth. Damian W. Betebenner Normative Student Growth
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  15. Overview Normative Student Growth Describing Actual Student Growth Descriptive/Prescriptive Growth References Student Growth Percentiles 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. 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 Normative Student Growth
  16. Overview Normative Student Growth Describing Actual Student Growth Descriptive/Prescriptive Growth References Student Growth Percentiles Student growth percentiles norm each student’s growth relative to their academic peers. 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 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. However, judgment of whether the student’s growth was adequate requires external criteria. Damian W. Betebenner Normative Student Growth
  17. Overview Normative Student Growth Combining Actual and Aspirational Growth Descriptive/Prescriptive Growth References Combining Actual and Aspirational Growth Using student growth percentiles it is simple to reconcile actual growth measures with aspirational growth targets. Each student receives a growth percentile derived from present performance conditioning upon past performance. Growth standard setting is conducted to determine what growth percentiles will be considered adequate and what growth percentiles will be considered inadequate. For example, consider a student just completing the 5th grade Their reading was at the partially proficient level. However, considering their 3rd and 4th grade achievement, they grew in the last year at the 95th percentile. Damian W. Betebenner Normative Student Growth
  18. 100th 600 97th 90th 95th ● 47th 90th 65th 50th 65th 35th 50th 35th 10th 8th ● 10th Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008
  19. Overview Normative Student Growth Descriptive/Prescriptive Growth 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. 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. 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 Normative Student Growth