## Methods Used and Key Growth Model Terms

The West Virginia Growth Model uses the statistical methodology pioneered by the State of Colorado and Dr. Damian Betebenner to develop several new and easy to understand measures of student growth. The two primary measures with which users must be familiar are:

1. Student Growth Percentiles (SGPs): The SGP is the core concept of the WV Growth Model. It provides descriptive and diagnostic information about how much growth has occurred for a given student over the course of a single year when compared with students across the state that have similar academic histories (i.e., their academic peers). The model uses a statistical analysis to examine a student’s growth on the WESTEST 2 relative to those students who have previously “walked the same performance path.” The student growth percentile can be interpreted as a relatively easily understandable probability statement that informs stakeholders about the amount of observed growth for the student.

For example, if a student has an SGP of 60 for mathematics in a given year, that means he/she grew at a rate that was faster than 60 percent of her/his academic peers. Similarly, it also means that 40 percent of her/his academic peers grew at a faster rate.

1. Student Growth Percentile Targets: Once we know what SGP a student has achieved, we can apply the results forward and determine potential future outcomes for that student based upon several different growth scenarios. These “trajectories” provide a real time view of what levels of growth are necessary for the student to reach a given level of performance on the WESTEST 2 within a certain period of time. The trajectories allow stakeholders to quantify a Target SGP which indicates what level of growth it will take for the student to reach her/his desired academic outcome. In conjunction with pre-defined performance goals and timelines, the results can be used to define what level of growth is adequate to achieve or retain mastery of the West Virginia CSOs within a reasonable period of time.

### How student growth percentiles are calculated:

Student growth percentiles are determined through a regression-based statistical technique (i.e., quantile regression) using all consecutive prior scale scores within a given content area and grade. For example, to calculate a 5th grade student’s reading/language arts growth percentile for the 2009-2010 academic year, all students taking the 5th grade exam in 2010 are first selected. Those with at least a grade 4 reading/language arts scale score for the previous academic year are analyzed to calculate student growth percentiles ranging from 1 to 99 for each student. The quantile regression analyses allow the state to calculate percentiles associated with the conditional distribution for each student with at least two consecutive scores in consecutive grades in the state (i.e., conditional percentiles). The conditional percentile indicates where each student’s current score resides in that distribution and serves to quantify how unlikely each student’s current score is given their prior academic scores.

### For whom student growth percentiles can be calculated

As noted above, the proposed growth model requires at least two consecutive years of academic performance data for each student. Because WESTEST 2 is administered annually to all students in grades 3 through 11, West Virginia expects to be able to calculate student growth percentiles for all students with at least two consecutive scale scores in grades 4 through 11. Students with only one data point (e.g., 3rd grade students, incoming students, etc.) or students with multiple data points, none of which are consecutive, would not receive growth calculations. Furthermore, students who are retained and have two consecutive scale scores measured at the same grade level, would also not be included in the calculation. Finally, at least during initial implementation, students who are assessed with the Alternate Performance Task Assessment (APTA), West Virginia’s statewide assessment based on alternate academic achievement standards, will not be included in growth calculations. The state will investigate whether these students can be included or analyzed separately in future West Virginia growth analyses.

West Virginia has defined three classifications of academic growth (low, typical, and high). You can easily see which level of growth a student has achieved by comparing her/his SGP to the ranges in Figure 1 below.

Figure 1. Three Levels of Growth

Figure 1 clearly illustrates that Low Growth is defined as any SGP that is below 35. This means that students who exhibit low growth are only growing faster than 34 percent of their academic peers. Conversely, it also means that 65 percent of their academic peers grew at a faster rate. It is considered low because a majority of academic peers are outpacing the student.

Typical growth is defined as any SGP between 35 and 65. Consider a student with an SGP of 55. This means she/he grew faster than 55 percent of her/his academic peers, but it also means that 45 percent of her/his peers grew faster. This level of growth is typical because the student is near the middle of her/his academic peers in terms of growth.

High growth is defined as any SGP higher than 65. Consider a student with an SGP of 90. This indicates that she/he grew faster than 90 percent of her/his academic peers, and that only 10 percent of her/his peers grew faster—a very high level of growth.

Figure 2 provides another way of looking at these ranges.

Figure2. Graphical Representation of Three Levels of Growth

#### Aggregating Student Growth Percentiles: The Median Student Growth Percentile

The median growth percentile is a summary measure of how much a group of students has grown during a single academic year. It is the middle value in a rank ordered list of individual student growth percentiles and, like an average, provides a measure of where the middle of the distribution is. For example, if a group of 5 students had student growth percentiles of 40, 56, 70, 88 and 90, the median growth percentile for the group would be 70. The median is used instead of an average because it is not mathematically appropriate to average percentile ranks. The median growth percentile is a summary statistic that can be calculated for any group of interest (e.g., state, district, school, classroom, student participating in a specific curriculum etc.). As such it can provide useful information about which districts, schools, classrooms and programs are demonstrating probabilistically low or high levels of growth. It can also be used to determine the level of growth for particular subgroups of interest such as students with disabilities or students of various racial/ethnic groups.

#### Determining Growth-to-Standard

Student growth percentiles and the median growth percentile provide descriptive and diagnostic information about how much growth a given student or group of students has achieved relative to other academically similar peers. This norm-referenced information is easily understandable and greatly useful to a variety of stakeholders for many purposes, but there are limitations to what the student growth percentile can tell us. In order to determine the extent to which exhibited growth is adequate for non-proficient students to attain mastery (i.e., catch up) or for proficient students to retain mastery (i.e., keep up) of the West Virginia CSOs, the concept of the student growth percentile must be extended and applied forward. This requires embedding the norm-referenced student growth percentile descriptions which explicate “what growth has occurred” within a criterion-referenced framework of pre-established performance goals and timelines for each student. These goals, combined with the student growth percentiles, yield criterion-referenced estimations of “what growth needs to occur” if students are to meet or maintain proficiency. These calculations are often referred to as “growth-to-standard.”  As such, each year, all eligible students receive a student growth percentile as well as a target student growth percentile indicating what student growth percentile the states estimates is necessary for that student to reach their performance goal within a policy-defined time frame.

Growth-to-standard currently finds favor amongst federal policy makers as the means to incorporate growth into accountability systems. The Growth Model Pilot Program instituted by USED in 2005 culminated in 15 states being approved for the use of student growth data within AYP calculations. These models were built around the expectations of No Child Left Behind, specifically the universal proficiency mandate. In the current ESEA reauthorization blueprint, the discussion of growth-to-standard is featured prominently vis-à-vis the 2020 mandate for universal college and career readiness.