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Class Size and School Performance: An Analysis of Elementary and Middle Schools

The class size debate is still ongoing among researchers, even though smaller class sizes are widely supported by parents, teachers, and the public. To contribute to this discussion, data was taken from the North Carolina (NC) School Report Cards (SRC) datasets and used to address two questions: First, is there a relationship between an elementary school’s performance score and average class size? Second, is there a relationship between a middle school’s performance score and average class size? Using the results from a linear regression and ordered logit, we find that average class size significantly predicts both NC elementary and middle school performance. However, the estimates suggest that higher average class size is negatively related to elementary school performance, but positively related to middle school performance. These results suggest that the impact of class size on student and school performance may depend on the grade levels in question, for example, elementary or middle school. We conclude that policymakers should act carefully when manipulating class sizes, since the effect may depend on the grade levels.


Introduction
The class size debate is still ongoing (Jepsen, 2015;Paola, Ponzo and Scoppa, 2013;Hanushek, 2003;Shen and Konstantopoulos, 2019;Shin and Chung, 2009;Goldstein and Blatchford, 1998). Reductions in class size are widely supported by parents, teachers, and the public (Chingos, 2013). Woods (2015) notes that "teachers unions from Oakland, California to Auckland, New Zealand are advocating for smaller class sizes. A call for smaller class sizes was second only to higher salaries for the LA teachers union at recent protests." Woods (2015) continues by stressing that we need good data and strong analytic methods to find out the level and extent of the effect of class size on student achievement.
There are many factors associated with student learning at the K-12 levels. In their 1994 study, Wang, Haertel and Walberg find that 28 different variables are significantly related to student learning. According to Teodorovic (2011), several classroom-level factors have positive effects on student achievement. Teodorovic (2011) writes that "clear and structured classroom instruction, emphasis on complex (as opposed to basic) skills, whole-class instruction (rather than individual or group work), teacher feedback, orderly climate, moderately frequent reinforcement of student effort…" are all important for achievement (p. 215). Marzano (2003) underscores that there are several school, teacher, and student factors critical to student outcomes. School factors include a guaranteed and viable curriculum, challenging goals and effective feedback, parent and community involvement and safe and orderly environment (Marzano, 2003). Teacher related factors include effective instructional strategies and classroom management, while student related factors include prior achievement, motivation, and home environment (Marzano, 2003). Thus, there are a myriad of factors that affect achievement, making analyses of class size, specifically, especially challenging.
Class size can affect how students learn and even determine the amount of material covered during a class period. For example, a large class with a lot of noise may mean less time for the teacher to cover academic tasks slated for the day. The teacher may also be deterred from assigning group work, which is a best practice in education, because there are simply too many groups to manage. A small class, in contrast, may encourage more teacher pupil interactions, which has been shown to improve student outcomes (Blatchford, Bassett, and Brown, 2011;Leyva, Weiland, Barata, Yoshikawa, Snow, Treviño, and Rolla, 2015). As Paola, Ponzo and Scoppa (2013) emphasize, the effects of "educational inputs, such as class size, teaching quality, school resources, on student achievement have been deeply investigated in the economic literature. However, there is still an ongoing debate and no consensus has been reached about how these factors influence student performance" (p. 135).
https://abc11.com/1912645/ Table 1 above shows that student-teacher ratios have decreased in Kindergatten, from 19 to 18 students per teacher, and in Grade 3, from 18 to 17 students per teacher between the 2013 and 2019 school years. Accompanying these class size reductions, however, has been a tremendous rise in additional costs (see Table  2). Therefore, considering the strong public support for smaller class sizes, the additional costs need to implement reduction programs, and mixed empirical findings on the matter, more research is critical to continue the debate.

Purpose of the Study
Given the interest by parents, educators and policy makes and with the results from other studies being mixed at best, the purpose of this study are to answer the following research questions: 1. Is there a relationship between a school's performance score and average class size for NC elementary schools? 2. Is there a relationship between a school's performance score and average class size for NC middle schools?
Our data come from the North Carolina (NC) School Report Cards (SRC) datasets. Using the results from a linear regression and ordered logit, we find that average class size significantly predicts both NC elementary and middle school performance. However, the estimates suggest that higher average class size is negatively related to elementary school performance, but positively related to middle school performance.

Class Size
Numerous studies have examined the effects of small classes on student achievement. However, the findings "on the educational effects of class size differences [have] not been clear" (Filges, Sonne-Schmidt and Nielsen, 2018, p. 5). Indeed, the results have been "mixed at best" (Borland, Howsen, and Trawick, 2005, p. 73;Chingos, 2013). According to Chingos (2013), "the evidence on the efficacy of class size is clearly mixed, with one highquality study finding quite large effects, another finding no effects, and a handful finding effects in between" (p.430). In their meta-analysis of class size research, Filges, Sonne-Scmidt and Nielson (2018) find that "there is some evidence to suggest that there is an effect of reducing class size on reading achievement, although the effect is very small. There is no significant effect on mathematics achievement, though the average is negative meaning a possible adverse impact on some students cannot be ruled out." (p. 6). Finn, Pannozzo and Achilles (2003) conduct a similar meta-analysis and conclude that the "results favored small classes in at least 38 of the 42 measures employed. While some individual changes were small, no measure in any study was statistically significant in favor of larger classes" (p. 334).
In a 2003 paper, Buckingham stresses that "several large scale studies and many smaller ones find a relationship between learning and class size. But a closer examination reveals crucial methodological problems and generalizations that make the findings far less than definitive, even meaningless" (p. 72). In contrast, Glass and Smith (1979), in their meta-analysis of research on class size and academic achievement, came to the conclusion that there is a clear and strong "relationship between class size and achievement…The relationship seems slightly stronger at the secondary grades than the elementary grades; but it does not differ appreciably across different school subjects, levels of pupil IQ, or several other obvious demographic features of classrooms" (p.15). In a large scale study of the California Class Size reduction program, Jepsen and Rivkin (2009) find that reduction in class size raised schools' average mathematics and reading achievement by roughly 0.10 and 0.06 standard deviations, respectively. However, the accompanying rise in the shares of new and not-fully certified teachers offset some of the benefits of class size reductions (Jepsen and Rivkin, 2009, p.224). Complicating the class size debate further, Chingos (2012) concludes that mandated class size reductions in the state of Florida had little, if any, effect on student achievement. In their study of class size during elementary school, Nye, Hedges and Konstantopoulos (2002) draw the following conclusions: a. Small classes in early grades lead to higher academic achievement. b. The advantages of smaller classes are larger for lower achieving students for reading, but larger for higher achieving students in mathematics. c. While there is strong evidence that small classes can benefit all students, evidence for the differential benefit for lower achieving students is both weak and contradictory (p.215).
Baker, Farrie and Sciarra (2016) argue that there is ample research showing that elementary school "children in smaller classes achieve better outcomes, both academic and otherwise, and that class size reduction can be an effective strategy for closing racially or socioeconomically based achievement gap" (p.5). They also emphasize that reductions in class size may positively influence teacher recruitment and retention. Odden (1990) concludes that smaller classes enable opportunities for teachers to engage in research-backed instructional strategies that have been shown to promote higher student performance, like group work and class discussions (p.219). In a review of the relevant research from Australia and New Zealand, Zyngier (2014) concludes that the gains from small classes in early grades are larger when class size is reduced to fewer than 20 students. (p.16).
In a 2012 study, Shin finds that Black students benefit more than others ethnic groups from reduced class sizes regarding first-, second-, and third-grade academic achievement. Indeed, in an analysis of data from the National Education Longitudinal Study, Akerhielm (1995) finds that for 8th graders, students in smaller classes performed better than students in larger classes. Loveless and Hess (2007) find that smaller class sizes offer teachers more time to address the individual needs of each student, and the smaller settings provide better structure, safety and discipline (p. 2). Finn, Gerber and Boyd-Zaharias (2005) found that students attending small classes over three years increased their likelihood of graduating from high school, especially among economically disadvantaged students.
In an experiment on class size and student outcomes, Mosteller (1995) finds that "minority groups gained more than others in the first two years of the experiment; and although the last two years showed benefits comparable with those of the majority, there was a falling off of benefits" (p.125). Folemer-Anneverlink, Doolard, Mascareno and Bosker (2010) conclude that more "student-teacher interactions occurred in smaller classes than in larger classes. This is true both for interactions related to instruction and classroom management in kindergarten and Grade 1" (p.36). Greater student teacher interactions may facilitate higher quality instructions, especially at the lower grades. Indeed, a 2015 Hanover Research Report notes that several studies find that "enrollment in smaller classes can lead to higher standardized test scores, an increased likelihood of taking college entrance exams, increased earnings, and higher college attendance rates, especially among certain subpopulations" (p.4). In his 1990 paper, Robinson (1990) concludes the following: a.The most promising effects of small classes on pupil learning occur in grades K-3 (p.82). b. There is some evidence that smaller classes can have greater positive effects on the achievement of disadvantaged and minority students (p.83). c.There is more positive student attitudes and behaviors in smaller classes (p.86). (2014) advocates for smaller class size as a means of improving student learning. Nevertheless, they stress that "for many high school students smaller classes do not make a significant difference in academic performance. However, for minority and at-risk students as well as those who struggle with English literacy, smaller classes enhance academic performance." In the statement, educators are advised to note that benefits from reduced class sizes are not uniform across all grades and populations.

Method Participants
Data are from the North Carolina (NC) School Report Cards (SRC) datasets (NCDPI, 2019). In NC, SRCs are available for each public school. Schools receive report cards with their performance score, in addition to other reporting material, like details on student and teacher characteristics. SRCs are sources of information for government administrators and researchers. The data used for these reports are available at the public school system's website.
The NC General Assembly dictates that student outcome information be used to calculate and ascribe grades to public schools in the state. Two components are used to calculate grades: 1) school achievement scores, which form 80 percent of the grade and 2) school academic growth amongst students, which comprise the final 20 percent. Performance scores fall along a 100-point scale, which then determines letter grades. These letter grades follow a standard 15-point grading scale: A: 85-100 B: 70-84 C: 55-69 D: 40-54 F: Less than 40 (NCDPI, 2019).
We have two separate analysis samples. One sample contains data for NC elementary schools, and the other sample contains data for NC middle schools. The analysis samples contain two years of data, namely for 2018 and 2017. The elementary school dataset includes 2,452 observations for 1,226 elementary schools. Therefore, the set contains two records for each school. Since there are 1,329 elementary schools in NC, our dataset contains over 92 percent of all public elementary schools in the state. The 103 excluded schools were dropped from the final sample because they had missing information for key variables. The middle school dataset has 850 observations for 425 middle schools. Hence, the dataset has two records for each school. There are 465 public middle schools in the state, so the dataset comprises over 91 percent of all public middle schools in NC. Forty schools were excluded because they had missing information for key variables. We only use observations for 2018 and 2017 because a major part of the performance score formula, namely the accountability measures, changed for these years relative to the other years. Hence, performance score comparisons to the years prior to 2017 are problematic.

Measures and Variables
School Performance -Public schools in NC receive a score based on their performance, which varies from 100 to 0. A score corresponds to a letter (A to F) and is composed of two factors. The first (80%) is determined by a school's achievement scores, which come from accountability measures. These accountability metrics include grade level assessments, end-of-grade-tests that evaluate mathematics and reading, and English language assessments for English Learners. The second factor integrates the academic growth of a school's students. Academic growth is measured as the development children experience relative to the mean devolvement experienced by children across NC (for a subject and grade level). Hence, this evaluates the progress students have made since the previous academic year, as a result of the academic instruction they received.
Average Class Size -The average class size at a school, across all subjects and grade levels.

Other Covariates
Years of Teaching Experience -This variable is measured as a set of three mutually exclusive and exhaustive variables.
 0 to 3 Years of Teaching Experience -The share of teachers at a school with 0 to 3 years of experience.  4 to 10 Years of Teaching Experience -This share of teachers at a school with 4 to 10 years of experience.  Over 10 Years of Teaching Experience -This share of teachers at a school with over 10 years of experience.
Teachers with Advanced Degrees -The share of teachers with education or licensing levels above bachelor degrees.
Teachers with Full Licenses -The share of teachers who are fully licensed, meaning they meet all examination and certification requirements.
Teacher Turnover -The share of teachers that worked for a school the previous year, but are no longer employed there.
Student Attendance -The average daily share of students that attend school, across grade levels.
Economically Disadvantaged Students -The share of children at a school that are considered economically disadvantaged.
Year 2018 -Dummy variable equal to 1 if the year is 2018 and 0 if the year is 2017.

Results
The analysis and results are as follows -First, the frequencies of performance grades received by NC middle and elementary schools are presented in tables. Second, descriptive statistics and data visuals, followed by our study's hypotheses, are provided. Third, we test our hypotheses with the results from a linear regression and ordered logit.

Class Size Hypotheses
Before we present statistics related to the analysis on class size and performance, we formally state the two hypotheses, corresponding to our two research questions. Hypothesis 1: H 1,N : There is not a relationship between average class size and school performance in NC public middle schools. H 1,A : There is a relationship between average class size and school performance in NC public middle schools. Hypothesis 2: H 2,N : There is not a relationship between average class size and school performance in NC public elementary schools. H 2,A : There is a relationship between average class size and school performance in NC public elementary schools.  middle schools, and the second row contains the results for elementary schools. The first column contains 2018 data, and the second contains 2017 data. For NC middle schools, surprisingly, better performing schools average larger class sizes, while lower performing schools average smaller class sizes. For NC elementary schools, a clear pattern does not exist. In 2018, average class sizes are approximately the same, regardless of a school's performance grade. In 2017, however, it appears that better performing schools average slightly higher class sizes compared to lower performing schools.

Regression Analysis Plan and Results
To examine the relationship between school performance and class size, we estimate the following model separately for middle and elementary schools. Model (1): Where [SchoolScore i ] is the performance score of the ith school. [ClassSize i ] is the average class size at the ith school. X is an array of other control variables for the ith school. These variables include year, share of teachers with 4 to 10 years of experience, share of teachers with over 10 years of experience (the share of teachers with 0 to 3 years of experience is omitted to avoid perfect multi-collinearity), share of teachers with advanced degrees, share of teachers with full licenses, rate of teacher turnover, share of economically disadvantaged students, unique book titles per student, and average daily student attendance. β 0 is the intercept term, Ɛ i is the error term, and β 1 is the slope coefficient of interest, which corresponds to the primary independent variable of interest for this study.
Model 1 is estimated under two econometric frameworks. First, it is estimated as a multiple linear regression and second, it is estimated as an ordered logit. For the first, the dependent variable of Model 1, SchoolScore, is treated as a continuous variable ranging from 100 to 0. For the second, SchoolScore is treated as an ordinal variable corresponding to the letter grade a school receives, A, B, C, D, and F (A = 5, B = 4, C = 3, D = 2, and F = 1). The results of the ordered logit are used to obtain the marginal effect of the change in a covariate on the probability that a school receives a particular letter grade.     Table 9 displays key results from the ordered logit estimation of Model 1, for both middle and elementary schools. The table presents the estimated marginal effects (ME in the tables) associated with earning an A and earning an F (denoted with a subscript A or subscript F). We begin by interpreting the marginal effects associated with earning an A for the key variable. For middle schools, average class size is positively related to the probability that a school earns an A and the estimate is significant at the 10% level. When the average middle school class size increases by 1 student, the probability that a school earns an A increases by 0.00011, holding all other covariates constant at their means. For elementary schools, average class size is negatively related to the probability that a school earns an A and the estimate is significant at the 1% level. When the average elementary school class size increases by 1 student, the probability that a school earns an A decreases by 0.00062, holding all other covariates constant at their means.
We now interpret the marginal effects associated with earning an F for the key variable. For middle schools, average class size is negatively related to the probability that a school earns an F and the estimate is significant at the 10% level. When the average middle school class size increases by 1 student, the probability that a school earns an F decreases by 0.00037, holding all other covariates constant at their means. For elementary schools, average class size is positively related to the probability that a school earns an F and the estimate is significant at the 1% level. When the average elementary school class size increases by 1 student, the probability that a school earns an F increases by 0.00075, holding all other covariates constant at their means. To summarize the statistical results, the linear regression and ordered logit estimates complement one another.
 We reject H 1,N . Hence, we find evidence of a relationship between average class size and school performance in NC public middle schools. Average class sizes significantly predict school performance. Larger class sizes are positively related to middle school performance scores.  We reject H 2,N . Hence, we find evidence of a relationship between average class size and school performance in NC public elementary schools. Average class sizes significantly predict school performance. Larger class sizes are negatively related to elementary school performance scores.

Discussion
This study based on the 2017 and 2018 data from the NC Schools Report Cards finds that in NC, average class size significantly predicts elementary school performance. As average class sizes increase, elementary school performance scores tend to fall. For middle schools, as average class sizes rise, school performance scores tend to increase. Our elementary school findings mesh well with the many other studies that find that students benefit from smaller classes, especially at the K-3 level (Baker, Farrie and Sciarra, 2016;Bascia, 2010;Zyngier, 2014). Indeed, according to Ehrenberg, Brewer, Gamoron, and Willms (2001), instruction in smaller classes could be more effective since "certain practices may work better in smaller classes. For example, students may pay better attention when there are fewer students in the room" (p.21). Robinson (1990) and Shin (2012) conclude that smaller classes may be very beneficial to minority and disadvantaged students. Mckeachie (1980) concluded that for the "Goals of higher level thinking, application, motivation, and attitudinal change are most likely to be achieved in small classes" (p.26).
Annie Duncan (2011), the Secretary of Education for the Obama Administration, declared that education is the civil rights issue of our generation. He indicated that "if you care about promoting opportunity and reducing inequality, the classroom is the place to start. Great teaching is about so much more than education; it is a daily fight for social justice." Smaller classrooms in elementary school may be one way of improving achievement for lower performing students. Moreover, since many states have adopted policies aimed at reducing class sizes, especially at the K-3 level, our findings suggest that they could be beneficial in NC elementary schools and should continue.
Our finding regarding NC middle schools are a bit more controversial. We find that larger class sizes are positively related to middle school performance. This result does not mesh as well with the literature, like our elementary school findings do. Considering the surprising nature of these results, we feel it unwise to conclude that they offer evidence in favor of larger classes in NC middle school. More research is needed, along with more data, to ensure this finding is not simply a spurious correlation.

Conclusion
Class size reduction is one way to improve student achievement in NC, at least at the elementary school level. This study has shown that at the elementary school level, reduced class size significantly predicts school performance. The costs of implementing class size reduction are often high for many counties and school systems. States should continue the policy of reducing elementary class sizes. Researchers should also continue the investigation into whether class sizes have differential effects depending on the school level in which they occur.