New Directions for Student Growth Models

Metametrics · January 18, 2011

New Directions for Student Growth Models — Metametrics, January 18, 2011.
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January 18, 2011

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  1. Intro Student Growth Percentiles and Accountability References New Directions for Student Growth Models Damian W. Betebenner National Center for the Improvement of Educational Assessment Dover, NH Metametrics Raleigh-Durham, North Carolina January 18th, 2011 Damian W. Betebenner New Directions for Student Growth Models
  2. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth About Me Dr. Damian Betebenner, PhD - Senior Associate at the Center for Assessment (NCIEA). - Developed student growth percentiles and percentile growth trajectories to help states and educational associations employ student growth in decision making [Betebenner, 2008, Betebenner, 2009]. - Currently refining and sharing these techniques with other states including Colorado, Massachusetts, Indiana, Virginia and 15 other states in various stages of investigation/adoption. Damian W. Betebenner New Directions for Student Growth Models
  3. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Lessons Learned On Questions John Tukey It is better to have an approximate answer to the right question than a precise answer to the wrong question. On Statistical Models George E. P. Box All models are wrong but some are useful. On Understanding Aristotle We understand best those things we see emerge from their very beginnings. On Accountability Sherlock Holmes It is a capital mistake to theorize before you have all the evidence. It biases the judgment. On Theories of Action Confucius Tell me and I will forget, show me and I will remember, involve me and I will understand. Damian W. Betebenner New Directions for Student Growth Models
  4. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Describing Student Growth Measuring student growth, even with a vertical scale, is not a simple task. Some believe a vertical scale simplifies 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. The 4 inch increase becomes really meaningful only when understood alongside the growth of other 3 to 4 year olds. Student growth percentiles were developed to provide a normative context for describing student growth. Damian W. Betebenner New Directions for Student Growth Models
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  9. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Student Growth Percentiles Should we be surprised with a child’s current achievement given their prior achievement? 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. 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 New Directions for Student Growth Models
  10. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Student Growth Percentiles Should we be surprised with a child’s current achievement given their prior achievement? Student growth percentiles answer this question. Consider a low achieving student with 90th percentile growth and a high achieving student with 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. The low achiever’s growth is more exemplary (probabilistically) than the high achiever’s. Judgments about the adequacy of student growth require external criteria. Damian W. Betebenner New Directions for Student Growth Models
  11. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Model for Student Growth Percentiles Student growth percentiles are calculated using quantile regression with B-spline smoothing, a generalized additive model. Quantile regression is used to model the complete distribution of the response variable (current achievement) B-spline smoothing is uses to accommodate non-linearity and heteroscedasticity of the data. The model/method is descriptive and all about data fit—it’s a data mining procedure. The model quantifies distance = rate · time probabilistically. Damian W. Betebenner New Directions for Student Growth Models
  12. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Model for Student Growth Percentiles Conditional Decile Regression Curves Conditional Decile Regression Lines 2006−07 Math: Grade 5 versus 6 2006−07 Math: Grade 5 versus 6 1000 Unsatisfactory Partially Prof. 1000 Unsatisfactory Partially Prof. Proficient Proficient Partially Prof. Proficient Advanced Partially Prof. Proficient Advanced Grade 6 Scale Score Grade 6 Scale Score Grade 5 Scale Score Grade 5 Scale Score Damian W. Betebenner New Directions for Student Growth Models
  13. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Software for Student Growth Percentiles Student Growth Percentiles and Percentile Growth Trajectories are calculated using the open source R Software Environment [R Development Core Team, 2010] and the SGP package [Betebenner, 2011] In working with state departments of education, the goal is to build state capacity so states can perform and validate their own analyses using software available and easily used by the state. Colorado, Massachusetts, Indiana, and Wisconsin are four states (that I know of) who have state staff capable of generating the student growth percentiles together with aggregations that follow from their calculation. State ownership/oversight of the SGP calculations has been a big plus in terms of buy-in from the state, enhancing their ability to explain and work with local stakeholders. Damian W. Betebenner New Directions for Student Growth Models
  14. Describing Student Growth Intro Student Growth Percentiles Student Growth Percentiles and Accountability Model & Software for Student Growth Percentiles References Criterion Referenced Growth Establishing growth-standards based upon growth-norms The most common adequacy criterion are judging growth toward an achievement goal (i.e., growth-to-standard). Results from student growth percentile analyses can be used to calculate percentile growth trajectories for each student. These trajectories indicate what future rates of growth will lead to and are used to make adequacy judgments. This growth-to-standard approach was approved as part of Colorado’s successful application to the Growth Model Pilot Program. Damian W. Betebenner New Directions for Student Growth Models
  15. Advanced Reading High Achievement CSAP Reading ● Typical Scale Score Proficient Growth Low ● Level Percentiles High 66th − 99th Typical 35th − 65th Part Proficient ● Low 1st − 34th Unsatisfactory Grade 3 Grade 4 Grade 5 Grade 6 Next Year Scale Score 462 539 563 609 Achievement Level Unsatisfactory Part Proficient Part Proficient Proficient Achievement Growth Percentile 66 66 90 Growth Level High High High Growth
  16. Example Student 12 (1234567812) Sample Middle School Advanced Math Achievement High CSAP Math ● Scale Score Typical ● Growth Proficient ● Level Percentiles Low High 66th − 99th ● Typical 35th − 65th Part Proficient Low 1st − 34th Unsatisfactory Grade 3 Grade 4 Grade 5 Grade 6 Next Year Scale Score 379 388 444 462 Achievement Level Part Proficient Part Proficient Part Proficient Part Proficient Achievement Growth Percentile 16 69 51 Growth Level Low High Typical Growth Advanced Reading High Achievement CSAP Reading ● Typical Scale Score Proficient Growth Low ● Level Percentiles High 66th − 99th Typical 35th − 65th Part Proficient ● Low 1st − 34th Unsatisfactory Grade 3 Grade 4 Grade 5 Grade 6 Next Year Scale Score 462 539 563 609 Achievement Level Unsatisfactory Part Proficient Part Proficient Proficient Achievement Growth Percentile 66 66 90 Growth Level High High High Growth Advanced Writing Achievement High CSAP Writing ● Scale Score Typical ● Growth Proficient Level Percentiles ● Low High 66th − 99th Part Proficient ● Typical 35th − 65th Low 1st − 34th Unsatisfactory Grade 3 Grade 4 Grade 5 Grade 6 Next Year Scale Score 425 449 469 504 Achievement Level Part Proficient Part Proficient Part Proficient Part Proficient Achievement Growth Percentile 55 53 79 Growth Level Typical Typical High Growth Copyright 2009, Colorado Department of Education/Center for Assessment, Inc.
  17. 2008 CSAP Mathematics Growth and Achievement Chart 2008 Achievement Percentile Percentile Growth Trajectory Scale Score Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10
  18. Intro School Accountability Student Growth Percentiles and Accountability Concluding Remarks References Going from Students to Schools/Classrooms It’s of interest to examine schools or classrooms/teachers where students demonstrate, on average, extraordinarily high and low student growth. To summarize the student growth percentiles associated with a school (or other grouping) calculate the median of the student growth percentiles. If students were randomly assigned to schools, expect to see a median of 50. Values greatly above or below 50 are of interest in identifying best practices or providing extra support. Examining growth with achievement sheds new light on school performance. Damian W. Betebenner New Directions for Student Growth Models
  19. District C: 2008 CSAP Math School Results Student Growth versus Student Achievement by Percent Free/Reduced Lunch School Percent Higher Achievement Higher Achievement Free/Reduced Lunch Lower Growth Higher Growth Percent at/above Proficient in School Less than 20 percent ● 20 to 40 percent ● 40 to 60 percent ● 60 to 80 percent ● More than 80 percent School Size 50 Students 100 Students 200 Students 30 500 Students 1,000 Students 10 Lower Growth Higher Growth Lower Achievement Lower Achievement Median of Student Growth Percentiles in School
  20. Intro School Accountability Student Growth Percentiles and Accountability Concluding Remarks References What’s Next? Colorado, Massachusetts, and Indiana have publicly released growth results. The response has been overwhelmingly positive. Calculating of the quantities is the easy part. Getting people to understand them and use them correctly is the hard part. Colorado, Massachusetts, Indiana, Virginia, and other states are investigating a multi-state platform for data visualization and reporting built from a common growth analysis. Damian W. Betebenner New Directions for Student Growth Models
  21. The Colorado Growth Model Adopted Model Near Model Adoption Interested in Model
  22. Intro Student Growth Percentiles and Accountability References References Betebenner, D. W. (2008). Toward a normative understanding of student growth. In Ryan, K. E. and Shepard, L. A., editors, The Future of Test-Based Educational Accountability, pages 155–170. Taylor & Francis, New York. Betebenner, D. W. (2009). Norm- and criterion-referenced student growth. Educational Measurement: Issues and Practice, 28(4):42–51. Betebenner, D. W. (2011). SGP: Student Growth Percentile and Percentile Growth Projection/Trajectory Functions. R package version 0.0-6.7. R Development Core Team (2010). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Damian W. Betebenner New Directions for Student Growth Models