Introduction
The COVID-19 pandemic led to historic changes in public school enrollment in the US. There has been considerable interest in quantifying the magnitude of these changes, and in understanding their causes and consequences (e.g., Dee & Murphy, 2021). An analysis of enrollment data across all 50 states and the District of Columbia by EdWeek documented a nearly 3% decline in public school enrollment in the 2020-21 academic year (AY), relative to 2019-20 AY enrollments (Pendharkar, 2022). Although enrollments declined in all states, the declines tended to be larger in lower grades; kindergarten enrollment declined by more than 10% in 20 states, for example, which was often larger than the declines in other grades. In Colorado, for example, while total preschool through 12th grade enrollment declined by about 3.3%, kindergarten enrollment declined by about 9.1% (Colorado Department of Education, 2021).
Tracking changes to public school enrollments is critical to understanding the impacts of the pandemic and planning to support schools and students moving forward. Studying the within-grade changes in enrollment, however, can potentially be misleading when comparing the changes across different grade levels, because these statistics confound changes due to pandemic-related factors with pre-existing trends in changing cohort sizes over time.
This brief describes two different ways that grade level enrollment changes can be calculated. The first is the within-grade change in enrollments, which has been most commonly reported. The second is the cohort-adjusted change in enrollment that calculates changes to grade level enrollment adjusting for prior grade enrollment. State level enrollment data from two states are used to illustrate the differences between these two methods. The brief also highlights the importance of comparing changes to pre-pandemic trends and shows how comparing enrollment change patterns across states, particularly with the cohort-adjusted metric, can document variation in cross-state enrollment dynamics that may provide opportunity for future studies.
Data
The analyses in this brief are based on publicly reported state level enrollment data (the fall census counts of enrolled students) in Colorado and Massachusetts, as reported by the Colorado Department of Education (CDE) and the Massachusetts Department of Elementary and Secondary Education (MDESE) for the 2015-16 through 2021-22 AY1.
Two Methods for Calculating Grade Level Enrollment Change
Although Colorado public school enrollment declined drastically in 2020-21, these changes were not consistently distributed throughout the state or across grade levels. Declines in enrollment were much larger in the lower elementary grades. These changes have primarily been tracked by comparing the grade level enrollment in the 2020-21 AY to the grade level enrollments in the prior 2019-20 AY. These changes in enrollment are what I will refer to as “within-grade” changes, and are calculated as:
where 
is the enrollment in grade g in year y, and 
is the enrollment in grade g in the prior year2. Figure 1 plots the within-grade percent changes in enrollment from kindergarten through 12th grade in the 2020-21 AY in Colorado. As reported, the largest decline was observed in kindergarten. The figure also illustrates within-grade declines were larger in elementary and middle school grades, with either very small declines or in some cases positive changes in enrollment in high school. But the pattern is not entirely easy to explain. Aside from kindergarten, the largest decline was observed in 5th grade, with slightly smaller declines in other elementary grades. The smallest decline in elementary school was in first grade, which seems counterintuitive given the much larger decline in kindergarten enrollment.
Figure 1. Within-Grade Percent Change in Grade Level Enrollments in CO (2020-21).
These counterintuitive results may occur at least in part because the within-grade changes in enrollment confound year specific changes in enrollment with changes to the size of Colorado public school student cohorts. To illustrate this, Table 1 presents 4th and 5th grade enrollment counts from 2019-20 and 2020-213. The gray cells highlight an intact “cohort” – students who were enrolled in 4th grade in 2019-20 and 5th grade in 2020-21 as an example. Since the 2015-16 AY, the size of the incoming first grade cohorts in Colorado have been steadily declining, by as much as 3% in some years. The relatively large decline in 5th and 6th grade enrollment seen in Figure 1 were due in part to the fact that these cohorts of students were already smaller than the cohorts ahead of them. The within-grade change in enrollment for 5th grade in 2020-21 can be calculated as:
Table 1 also shows that in 2019-20, prior to the pandemic, the cohort of students who would move on to 5th grade in 2021 was 66,172, substantially smaller than the cohort of 68,592 students ahead of them. Even if all 66,172 of the 2019-20 4th graders had progressed to 5th grade in 2020-21, the within-grade decline in enrollment would have been about -3.5%, similar in magnitude to the average changes across elementary grades in Figure 1. This occurs because the within-grade change in enrollment is sensitive both to students disenrolling from school and to differences in the size of successive cohorts.
Table 1. Grades 4 and 5 Enrollment Counts in Colorado in 2019-20 and 2020-21.
Calculating the within-grade change to enrollment is important and is certainly in no way “incorrect.” For funding and planning purposes, it is often necessary to know, for example, how many kindergarten or first grade students are enrolled in the current year, and how this compares to enrollments the prior year. However, to understand the dynamics that cause changes to enrollments or to track trends over time, this within-grade change in enrollment can potentially be misleading.
A better metric for measuring changes to grade level enrollment for some purposes is the “cohort-adjusted” change in enrollment. The cohort-adjusted change in enrollment compares the grade level enrollment in a given grade and year relative to the number of students enrolled in the prior grade in the prior year. That is, it compares the relative change in the size of a particular cohort as they progress from one grade to the next. This metric can be calculated as:
In this example, we would compare the number of 5th grade students in 2020-21 to the number of 4th grade students in 2019-20, to calculate a cohort-adjusted change in 5th grade enrollment of:
Enrollment in 5th grade did decline relative to what we would have expected if all 4th graders from 2019-20 had progressed one grade and returned to public school, but the decline is significantly smaller than the within-grade change suggests.
Figure 2 shows the cohort-adjusted changes to grade level enrollments in Colorado in 2020-21. Note that because preschool is not universal in Colorado, public preschool enrollments tend to be inconsistent and substantially smaller than kindergarten enrollments. The cohort-adjusted enrollment change is calculated starting in first grade, which uses kindergarten enrollments in the prior year in the calculation.
Figure 2. Cohort-Adjusted Percent Change in Grade Level Enrollments in CO (2020-21).
Although the cohort-adjusted changes tell a similar overall story (larger declines to enrollment in lower grades) there are three important substantive differences that the cohort-adjusted metric highlights. First, there is now a clear trend across the elementary and middle school grades that is straightforward to explain – it appears that parents were most often holding their youngest children out of school, and the proportion of families doing so became steadily smaller from 1st through 8th grade. This pattern was not obvious in the within-grade changes that confounded enrollment changes due to the pandemic with changes in overall cohort sizes over time. Second, there were noticeable increases in enrollments in 9th and 12th grade, relative to the number of 8th and 11th graders enrolled in school in the 2019-20 AY. The increase in cohort-adjusted 12th grade enrollment was nearly 6.5%, or about 4,350 students. Finally, while the within-grade changes in enrollment suggested either very small declines or increases in 10th and 11th grade enrollments relative to 2019-20, the cohort-adjusted rates suggest fairly sizable declines in 10th and 11th grade enrollments relative to the number of students in 9th and 10th grade in 2019-20.
Because both metrics are based on aggregate enrollment counts rather than longitudinal student-level data, neither metric can directly quantify the number of students leaving and entering the public school system. Both metrics are affected by students who repeat a grade and by students who enter the public school system (for example if they move into the state), in addition to students who leave the school system. As an example, the count of 64,791 5th graders in 2020-21 will include students who are new to the state (and were not enrolled in 4th grade in 2019), students who skipped 4th grade, and students who remained in 5th grade in both 2019-20 and 2020-21. Each metric adjusts for (and is sensitive to) different regularities and trends over time. The within-grade enrollment change adjusts for changes in grade level enrollment caused by structural features of the school system that are constant over time. If many students enter the public school system in 9th grade each year after enrolling in private school in K-8, for example, the within-grade change metric will “adjust” for this phenomenon by comparing enrollments to the same grade in the prior year. The cohort-adjusted metric, however, will be affected by this because it will lead to an increase in the cohort enrollment relative to 8th grade. The opposite is true for changes in the size of cohorts over time, which the cohort-adjusted metric adjusts for, and the within-grade metric does not.
Analyzing the changes in grade level enrollments raises a natural question: to what extent are these changes unique to the pandemic in 2020-21, and to what extent do these reflect stable patterns of school enrollment dynamics? Comparing the changes in Figure 1 and Figure 2 to historical trends can provide a more complete understanding of the changes that occurred in 2020-21 and any potential re-enrollments in 2021-22.
Putting Values in Historical Context
Figure 3 shows the within-grade and cohort-adjusted changes in enrollment in Colorado for grades 1-12 from 2015-16 through 2021-22. These figures highlight that the declines in enrollment in the elementary and middle school grades in 2020-21 clearly stand out regardless of which metric we use. The changes were more obvious when looking at the cohort-adjusted rates, where 2020-21 was the first year that there were noticeable negative changes in elementary grades. While the negative changes to within-grade enrollment were much larger in 2020-21 relative to prior years, we also see that some of these negative changes were likely due to pre-existing trends. We see, for example, that the 1st grade cohort in 2015-16 was smaller than the prior cohort, and this difference continued to show up in successive grades and years.
Figure 3. Cohort-Adjusted and Within-Grade Changes in Enrollment in CO, 2015-16 to 2021-22.
Other features of the cohort-adjusted rates are also noteworthy. The increase in 9th and 12th grade cohort-adjusted enrollments is not unique to 2020-21. This may occur because students who were enrolled in home schooling or private school in elementary and middle school enter the public school system in 9th grade for high school. The large and consistent changes in 12th grade are more difficult to explain. It could be caused by students who remain enrolled in 12th grade for a second year to complete additional credits needed to graduate, but there could be other explanations. The consistent declines in 10th and 11th grade may be due to students who leave school before graduating and are another regularly occurring phenomenon that is not apparent based on within-grade changes.
Understanding Changes in 2021-2022
The final column of Figure 3 shows changes to enrollment for the most recent year, 2021-22. These enrollment counts have been of great interest to evaluate whether students appear to be returning to public schools. Both sets of metrics are skewed by the atypical decline seen in 2020-21, but they also point to different stories about students’ return to public school. Statewide, Colorado saw an overall increase in PreK-12 enrollment of about 0.4% in 2022 relative to the prior year, with the largest within-grade changes to enrollment in preschool and kindergarten (Colorado Department of Education, 2022). Based on the within-grade changes, half of all grades saw additional declines relative to 2020-21. However, the cohort-adjusted values tell a different story. The large positive change in 1st grade indicates that there were about 4% more 1st grade students enrolled in school this year relative to the number of kindergarten students in 2020-21. This suggests that a non-trivial number of families may have decided to enroll their children in first grade, despite not having attended public kindergarten in the prior year. The consistent small positive changes in other elementary grades suggest that there was potentially a small return to school in these grades, although the increases in grades 2-6 were similar to those seen prior to the pandemic and could reflect more typical annual patterns of students moving into the Colorado system or potentially being retained within grade.
Variation Across States
A final question to consider is: To what extent do these findings generalize to other states? Variation in enrollment changes suggest decisions about sending children to school varied across states, and not all states will have observed such large changes to cohorts of students over the past 10 years. The consistent increases in 9th and 12th grade enrollment seem to happen annually in Colorado but may not occur elsewhere.
Figure 4 shows both cohort-adjusted and within-grade enrollment changes in Massachusetts for the same time span as a contrasting example. The within-grade changes in MA were similar in 2020-21 to those in Colorado and also show signs of being impacted by changing cohort sizes over time (i.e., inconsistent trends across grades).
The cohort-adjusted trends tell a different story, however, both relative to the within-grade changes and relative to Colorado. There is a consistently positive change in cohort-adjusted enrollment in first grade, suggesting that many students do not enroll in public kindergarten before enrolling in first grade. Thus, while the decline in 2020-21 cohort-adjusted enrollment appeared smaller in first grade relative to other grades, in historical context this negative change was noteworthy relative to the positive changes in cohort-adjusted 1st grade enrollment observed in every prior year. There is also a spike in 9th grade enrollments as in Colorado, but rather than an additional spike in 12th grade enrollments, there are consistent declines in 10th-12th grade cohort-adjusted changes, and these appear to have been about the same in 2021 as they were in the prior five years. This is similar to Colorado in that the pattern of cohort-adjusted high school enrollment appears to have been less impacted by the pandemic, but differs from Colorado in the overall pattern of high school enrollments.
Figure 4. Cohort-Adjusted and Within-Grade Changes in Enrollment in MA, 2015-16 to 2021-22.
Finally, the most recent data from 2021-22 are similar to Colorado. The cohort-adjusted changes suggest enrollments are rebounding in first grade and were similar to historic norms in other grades, while the within-grade enrollment changes tell a more mixed story suggesting additional but inconsistent declines in enrollment. Taken together, these comparisons suggest there might be meaningful variation in the state-specific patterns of student enrollment across grades that would be worth studying further both in general and to better understand how the pandemic may have impacted students’ trajectories through school.
Conclusion
Tracking the historic changes in public school enrollments will continue to be important in the coming years. Analysts should consider using both within-grade and cohort-adjusted change metrics to do so, which can provide a more complete understanding of enrollment changes. This is particularly true when investigating variation in changes across grade levels, as the analyses in this brief illustrate that each metric is sensitive to different changes and thus helps us to understand different aspects of changing enrollments. When calculating total public school enrollment across all grades, the two metrics will likely not yield such different results. The two metrics can also lead to different inferences about students returning to public schools in 2021-22, and the same will likely be true in future years. Finally, the differences observed between Colorado and Massachusetts, particularly in the regular patterns of within-cohort grade level changes, suggest there is interesting heterogeneity of state-specific enrollment dynamics that could be investigated further.
1Data from CDE are available at: https://www.cde.state.co.us/cdereval/pupilcurrent in the file “2021-22 PK-12 Pupil Membership by Grade with Historical Data.” Data from the MDESE are available here: https://profiles.doe.mass.edu/statereport/enrollmentbygrade.aspx. For these analyses, MA students enrolled in special education beyond grade 12 (reported as grade “SP”) are not included in grade level enrollment counts.
2Although enrollments are based on fall census counts, when using a single year to represent an AY I refer to the spring of the AY. For example, referencing year = 2020 would refer to enrollment counts for the 2019-20 AY.
3A complete table of all grade levels is included in the Appendix.
References
Colorado Department of Education. (2021, January 22). News release—Official count of 2020-21 Colorado students confirms 3.3% decrease in state enrollment with biggest drop in early grades. https://www.cde.state.co.us/communications/newsrelease-enrollment
Colorado Department of Education. (2022, January 19). News release—Colorado school enrollment increases slightly after 2020’s decline. https://www.cde.state.co.us/communications/newsrelease2021enrollment
Dee, T. S., & Murphy, M. (2021). Patterns in the pandemic decline of public school enrollment. Educational Researcher, 50(8), 566–569. https://doi.org/10.3102/0013189X211034481
Pendharkar, E. (2022, February 1). More than 1 million students didn’t enroll during the pandemic. Will they come back? https://www.edweek.org/leadership/more-than-1-million-students-didnt-enr...
Appendix: Complete Grade Level Enrollment Changes in 2020-21 and 2021-22
Colorado K-12 public school enrollment counts and changes for the past three years.
Massachusetts K-12 public school enrollment counts and changes for the past three years.
