Growth Model

Superintendent Tom Luna made headlines across the country when he chose to freeze Adequate Yearly Progress (AYP) benchmarks for a year while Idaho began moving toward a new accountability system based on academic growth. For years, states, including Idaho, had talked about the benefits of measuring academic growth as well as proficiency but had not moved in that direction. Many were waiting for the reauthorization of No Child Left Behind. Idaho, however, could not afford to keep waiting.

We know that a statewide accountability system based solely on proficiency is not sufficient to gauge the success of our schools, our classroom teachers or the performance of individual students. Instead, to gain a better idea of how our schools, teachers and students are performing, Idaho must measure how much academic growth a student shows in a given year as well as overall proficiency. This is the foundation for the Idaho Growth Model.

Idaho's growth model is based on the work of Damian W. Betebenner of the Center for Assessment in Dover, New Hampshire. It shares this origin with the successful growth models of Colorado and Massachusetts—two states who also built their systems off Dr. Betebenner's model.

The goal behind including growth in Idaho's assessments is to maximize student progress toward college and career readiness. If our objective is to ensure that all students are ready by the time they graduate high school, we need both a definition of "readiness" and a comprehensive measurement system that determines how well students are progressing toward that goal throughout their time in school.

The current system, NCLB's AYP metric, determines school and student success using ISAT proficiency scores. But proficiency scores alone don't give us the full picture. Today's AYP measurements cannot fully capture the true performance of teachers and schools because a narrow focus on increasing the number of students passing the test does not take into account student growth. For example, a 5th grade student who begins the year reading at a 2nd grade level and finishes the year reading at a 4th grade level has made great gains—two crucial years' progress in just one year—but his/her school may still be labeled as "needs improvement" because the student has not yet passed the test. In short, AYP, as it is currently structured, has been a useful but somewhat blunt accountability model that does not acknowledge important academic gains made in those schools.

A growth model built on assessment data aims to fix this problem. It relies on high-quality information to drive student, teacher, school, district and state performance. Through the Elementary and Secondary Education Act (ESEA) waiver process, Idaho will seek to transition from the current AYP accountability system to a system of increased accountability based on academic growth. Doing so will allow the state to further identify student challenges and engineer interventions that will guide students back on track toward the ultimate goal: readiness when they graduate.

Determining what constitutes adequate student growth is not simple. In order to determine reasonable expectations of growth, we need context. The Student Growth Percentiles (SGP) formula was developed to provide a norm-referenced basis for describing student growth. These percentiles provide the necessary information to answer three crucial growth questions:

  1. How much growth did a child make in one year?
  2. How much growth is enough to reach college and career readiness?
  3. How much growth have other students made with the same starting point?

The answers to these questions give us valuable insight, providing a broader contextual perspective of teacher and school performance. The growth model adds value to proficiency assessments because it takes into account where a student starts the year academically. By grouping students who perform similarly at the beginning of the year, we can compare a student's growth against that of his/her academic peers over time. This helps shape our expectations of how a student should grow.

In his address to Idaho's superintendents at the 2011 Annual Superintendents Meeting, Dr. Betebenner likened the challenge of educating a diverse group of students to the same standard in the same amount of time to driving two different groups of kids to Salt Lake City in the same amount of time. If we have nine hours to get these students to Salt Lake City, but one group starts in Boise and one group starts in Coeur d'Alene, the disproportionate challenge of this task becomes apparent. The students who start in Boise will have no trouble making it to Salt Lake City on time, but the students from Coeur d'Alene might not be able to make it in that time at all. When we realize this, we may have pause to consider other factors, like whether there are other vehicles we can use to get them to Salt Lake City, or whether we may need to adjust the time allotted for their trip.

The growth model will be a valuable addition to the way Idaho measures its school, teacher, and student performance. With it, we can see how students from different schools are growing and performing relative to one another; we can better recognize the teachers who might not get their students to Salt Lake City because they had to start in Coeur d'Alene; and we can reward not just schools and teachers whose students meet standards, but who demonstrate the kind of student growth that allows struggling students to get back on track to meet those standards.


What is the Idaho Growth Model?

The Idaho Growth Model is both:

  • A statistical model to calculate each student's progress on state assessments.
  • A tool for displaying student, school, and district results to educators and to the public.
What will the Idaho Growth Model tell us?

The Idaho Growth Model will show us:

  • how individual students (and groups of students) progress from year to year toward state standards. Each student's progress is compared to the progress of other students in the state with a similar score history on the spring ISAT in mathematics, language arts, and reading (their "academic peers").
  • the observed growth among different groups of students at the state, district, and school level.
  • the level of growth that we need to observe in order for students, on average, to be "ready" for graduation.
  • schools and districts that produce the highest rates of growth in academic achievement. These schools or districts may not be ones with the highest test scores every year; growth level is completely independent of achievement level for individual students.
How do we define growth?

For an individual student, growth is a measure of progress in academic achievement. In the past, this was measured only by a change (a gain or a loss) in test scores from one year to the next. These scores told us how a student was performing relative to state grade-level standards. With the implementation of the Idaho Growth Model, the state will supplement this measure of proficiency with a new growth measurement, which will be expressed in student growth percentiles. The student growth percentile (a student's individual growth score) is derived through quantile regression of all available test scores. The student growth percentile tells us how a student's current test score compares with that of their "academic peers" (students across the state with a history of similar ISAT test scores in a given subject). So, Idaho can now measure growth in two complementary ways, one normative and one achievement-based.

As an example, take the fictional student "Daniel." Daniel scores a 240 on his 5th grade mathematics assessment. This score places Daniel in the "proficient" category. The following year, Daniel takes the 6th grade mathematics assessment and again scores 240. Again, Daniel's score is "proficient." Year-over-year, Daniel's score remains the same, but we know that the 6th grade mathematics assessment is more difficult than the mathematics assessment in 5th grade. We are pleased to see that Daniel is hitting the benchmark for state grade-level standards, but did he grow? If so, how much? Is his growth typical? Extraordinary? Since we know that the 6th grade assessment is more challenging, we can assume that in the year between assessments Daniel gained mastery of a host of new mathematics concepts. Unfortunately, we can't quantify or evaluate the quality of his growth with only a proficiency measure. Idaho's growth model, with its student growth percentiles, is the missing puzzle piece. By comparing Daniel's performance to that of his academic peers, we get a fuller picture of the progress he made over the course of that year. Perhaps his growth has stagnated compared to students who've consistently demonstrated a similar proficiency in the past. Or perhaps, even with a flat year-over-year test score, Daniel is outperforming his academic peers. Daniel's student growth percentile gives us these answers, showing us how much Daniel is growing relative to students in his academic peer group.

The same scenario would be true if David's score had improved to 253 on his 6th grade mathematics assessment. By comparing students with the same achievement history, we can assess whether their growth is high, typical, or low. We are not stuck trying to understand what a 13-point increase really means; we can understand how surprising or unsurprising the new score is based on the scores of other students who have historically performed similarly to Daniel. We use other students' scores to gain context and better understand every student's academic progress.

What is a student growth percentile?

A student growth percentile is a measure of how much growth an individual student made relative to a student's "academic peers." The Idaho Growth Model arrives at a student's individual student growth percentile by comparing each student's current achievement to the achievement of students in the same grade throughout the state who had similar spring ISAT scores in past years. This comparison yields a percentile, between 1 and 99, that describes a student's growth relative to his/her academic peers. The higher the percentile, the more growth the student has made.

The growth model does not compare a student's test score to all the other test scores; it compares a student's test scores to that of his/her academic peers. Therefore, even students with very low test scores can receive high growth scores if they outperform their academic peers.

What is an academic peer?

Academic peers are defined as students in a particular grade with a similar spring ISAT score history. So, for a student who has had consistently low spring ISAT scores for the last few years, his/her growth will be compared to students who have scored similarly.

What is a median growth percentile?

The median growth percentile summarizes student growth rates by district, school, grade level, or other group of interest. The median is calculated by taking the individual student growth percentiles of all the students in the group being analyzed, ordering them from lowest to highest, and identifying the middle score, the median. The median may not be as familiar to people as the average, but it is similar in interpretation - it summarizes the group in a single number that is fairly calculated to reflect the group as a whole. (Medians are more appropriate to use than averages when summarizing a collection of percentile scores because a median is not disproportionately skewed by extreme high and low numbers).

So, the median growth percentile tells us how well a group of students is growing in comparison with other groups. It tells us how much growth a group as a whole is achieving. Knowing these growth levels helps us identify and reward the schools that are seeing high levels of growth and that may have strategies or practices that might help others schools whose student achievement growth could be improved.

How can I help my school get a higher median growth percentile?

For a school to have a higher median growth percentile, the students in the school need to have higher student growth percentiles. This means students' growth rates in that school need to rise. One goal of the Idaho Growth Model is to focus educators' attention on the improvement of all students' growth rates, not just those of students near the boundaries of achievement levels.

Will all students be included in growth reports?

No, only students with at least two points of data (two years of scores) will be included in growth reports. At least two points of data are needed to calculate growth. Students who are not continuously enrolled as defined by Idaho State Board Rule for Adequate Yearly Progress will also not be included. Additionally, students who take the ISAT-Alt (the alternate assessment for the most severely cognitively impaired students) will not be included in a school or district growth percentile calculation because their growth will be measured on an independent scale.

Does the model account for student characteristics such as low socioeconomic status, special education, or LEP students?

No. One of the many benefits of the system is that it is blind to these factors, comparing students based not on categories, gender, or race, but based on their performance relative to the performance of their academic peers. However, schools that demonstrate high growth overall and that posses high populations of certain categories of students may serve as an example to schools seeking to find success with similar populations.

Is growth a better measure of student performance than the ISAT proficiency scores?

No. It simply answers a different question. Student performance toward the end goal of proficiency is still of critical importance. If you want to know how well a student performed on the standards for mathematics or English language arts by the end of 6th grade, the ISAT scale score and performance levels are the best indicators. If you are trying to determine how much an individual student's performance has changed from 2011-2012 relative to the student's academic peers, the growth model is the best indicator. A more complete understanding of performance can be obtained by using both measures.

Material for this document was created with the help of the education departments in the states of Colorado and Massachusetts.