What is a student growth percentile?

A student growth percentile (abbreviated SGP) measures how much a student's performance has improved from one year to the next relative to his or her academic peers: other students statewide with similar MCAS test scores in prior years. The calculation answers the question, "Among other students with similar MCAS test score histories in previous years, what is the range of scores attained this year?" The model then uses the answer to determine whether a student grew at a faster or slower rate than the students' peers, or at a similar rate.

The statistic is interpreted as follows: if John Smith, currently a grade 5 student, has a student growth percentile of 65 in English language arts, that means that John improved more between grades 4 and 5 than 65 percent of students statewide with a similar historical pattern of MCAS test scores. Similarly, if John had a student growth percentile of 44 in mathematics, it means that he improved more than only 44 percent of students statewide with a similar MCAS test score history.

Against whom are students being compared to generate student growth percentiles?

Each student is being compared to his or her academic peers: other students statewide with similar MCAS test score histories. This makes for a fair comparison because it allows us to describe the likely range of scores observed among all students with a similar MCAS test score history, and therefore to see how quickly the student improved given his or her past test scores.

Can students who perform at the top range of the Advanced level (270-280) show growth?

Yes. One of the Department's criteria for selecting a model was that it had to measure growth even at the top (and bottom) of the MCAS performance scale. This way, all students would have the opportunity to exhibit growth. The model accounts for this by measuring each child's growth relative to his or her academic peers.

Let's suppose Jane Adams scored 280 on the grade 4 and 5 math tests. Students who scored similarly to this would comprise her comparison group-she would be compared only to other students who had performed similarly on those tests. Then, in grade 6, Jane again scores 280. She would probably have a very high student growth percentile in mathematics, as most of the students in her comparison group would likely score less than 280. In fact, most students who score 280 on one test will score less than 280 on the next year's test. Only about 5% of students repeat a 280 score from one year to the next, so Jane would likely be in the 95th percentile for growth.

What does the median student growth percentile at my school represent?

The median student growth percentile is the midpoint of student growth percentiles in the school. Half of the students had student growth percentiles higher than the median; half had lower. This is a good way of describing the typical growth of students in the school. It is not appropriate to use the average ("mean") when comparing percentiles.

Can the student growth percentile be interpreted the same way regardless of grade?

Yes. A student with a student growth percentile of 60 improved more than 60 percent of his academic peers relative to their performance the prior year, whether that student is enrolled in grade 4, 5, 6, 7, 8 or 10.

Can the student growth percentile be interpreted the same way regardless of the test's subject matter?

Yes. A student with a student growth percentile of 60 in English language arts improved more than 60 percent of his academic peers in English language arts relative to the prior year. A student with a student growth percentile of 60 in mathematics improved more than 60 percent of his academic peers in mathematics.

Can the student growth percentile be interpreted the same way regardless of the year?

Not necessarily. The same trajectory of scores could yield higher or lower student growth percentiles depending on the trend in performance statewide. Let's suppose a student scored 220 in mathematics in grade 4 in 2008, 222 in grade 5 in 2009, and 228 in grade 6 in 2010, and that the change from 222 to 228 represented a student growth percentile of 65. Now let's suppose that in 2011, the entire state's performance in mathematics improves quite rapidly, so that a substantially larger percentage of students are Proficient across all grades. In that case, the same test history might represent less than 65th percentile growth, since performance is increasing overall statewide.

Can two students with different score histories have the same student growth percentiles?

Yes. Each student's growth is compared only to that of others with a similar MCAS test score history. The performance of Student A or Student B is compared to that of their academic peers statewide with similar trajectories. Because Student A and Student B have different score histories, Student A is not compared to Student B

Can two different students with the same MCAS scaled score test histories have different student growth percentiles?

Yes. This can happen for at least two reasons. First, the growth calculation takes into account a student's entire MCAS test score history, not just that of the previous year. Therefore, two students could have the same scaled scores in 2010 but different scaled scores in 2009 or earlier and therefore receive the same student growth percentile. Second, the student growth percentile metric is calculated from a transformation of the raw scores that underlie the scaled scores, not the scaled scores themselves. As many as five different raw scores can translate into the same scaled score, especially for students at the Warning/Failing and Advanced performance levels. Students with the same scaled score history may not have the same raw scores and therefore would not receive the same student growth percentiles.

If the median growth of my district's African-American subgroup is 59, does this mean that the average African-American student in my district grew at a faster rate than 59 percent of African-American students statewide?

No. Students are compared to their academic peers-students with similar MCAS test score histories statewide-not their demographic peers. The correct interpretation of a median student growth percentile of 59 for the African-American subgroup in a district is, "The African-American students in my district improved more than 59 percent of their academic peers statewide." The fact that 59 is slightly higher than 50 means that the African-American subgroup performance in your district is improving slightly more than one would expect given the performance of its academic peers.

Research shows that there are correlations between a student's demographic group and their performance on the MCAS. Is the same true with growth?

Not necessarily. The relationship between demographics and growth is complex, much more so than the relationship between demographics and achievement. For instance, because there are numerous studies that have established a correlation between economic disadvantage and achievement level, one might expect that low income students would achieve at a lower level than students without such economic disadvantages. However, it is not so clear that low income students should grow slower once you've taken performance level into account, given the way we calculate growth.

How does the median student growth percentile relate to the Composite Performance Index?

The Composite Performance Index (CPI) describes a group of students' progress toward proficiency based on the students' current level of achievement. Students are assigned points based on how close they are to proficiency. All students scoring Proficient and above receive the same score of 100; because of this, the measure is not sensitive to changes in achievement among students who have attained Proficient or Advanced. Changes in a group's CPI over time can show its progress toward proficiency.

The median student growth percentile describes a group's progress in terms of its students' change in achievement relative to the prior year, as compared to that of their academic peers. Thus it is more directly related to changes in CPI than it is to the CPI level itself. It also captures growth at all levels of achievement, not just among students below Proficient. And finally, it is calculated for a narrower range of students-only those with at least one year of prior test history.

As a result, the two measures can sometimes show different results. For instance, in a district where most of the students achieve at Proficient or above, its CPI may not show much change from year to year, but its median SGP could show that its students are growing quickly relative to their academic peers. On the other hand, in a district with relatively low overall achievement, CPIs could change substantially while the median SGP held steady, especially if overall statewide achievement increased or if the district experienced a high rate of student mobility (and therefore had relatively fewer students with SGPs).

If my school's Composite Performance Index and/or percent Proficient are increasing, will its median student growth percentile increase too?

Not necessarily, it depends on how overall state performance is changing. If your school's achievement is increasing but not as quickly as that of the state overall, your CPI would increase but your school's median student growth percentile would be below 50.

If my school made AYP, does that mean my students are growing faster than their academic peers?

No. AYP determinations are based on absolute achievement and not related to growth measures. Therefore, it is possible for schools to make AYP and have low growth, if most of the school's students have achieved at the Proficient level but their performance grows more slowly than that of their academic peers. Likewise, it is possible for a school to have most of its students growing at high rates and still not make AYP.