Colorado’s Growth Model: A Harmonious Marriage of Normative and Standards-based Growth

CCSSO · June 2008

Colorado’s Growth Model: A Harmonious Marriage of Normative and Standards-based Growth — CCSSO, June 2008.
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June 17, 2008

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  1. Overview Normative Student Growth Descriptive/Prescriptive Growth References Colorado’s Growth Model A Harmonious Marriage of Normative and Standards-based Growth Damian W. Betebenner National Center for the Improvement of Educational Assessment Dover, NH CCSSO — June 17th, 2008 Damian W. Betebenner Colorado’s Growth Model
  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. Colorado Started at the End What are the questions and uses Colorado would ultimately like stu- dent growth analyses to address? Damian W. Betebenner Colorado’s Growth Model
  3. 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. These questions/concerns formed the basis for Colorado’s discussions. 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 Colorado’s Growth Model
  4. 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. These questions/concerns formed the basis for Colorado’s discussions. 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 Colorado’s Growth Model
  5. 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. These questions/concerns formed the basis for Colorado’s discussions. 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 Colorado’s Growth Model
  6. 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. 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. Fundamental in the development of Colorado’s Growth Model was to distinguish between growth and effectiveness. Damian W. Betebenner Colorado’s Growth Model
  7. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models References Value-added Models/Inferences Who/What is responsible for student growth? The most common application of student growth analyses is 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. These models and their effectiveness claims are controversial for a number of reasons [Briggs and Weeks, 2008, Braun, 2005, Rubin et al., 2004]. Value-added models are better described as effectiveness models than as growth models. Damian W. Betebenner Colorado’s Growth Model
  8. Overview Normative Student Growth Relevant Questions Descriptive/Prescriptive Growth Growth Models References Descriptive Growth Models Describing Growth versus Ascribing Responsibility 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 understandable to stakeholders. Student growth percentiles—a normative description of growth—forms the basis of Colorado’s Growth Model. Damian W. Betebenner Colorado’s Growth Model
  9. Overview Normative Student Growth Describing Actual Student Growth Descriptive/Prescriptive Growth References Describing 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 Colorado’s Growth Model
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  14. 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 Colorado’s Growth Model
  15. 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, most commonly state established performance standards. Damian W. Betebenner Colorado’s Growth Model
  16. Overview Normative Student Growth Combining Actual and Aspirational Growth Descriptive/Prescriptive Growth References Combining Actual and Aspirational Growth Broadly, Colorado’s Growth Model addresses three related questions using the same percentile metric: What is a the level of growth for a student (i.e. Actual Growth) What should the level of growth for a student be (i.e. Aspirational Growth) What level of growth for the student is possible (i.e., Realistic Growth) Damian W. Betebenner Colorado’s Growth Model
  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-to-standard achievment targets. Actual Growth In Colorado, each student receives a growth percentile quantifying their growth in each of three subject for the academic year. Aspirational Growth In Colorado, each student receives growth percentile projections esti- mating: What level of growth is required to reach each of the 3 performance levels in 1 year. What level of growth is required to reach each of the 3 performance levels in 2 years. What level of growth is required to reach each of the 3 performance levels in 3 years. Damian W. Betebenner Colorado’s Growth Model
  18. 90th 65th 50th 500 35th 10th 8th ● Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
  19. 90th 95th ● 90th 65th 50th 65th 35th 50th 35th 10th 8th ● 10th Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
  20. 700 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 Grade 7/2009 Grade 8/2010
  21. 100th 93rd 61st 90th 95th ● 90th 65th 50th 65th 35th 50th 35th 10th 8th ● 10th Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
  22. 100th 89th 54th 90th 95th ● 90th 65th 50th 65th 35th 50th 35th 10th 8th ● 10th Grade 3/2005 Grade 4/2006 Grade 5/2007 Grade 6/2008 Grade 7/2009 Grade 8/2010
  23. 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. Briggs, D. C. and Weeks, J. (2008). The persistence of value-added school effects. Paper presented at the 2008 AERA Annual Meeting, New York, NY, March 27, 2008. 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 Colorado’s Growth Model