The Impact of One State's Class Size Reduction Legislation on Teacher Staffing Gerald M. Eads II, Ph.D. Winifred Nweke, Ph.D. Comfort Y. Afolabi, M.P.A. Cynthia E. Stephens, Ed.D. Thomas Hall, Ph.D. Katherine Potter, B.Sc. Division for Educator Workforce Research and Development Georgia Professional Standards Commission The Impact of One State's Class Size Reduction Legislation on Teacher Staffing Abstract In March of 2006 the Georgia legislature passed a K-12 public school class size reduction (CSR) initiative to take full effect at the beginning of the 2007 school year in August of 2006, providing the school systems four months to prepare for the acquisition of the requisite additional teachers and classroom space. This study analyzes the law's impact on teacher staffing using extant individual student and teacher data collected semiannually from all state public schools. While more than 20 states and several countries have adopted various policies to reduce class size (Ehrenberg, Brewer, Gamoran & Willms, 2001; Willms & Somers, 2001), this study may be the first to investigate a statewide CSR implementation since the mid-1990's effort in California. It first documents the methodology used to predict the level of staffing required by the new law, then investigates the impact of the legislation on average class size, incidence of classes over the size limits, and age and experience level of new teachers. The data from a statewide teacher vacancy reporting system begun in the 2006-2007 (FY07) school year are used to study variation among schooling levels and proportions of student enrollment eligible for free and reduced lunch. Review of Literature While interest in CSR has remained high in the United States, economics, psychology and education literature also suggests interest in England (e.g. Blatchford, 2005; Blatchford, Basset & Brown, 2005; Dustmann, Rajah & van Soest, 2003; Iacovou, 2002; Pedder, 2006), The Netherlands (Dobbelsteen, Levin, and Oosterbeek, 2002; Levin, 2001), Scotland (Wilson, 2002), and Latin America (Willms & Somers, 2001). The value of CSR has been questioned (e.g., Borland, Howsen, & Trawick, 2005; Dobbelsteen, Levin and Oosterbeek, 2002; Hanushek, 1998, 2003; Levin, 2001; Normore & Ilon, 2006; Office for Standards in Education (OSTED), 1995; Stecher, McCaffrey & Bugliari, 2003). Several authors have criticized the methodologies used by detractors of CSR such as OSTED (Iacovou, 2002) and Hanushek (1998, 2003) (Biddle & Berliner, 2002; Kreuger, 2002, 2003). Kreuger (2002) argued CSR to be a cost effective policy mechanism to improve student achievement. Reichardt (2000) noted that CSR may be one of the more likely reform interventions to succeed because of its simplicity. Evaluations of CSR studies and initiatives (Bohrnstedt & Stecher, 2002; Molnar, Smith, Zahorik, Halbach, Ehrle, Hoffman, & Cross, 2001; Mosteller, 1995) and ongoing analyses of these and other data (e.g., Finn, Gerber, & Boyd-Saharias, 2005; Iacovou, 2002; Nye, Hedges, & Konstantopoulos, 2001, 2002, 2004) have generally supported CSR as an effective policy to improve both student achievement as measured by tests as well as more evocative improvements to education, including long term achievement impacts, reduced dropout and increased graduation rates. Literature reviews (e.g., Biddle & Berliner, 2002; Reichardt, 1 Statewide class size reduction staffing impact 2000; Wilson, 2002) tend to support CSR as a viable intervention. The literature also suggests that CSR is likely more effective in the early grades (K-3), but most of the research has focused on the early grades, and very little data exist on the effect of implementing CSR after grade four. Ehrenberg, Brewer, Gamoran, and Willms (2001) concluded that although some research has been convincing, "Class size reduction initiatives presuppose the availability of teachers who are equivalent in quality to existing teachers to staff the extra classrooms." Implementation difficulties documented from the California CSR initiative were: (1) The increase in demand for teachers resulting in a decrease in teacher quality, (2) an exacerbated difference in teacher quality between schools with low and high proportions of disadvantaged students (low and high socioeconomic status (SES)), (3) greater classroom shortages experienced by low SES districts and (4) insufficient funding for low SES districts to meet class size targets. These consequences may have limited the benefit of California's initiative compared to the well regarded Tennessee CSR experiment (Imazeki, 2003; Jepsen & Rivkin 2003; Reichardt, 2000; and Stecher, Bohrnstedt, Kirst, McRobbie & Williams, 2001). Introduction California's voluntary initiative reduced average class size from more than 29 to just less than 20 over three years (Reichardt, 2000). Georgia's mandatory initiative required smaller decreases in class size, but specified that class size must not exceed certain levels for elementary grades and certain middle and high school classes. Georgia classes were already legislated to average 21 in grades 1-3; the new law now specified that class size must not exceed 21 in those grades for mathematics, language arts, science and social studies classes. Similarly, Kindergarten classes must be limited to 18 (20 with an aide). Grades 4-8 academic classes were limited to 28 students; formerly such classes could average 30. High school classes in language arts, social studies, mathematics and foreign language were required to average 30 and must now not exceed 32; science classes were required to average 28 and now must not exceed 30. Although class size limits existed in the previous law and are used for comparison, the size average was the focus of prior law. While districts still must monitor average class size; classes affected by the law must not exceed lower specified size limits. Based on California's CSR experience, Georgia's predicted increases in staffing demand should require significantly increased recruiting effort to achieve full staffing without concomitant decreases in the experience levels of newly hired teachers. The literature also documents greater difficulties in staffing for schools with greater proportions of disadvantaged students; whether this outcome occurred at the initial implementation of the Georgia law is investigated. Unlike most previous initiatives focusing on early elementary grades, all Georgia grades are affected, and districts are required by the new law to be fully staffed by 2 Statewide class size reduction staffing impact the fall of 2006, four months after passage of the legislation. The reserve supply of teachers is limited; recently only 20-25% of new teacher demand had been supplied by the state's teacher colleges. The No Child Left Behind Act of 2001 (NCLB) now requires all teachers to be fully certified ("highly qualified"); California's response to staffing prior to NCLB was to place uncertified teachers in classrooms, which is in Georgia only an option by formal request for exception to the state Board of Education. This study assesses the impact of Georgia's CSR initiative on staffing and staffing needs. As of this writing, the 2007 Georgia legislature is considering an amendment to delay class size reduction for one or two years in response to school systems' many violations of the maximum class size limitations, and in light of the "temporary austerity reductions" which have reduced school funding below legislated levels for five years. Methods and Analyses All analyses were undertaken using tools available in SPSS14. Analysis of future teacher staffing demands Numerous curvilinear regression models were compared to twelve years' past state student enrollment. The best fit Gaussian model was used to project enrollment through the 2011-2012 (FY12) school year. The Gaussian regression function determined to best fit the data takes the form b1 * (1 - b3 * exp(-b2 * x **2)) where x in this case is the year of enrollment being predicted beginning with the base year 1995 represented as year 1, continuing through FY12 as year 18. The SPSS nonlinear regression tool iterates the factors b1, b2 and b3 to best fit the existing data. Teacher staffing demand was estimated by multiplying the student enrollment projections by the most recent five-year average gross student/teacher ratio. Separate linear projections provided future annual teacher attrition estimates. Impact of the class size limit legislation was estimated using the midpoint between of the legislated class size average and legislated class size limit for each of the various designated class sizes. The estimated impact of the legislation was treated as a constant rather than allowing it to impact the slope of the regressions. Similarly, the impact of substantial increased enrollment due to immigration from states affected by hurricane Katrina was treated as a constant. The Gaussian regression model was applied to the current production proportions of the various sources of the state's newly hired teachers to determine demands on each source to meet future full year projected staffing attrition as well as growth to meet student enrollment. Analysis of changes in class size. Data collection for class size was available for the fall of the 2005-2006 (FY06) and 2006-2007 (FY07) school years. Earlier data were not available to determine trends in class size variation; comparison could only be made immediately before 3 Statewide class size reduction staffing impact and after the change in legislation. Each school open for both years, excluding closed and newly opened schools, was classified as Elementary, Middle, High or Other. The Other category, representing 154 or 7.1% of the 2,159 schools, including charter, special education, alternative and regular schools combining levels, was excluded from the analysis. The state school free and reduced lunch dataset was used to determine the proportion of students in each school eligible for free or reduced lunch in FY07. Schools were placed in five categories of free/reduced lunch proportions: 0-20%, 21-40%, 41-60%, 61-80% and 81-100%. A repeated measures analysis of variance used average class size as the repeated measure, School Level (Level) and Free/Reduced Lunch (FRLunch) category as between subjects factors. Because special education class sizes were not changed by the legislation, and would confound the analysis because schools with higher proportions of free and reduced lunch eligible students also have higher incidence of special education classes, those classes were excluded from the analysis. Analysis of the number of classes over designated class limits Whether each class in each school exceeded the designated class size limit was also available in the annual datasets and was used in an Overlimit analysis. The proportion of Overlimit classes in each school for the same schools identified in the class size analysis was subjected to a repeated measures analysis of variance with the proportion of overlimit classes as the repeated measure and school Level and FRLLunch category as between subjects factors. Analysis of age and experience of teachers hired for enrollment growth and to replace attrition. The number of teachers hired in each school between the spring (May, FY06)) and fall (October) 2006 (FY07) Certified Personnel Information (CPI) collection dates corresponded to the period during which schools and districts were required to implement the class size limit legislation. The hiring patterns during this period were compared to the previous three comparable periods (Spring FY03-Fall FY06). Two separate repeated measures analyses of variance used four years of average newly hired teacher age by school and four years of average newly hired teacher experience respectively as the repeated measure and School Level (elementary, middle, high) and FRLunch categories as the between-subjects factors. Analysis of teacher vacancies The state teacher licensing agency (Georgia Professional Standards Commission, PSC) initiated the Vacancy Reporting System (VRS) in the fall of 2006 to monitor difficulties in hiring certified education personnel. These data were collected by district by teacher certification and the percentage of time for which a teacher is sought, or Full Time Equivalent (FTE). Because the system was initiated after the implementation of the legislation, effect of the class size law could not be 4 Statewide class size reduction staffing impact determined. Instead, an analysis of school district by FRLunch tested whether there was a differential impact of that socioeconomic proxy on vacancies at the 30 day and 90 day collections. A repeated measures analysis of variance used the proportion of vacancies to total number of positions in a school from the 30 and 90 day vacancy reports as the repeated measure, and FRLunch categories at the district level as the between subjects factor. Data sources Certified Personnel Information (CPI) data for educator staffing and Full Time Equivalent (FTE) data for student enrollment are collected biannually for all educators and all students in the state. The CPI provides data such as the hiring school, gender and ethnicity, years experience, salary, certification level, subject taught, and percent time employed. The FTE provides student data including enrolling school, gender and ethnicity, grade level, retention status, and dropout and graduation data. The FTE Class Size Report documents the number of students in each class in each school in the state by course, which enables class size and class size limit evaluation. The Certified Staffing Vacancy Reporting System (VRS), a new data collection beginning with the 2006-2007 school year, enables the analysis of educator vacancies at four points during the school year by certificate field at each school in the state. These data will be used to report on differences in vacancies among schools serving different socioeconomic levels as well as population density and geography. These datasets will be utilized to evaluate the impact on staffing of CSR legislation. Results Prediction of future teacher staffing levels Teacher staffing needs for the school years 2006-2007 (FY07) through 2011-2012 (FY12) were estimated from projections of student enrollment predicted on the basis of twelve years' previous enrollment. Fall 2004 enrollment attributed to migration from Gulf of Mexico states as a result of hurricane Katrina was reported at 10,332 students statewide. These students were removed from enrollment figures for regression model development, although they are included in Figure 1. The Gaussian model fit student enrollment relatively well (r2=0.978). Shown at FY07 is the new enrollment for the fall count (October 2006), which was 11,890 students (0.72%) under prediction. Projections of teacher staffing were derived by determining the most recent fiveyear average gross student-teacher ratio and projecting that ratio from Gaussian model student enrollment estimates. As shown in Figure 2, teacher staffing was projected at 115,250; reported staffing in the fall of 2006 was reported at 114,746. 5 Statewide class size reduction staffing impact Figure 1. Past and projected Georgia public school enrollment, FY95-FY12. 2,000,000 Number of Students 1,900,000 1,800,000 1,700,000 1,600,000 1,500,000 1,400,000 1,300,000 1,880,395 1,829,059 Enrollment Upper 95% CI Projected 1,779,000 1,730,652 1,684,498 Lower 95% CI 1,641,047 1,629,157 1,598,461 1,553,437 1,522,611 1,496,012 1,470,634 1,444,937 1,422,941 1,401,291 1,375,980 1,346,761 1,311,126 1,270,948 1,200,000 FY95 FY96 FY97 FY98 FY99 FY00 FY01 FY02 FY03 FY04 FY05 FY06 FY07 FY08 FY09 FY10 FY11 FY12 School Year Figure 2. Past and projected Georgia public school teacher staffing, FY98-FY12 140,000 Number of Teachers 135,000 130,000 125,000 120,000 115,000 110,000 105,000 100,000 95,000 90,000 85,000 132,059 128,454 124,939 121,543 118,302 115,250 114,746 110,135 106,934 104,845 103,350 99,470 Actual Upper 95% CI Projected Lower 95% CI 94,689 91,467 88,757 86,263 80,000 FY98 FY99 FY00 FY01 FY02 FY03 FY04 FY05 FY06 School Year FY07 FY08 FY09 FY10 FY11 FY12 Projected teacher staffing includes both attrition replacement and enrollment increase demand. Figure 3 shows past and projected teacher attrition rates from FY93 to FY12. Attrition has been gradually rising since data were first available in 1993, when annual teacher attrition was well under seven percent. The most 6 Statewide class size reduction staffing impact recent three years' attrition were above nine percent. The best fit regression model (r2=.89) projects attrition to exceed 9.8% by FY12. Figure 3. Past and projected statewide teacher attrition, FY93-FY12 11% 10% y = 0.0635x0.1459 R2 = 0.8858 Percent Attrition 9% 8% 7% 6% 5% FY93 FY94 FY95 FY96 FY97 FY98 FY99 FY00 FY01 FY02 FY03 FY04 FY05 FY06 FY07 FY08 FY09 FY10 FY11 FY12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Actual 6.59 6.95 7.03 8.03 7.51 8.13 8.41 9.40 8.80 8.70 9.13 9.16 9.12 Prediction 6.35 7.02 7.45 7.77 8.03 8.25 8.43 8.60 8.75 8.88 9.01 9.12 9.23 9.33 9.42 9.51 9.60 9.68 9.76 9.83 UCL 7.11 7.78 8.22 8.56 8.84 9.07 9.28 9.47 9.64 9.80 9.94 10.07 10.2010.32 10.4310.54 10.6410.74 10.8310.92 LCL 5.67 6.34 6.76 7.06 7.30 7.49 7.66 7.81 7.94 8.06 8.16 8.26 8.35 8.44 8.52 8.59 8.66 8.73 8.79 8.85 Figure 4 shows past teacher supply and projected demand from each teacher supply source for Georgia, assuming that each source produces a share equivalent to the most recent year's proportions. Supply from each source in the past has been highly variable. A prior radical increase in staffing demand caused by policy changes in 2002 was fulfilled primarily by recruiting out-of-state teachers. 7 Statewide class size reduction staffing impact Figure 4. Past new teacher staffing, FY98-FY06 and projected production requirements from each supply source, FY07-FY12 6,000 5,500 5,000 Number of Teachers 4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 FY98 FY99 FY00 FY01 FY02 FY03 FY04 FY05 FY06 FY07 FY08 FY09 FY10 FY11 FY12 Out of State 901 1,150 1,567 3,072 4,252 5,771 3,068 3,170 3,659 4,505 4,035 4,204 4,368 4,525 4,677 GA IHE Yield 2,974 2,277 2,525 2,725 2,347 2,273 2,421 2,578 3,042 3,754 3,362 3,503 3,640 3,771 3,898 Alternative Prep 441 418 723 1,182 2,316 1,501 1,995 2,281 2,853 3,515 3,147 3,280 3,407 3,530 3,649 Returning 3,071 3,327 3,501 3,427 2,761 2,053 2,051 2,456 2,708 3,339 2,990 3,116 3,237 3,354 3,466 Other 2,450 2,092 2,157 1,655 890 878 1,650 971 687 847 758 790 821 850 879 The state's universities and colleges supply about one quarter of the new teachers required each year. Slightly fewer than 70% of the system's new teachers (not including those who return to earn advanced degrees) actually enter Georgia public school classrooms the following year. Figure 5 depicts this discrepancy and projects the number of teachers the universities may need to produce in order to yield a number of teachers to the classroom equivalent to the proportion they now supply. 8 Statewide class size reduction staffing impact Figure 5. Past and projected state traditional teacher production and yield, FY98FY12 Number of Teachers 6,000 5,500 5,000 GA IHE Certified GA IHE Yield 4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 500 FY98 FY99 FY00 FY01 FY02 FY03 FY04 FY05 FY06 FY07 FY08 FY09 FY10 FY11 FY12 School Year Class Size The effect of the class size legislation on average class size at the school level was analyzed in a 2 x 3 x 5 repeated measures Anova using the repeated measure annual school average class size by school Level (elementary, middle and high) and the percentage of students eligible for free & reduced lunch in a school (FRLunch) categorized into five levels (0-20%, 21-40%, 41-60%, 61-80% and 81-100%). Table 1 shows the average class sizes in FY06 and FY07 for schools at each FRLunch category by school Level. Table 2 shows the Anova table for this analysis. 9 Statewide class size reduction staffing impact Table 1. Descriptive statistics for Average Class Size by Level by FRLunch. School Level Elementary Middle High FRLunch 0-20% 21-40% 41-60% 61-80% 81-100% Total 0-20% 21-40% 41-60% 61-80% 81-100% Total 0-20% 21-40% 41-60% 61-80% 81-100% Total FY06 Class Size 20.29 19.52 18.36 18.46 17.13 18.44 19.48 19.51 19.29 18.76 18.22 18.98 20.32 20.01 19.54 19.34 19.01 19.69 School Year FY07 SD Class Size 1.55 19.35 1.66 18.69 2.34 17.99 5.03 17.60 2.46 16.99 3.31 17.88 2.50 18.68 2.48 19.21 2.25 18.33 2.72 18.01 2.62 17.55 2.56 18.26 4.66 20.01 2.98 20.18 2.85 19.54 2.65 19.36 2.64 18.50 3.17 19.66 SD 1.44 2.13 2.13 2.35 2.29 2.29 2.18 2.54 2.17 2.52 3.55 2.68 4.61 3.33 3.06 2.52 2.50 3.27 N 108 194 289 311 297 1,199 34 67 111 128 76 416 50 70 118 79 13 330 Table 2. Yearly Average Class Size by Level by FRLunch Anova Tests of Within-Subjects Effects Source Class Size Class Size * Level Class Size * FRLunch Class Size * Level * FRLunch Error(Class Size) Tests of Between-Subjects Effects Intercept Level FRLunch Level * FRLunch Error Type III Sum of Squares 113.148 23.018 7.382 35.274 6141.807 696087.253 419.872 656.686 137.629 23724.224 df 1 2 4 8 1930 1 2 4 8 1930 Mean Square 113.148 11.509 1.846 4.409 3.182 696087.253 209.936 164.171 17.204 12.292 F 35.556 3.617 0.580 1.386 56627.707 17.079 13.356 1.400 Sig. 0.000 0.027 0.677 0.198 0.000 0.000 0.000 0.192 Partial Eta Squared 0.018 0.004 0.001 0.006 0.967 0.017 0.027 0.006 The interaction of Yearly Average Class Size and Level was significant at p=.027. The main effect of FRLunch was significant at p<.001. Table 3 shows the posthoc analysis for FRLunch. The 0-20% and 21-40% groups and 41-60% and 6180% groups were not significantly different. The difference between the 21-40% and 41-60% groups, and the difference between the 81-100% group and all others were significantly different. Class sizes are largest for schools with 0-40% free and reduced lunch, and smallest for schools with 81-100% free and reduced lunch. 10 Statewide class size reduction staffing impact Table 3. Tukey Honestly Significant Difference post hoc analysis of FRLunch Tukey HSD (I) FRLunch 0-20% 21-40% 41-60% 61-80% 81-100% (I) Mean 19.687 19.520 18.842 18.589 17.901 (J) FRLunch 21-40% 41-60% 61-80% 81-100% 41-60% 61-80% 81-100% 61-80% 81-100% 81-100% Mean Difference (I-J) 0.412 1.155 1.459 2.498 0.743 1.047 2.086 0.303 1.343 1.040 Std. Error 0.225 0.209 0.209 0.219 0.174 0.174 0.186 0.154 0.167 0.167 Sig. 0.355 0.000 0.000 0.000 0.000 0.000 0.000 0.281 0.000 0.000 Table 4 shows post-hoc 2x5 analyses of variance the elementary, middle and high school levels of the analysis. At the elementary school level, the Yearly Class Size x FRLunch interaction was significant (p=.005). At middle school, both Yearly Class Size (p<.001) and FRLunch (I=.002) main effects were significant, but high school showed no significant class size results. Table 4. Post-hoc Yearly Class Size by FRLunch Anova tables Source Type III Sum of Squares Elementary School Tests of Within-Subjects Effects Class Size 201.486 Class Size * FRLunch Error(Class Size) 58.835 4689.031 Tests of Between-Subjects Effects Intercept 695113.347 FRLunch 1673.041 Error 12969.342 Middle School Tests of Within-Subjects Effects Class Size 81.134 Class Size * FRLunch Error(Class Size) 9.165 905.727 Tests of Between-Subjects Effects Intercept 235339.045 FRLunch 190.941 Error 4578.732 High School Tests of Within-Subjects Effects Class Size 1.452 Class Size * FRLunch Error(Class Size) 5.000 547.049 Tests of Between-Subjects Effects Intercept 144863.316 FRLunch 91.221 Error 6176.150 df 1 4 1194 1 4 1194 1 4 411 1 4 411 1 4 325 1 4 325 Mean Square 201.486 14.709 3.927 695113.347 418.260 10.862 81.134 2.291 2.204 235339.045 47.735 11.140 1.452 1.250 1.683 144863.316 22.805 19.004 F 51.306 3.745 63994.407 38.506 36.817 1.040 21124.704 4.285 0.863 0.743 7622.965 1.200 Sig. 0.000 0.005 0.000 0.000 0.000 0.386 0.000 0.002 0.354 0.564 0.000 0.311 Partial Eta Squared 0.041 0.012 0.982 0.114 0.082 0.010 0.981 0.040 0.003 0.009 0.959 0.015 11 Statewide class size reduction staffing impact Figures 6, 7, and 8 show the elementary, middle and high school results. Elementary school post-hoc F-tests using ms error within showed that the 0-20%, 21-40% and 61-80% FRLunch schools significanty (p<.001) reduced class sizes between FY06 and FY07. The 41-60% and 81-100% schools did not significantly reduce class sizes. The middle school analysis revealed no interaction. The post-hoc Tukey HSD revealed only the 21-40% and 81-100% school groups were significantly different from one another (p=.002). Figure 6. Elementary school Yearly Average Class Size by FRLunch 20.5 20.0 Average Class Size 19.5 19.0 18.5 0-20% 21-40% 18.0 17.5 41-60% 61-80% 17.0 81-100% 16.5 0-20% 21-40% 41-60% 61-80% 81-100% FY06 20.29 19.52 18.36 18.46 17.13 FY07 19.35 18.69 17.99 17.60 16.99 12 Statewide class size reduction staffing impact Figure 7. Middle school Yearly Average Class Size by FRLunch Average Class Size 20.5 20.0 19.5 19.0 18.5 18.0 17.5 17.0 16.5 0-20% 21-40% 41-60% 61-80% 81-100% FY06 19.48 19.51 19.29 18.76 18.22 21-40% 0-20% 41-60% 61-80% 81-100% FY07 18.68 19.21 18.33 18.01 17.55 Figure 8. High school Yearly Average Class Size by FRLunch Average Class Size 20.5 20.0 19.5 19.0 18.5 18.0 17.5 17.0 16.5 0-20% 21-40% 41-60% 61-80% 81-100% FY06 20.32 20.01 19.54 19.34 19.01 21-40% 0-20% 41-60% 61-80% 81-100% FY07 20.01 20.18 19.54 19.36 18.50 13 Statewide class size reduction staffing impact Classes over legislated size limit The effect of the class size legislation at the school level on the incidence of classes exceeding the legislated size limits was analyzed in a 2 x 3 x 5 repeated measures Anova using the repeated measure annual average number of classes over the maximum allowed number of students (Overlimit) by school Level (elementary, middle and high) and the percentage of students eligible for free & reduced lunch in a school (FRLunch) categorized into five levels (0-20%, 21-40%, 41-60%, 61-80% and 81-100%). Table 5 shows the mean number of classes over limit by free/reduced lunch category and school level. Table 5. Descriptive statistics for OverLimit by Level by FRLunch. Elementary Middle High School Pct Free & Reduced 0-20% 21-40% 41-60% 61-80% 81-100% Total 0-20% 21-40% 41-60% 61-80% 81-100% Total 0-20% 21-40% 41-60% 61-80% 81-100% Total Average Number Classes Over Limit FY06 Mean SD FY07 Mean SD 0.54 1.69 0.26 0.96 0.36 1.92 0.48 3.23 0.23 1.14 0.76 3.46 0.50 1.90 0.92 2.96 0.68 2.97 1.39 4.43 0.46 2.07 0.87 3.45 1.44 4.05 1.82 4.03 0.97 2.90 1.45 3.59 0.64 2.82 0.70 2.51 1.05 3.82 1.50 5.40 1.58 3.64 6.13 17.31 1.06 3.43 2.15 8.47 2.78 6.28 1.50 3.55 1.77 4.68 1.93 7.16 2.06 6.50 1.13 3.31 2.44 6.81 1.89 5.50 0.08 0.28 0.08 0.28 2.12 6.07 1.49 4.89 N 108 194 289 311 297 1199 34 67 111 128 76 416 50 70 118 79 13 330 Table 6 shows the Overlimit by Level by FRLunch Anova table. The three-way interaction was significant (p<.001). 14 Statewide class size reduction staffing impact Table 6. Annual OverLimit by Level by FRLunch Anova Source Type III Sum of Squares df Mean Square F Partial Eta Sig. Squared Tests of Within-Subjects Effects Overlimit 50.798 1 50.798 3.939 0.047 0.002 Overlimit * Level 188.737 2 94.368 7.317 0.001 0.008 Overlimit * FRLunch 162.712 4 40.678 3.154 0.014 0.006 Overlimit * Level * FRLunch 407.768 8 50.971 3.952 0.000 0.016 Error(Overlimit) 24890.112 1930 12.896 Tests of Between-Subjects Effects Intercept 1649.229 1 1649.229 134.801 0.000 0.065 Level 391.649 2 195.825 16.006 0.000 0.016 FRLunch 72.083 4 18.021 1.473 0.208 0.003 Level * FRLunch 375.183 8 46.898 3.833 0.000 0.016 Error 23612.734 1930 12.235 Post hoc 2 x 5 analyses for each Level of OverLimit by FRLunch were performed and are shown in Table 4. To adjust for the loss of power in this post-hoc approach, a significance level of p<.10 was accepted. At the elementary and middle school levels, both main effects and the interaction were significant. No differences were significant at the high school level. The interactions at the elementary and middle school levels might suggest that there are two groups at each level. At elementary, schools with 40% or fewer free and reduced lunch eligible students had no difficulty with the new law, while those with more than 40% FRLunch appear to have seen an increase in the number of classes over limit subsequent to the law's implementation. At the middle school level, only those schools with more than 80% FRLunch appeared to have an increase in the incidence of overlimit classes, while there was no change for schools with lower percentages had no increase in difficulty meeting limits. 15 Statewide class size reduction staffing impact Table 7. Post-hoc repeated measures OverLimit by FRLunch Anovas Source Type III Sum of Squares Elementary School Tests of Within-Subjects Effects Overlimit 47.79 Overlimit * FRLunch 49.27 Error(Overlimit) 6,829.05 Tests of Between-Subjects Effects Intercept 764.47 FRLunch 136.99 Error 12,389.93 Middle School Tests of Within-Subjects Effects Overlimit 236.49 Overlimit * FRLunch 561.17 Error(Overlimit) 13,229.91 Tests of Between-Subjects Effects Intercept 2009.51 FRLunch 1012.48 Error 19,855.63 High School Tests of Within-Subjects Effects Overlimit 25.78 Overlimit * FRLunch 40.43 Error(Overlimit) 4,831.15 Tests of Between-Subjects Effects Intercept 925.27 FRLunch 120.16 Error 14,979.91 df 1 4 1194 1 4 1194 1 4 411 1 4 411 1 4 325 1 4 325 Mean Square 47.79 12.32 5.72 764.47 34.25 10.38 236.49 140.29 32.19 2,009.51 253.12 48.31 25.78 10.11 14.87 925.27 30.04 46.09 F 8.36 2.15 73.67 3.30 7.35 4.36 41.60 5.24 1.73 0.68 20.07 0.65 Significance 0.004 0.072 0.000 0.011 0.007 0.002 0.000 0.000 0.189 0.606 0.000 0.626 Partial Eta Squared 0.007 0.007 0.058 0.011 0.018 0.041 0.092 0.049 0.005 0.008 0.058 0.008 16 Statewide class size reduction staffing impact Figures 9, 10 and 11 portray the two-way interactions at each of the three school Levels. Figure 9. Elementary school OverLimit by FRLunch interaction. 1.60 Average Number Elementary Classes Overlimit 1.40 81-100% 1.20 1.00 0.80 0.60 0.40 0.20 61-80% 41-60% 21-40% 0-20% 0.00 0-20% 21-40% 41-60% 61-80% 81-100% FY06 0.54 0.36 0.23 0.50 0.68 FY07 0.26 0.48 0.76 0.92 1.39 Figure 10. Middle school OverLimit by FRLunch interaction 7.00 6.00 81-100% Average Number of Middle Classes Overlimit 5.00 4.00 3.00 2.00 1.00 0.00 0-20% 21-40% 41-60% 61-80% 81-100% FY06 1.44 0.97 0.64 1.05 1.58 0-20% 61-80% 21-40% 41-60% FY07 1.82 1.45 0.70 1.50 6.13 17 Statewide class size reduction staffing impact Figure 11. High school OverLimit by FRLunch interaction. 3.00 Average Number of High School Classes Overlimit 2.50 2.00 1.50 1.00 21-40% 61-80% 0-20% 41-60% 0.50 0.00 0-20% 21-40% 41-60% 61-80% 81-100% FY06 2.78 1.77 2.06 2.44 0.08 81-100% FY07 1.50 1.93 1.13 1.89 0.08 Elementary and middle schools were categorized into "Low" and "High" FRLunch groups according to the above criteria and each level entered into a 2 x 2 repeated measures analysis of variance. Tables 8 and 9 show the average number of classes over limit by free/reduced lunch category and school level and the Anova summary table for the elementary level. Figure 12 shows the interaction between Overlimit and FRLunch as categorized. The interaction indicates that the schools with higher free and reduced lunch proportions (more than 40%) had significantly more difficulty meeting the new class size requirements than did those schools with lower rates of FRLunch. Table 8. Descriptive statistics for elementary school Overlimit by two-category FRLunch interaction Pct Free & Reduced 0-40% 41-100% Total Average Number of Classes Overlimit FY06 FY07 Mean SD Mean SD 0.47 2.15 1.03 3.67 0.42 1.84 0.40 2.65 0.46 2.07 0.87 3.45 N 897 302 1,199 18 Statewide class size reduction staffing impact Table 9. Post-hoc elementary school Overlimit by two-category FRLunch Anova Tests of Within-Subjects Effects Source Type III Sum of Squares Overlimit 33.05 Overlimit * FRLunch Error(Overlimit) 37.22 6,841.11 Tests of Between-Subjects Effects Intercept FRLunch 608.35 50.95 Error 12,475.97 df 1 1 1,197 1 1 1,197 Mean Square 33.05 37.22 5.72 608.35 50.95 10.42 F 5.78 6.51 58.37 4.89 Sig. 0.016 0.011 0.000 0.027 Partial Eta Squared 0.005 0.005 0.046 0.004 Figure 12. Elementary school Overlimit by two category FRLunch interaction 1.2 41-100% 1.0 Average Number of Elementary Classes Overlimit 0.8 0.6 0.4 0-40% 0.2 0.0 0-40% 41-100% FY06 0.421 0.469 FY07 0.404 1.027 Tables 10 and 11 show the mean number of classes over limit by free/reduced lunch category and school level and the Anova summary table for the middle school level. Figure 13 shows the interaction between Overlimit and FRLunch as categorized. The interaction indicates that the schools with more than 80% free and reduced lunch proportions had significantly more difficulty meeting the new class size requirements than did those schools with lower rates of FRLunch. 19 Statewide class size reduction staffing impact Table 10. Descriptive statistics for middle school Overlimit by two-category FRLunch interaction Pct Free & Reduced 0-40% 41-100% Total Average Number of Classes Overlimit FY06 FY07 Mean SD Mean SD 1.58 3.64 6.13 17.31 0.94 3.37 1.26 4.15 1.06 3.43 2.15 8.47 N 76 340 416 Table 11. Post-hoc middle school Overlimit by two-category FRLunch Anova Tests of Within-Subjects Effects Source Type III Sum of Squares df Mean Square F Partial Eta Sig. Squared Overlimit Overlimit * FRLunch 738.46 555.48 1 738.46 1 555.48 23.10 17.37 0.000 0.000 0.053 0.040 Error(Overlimit) 13,235.60 414 31.97 Tests of Between-Subjects Effects Intercept 3050.44 FRLunch 943.09 1 3050.44 1 943.09 63.38 19.60 0.000 0.000 0.133 0.045 Error 19,925.02 414 48.13 Figure 13. Elementary school Overlimit by two category FRLunch interaction 7.0 6.0 81-100% Average Number of Middle School Classes Overlimit 5.0 4.0 3.0 2.0 0-80% 1.0 0.0 0-80% 81-100% FY06 0.938 1.579 FY07 1.262 6.132 20 Statewide class size reduction staffing impact Teacher age and experience The effect of the class size legislation on the average age and experience of newly hired teachers at the school level was analyzed in two separate 4 x 3 x 5 repeated measures Anovas using the repeated measure of four years school average new teacher age and experience by school Level (elementary, middle and high) and the percentage of students eligible for free & reduced lunch in a school (FRLunch) categorized into five levels (0-20%, 21-40%, 41-60%, 61-80% and 81-100%). Teacher age Table 12 shows the results of the repeated measures Anova for average Age at the school level for new teachers hired for the four years FY04-FY07. Age and Level were significant (p<.001). Table 13 shows the post-hoc Age contrasts and the post-hoc school Level tests. Figures 14 and 15 show the average new teacher ages over the past four years and the difference in ages among the three school levels, respectively. It would appear that the class size legislation had no significant effect on the age of newly hired teachers. A significant (p<.001) rise in age occurred between the FY04 and FY05 years, but the post-hoc Helmert contrast showed no significant change in age subsequently. Newly hired elementary teachers are significantly (p<.001) younger than middle and high school new teachers, but middle and high school new teachers are not significantly different in age. Table 12. New teacher age by Level by FRLunch Anova table Tests of Within-Subjects Effects Type III Sum Source of Squares Tr Age 1194.849 Tr Age * Level 179.470 Tr Age * FRLunch 606.341 Tr Age * Level * FRLunch 904.841 Error(TrAge) 153131.468 Tests of Between-Subjects Effects Intercept 3814315.316 Level 1887.158 FRLunch 130.994 Level * FRLunch 700.242 Error 66791.977 df 3 6 12 24 4245 1 2 4 8 1415 Mean Square 398.283 29.912 50.528 37.702 36.073 3814315.316 943.579 32.748 87.530 47.203 F 11.041 0.829 1.401 1.045 80806.953 19.990 0.694 1.854 Sig. 0.000 0.547 0.157 0.402 0.000 0.000 0.596 0.063 Partial Eta Squared 0.008 0.001 0.004 0.006 0.983 0.027 0.002 0.010 21 Statewide class size reduction staffing impact Table 13. Post Hoc new teacher age Helmert contrasts and school level Tukey Honestly Significant Difference tests New Teacher Age Helmert Test of Within-Subjects Contrasts Source Tr Age TrAge FY04 vs. Later Type III Sum of Squares 1466.304 FY05 vs. Later 67.869 FY06 vs. FY07 99.750 Error(Tr Age) FY04 vs. Later 77427.040 FY05 vs. Later 75566.852 FY06 vs. FY07 89366.572 School Level Tukey HSD (I) SchlLvl2 Elementary (J) SchlLvl2 Middle Mean Difference (I-J) -1.063 High -1.699 Middle High -0.636 df 1 1 1 1415 1415 1415 Std. Error 0.225 0.235 0.278 Mean Square 1466.304 67.869 99.750 54.719 53.404 63.157 F 26.797 1.271 1.579 Sig. 0.000 0.260 0.209 Sig. 0.000 0.000 0.058 Figure 14. Average new teacher age, FY04-FY07 36.5 Average New Teacher Age 36.0 35.5 35.0 34.5 34.0 Age FY04 34.477 FY05 35.671 FY06 35.789 FY07 36.152 22 Statewide class size reduction staffing impact Figure 15. Average new teacher age by school level 36.5 New Teacher Average Age 36.0 35.5 35.0 34.5 34.0 Age Elementary 34.609 Middle 35.659 High 36.299 New teacher experience Table 14 shows the results of the repeated measures Anova for average Experience at the school level for new teachers hired for the four years FY04FY07. School Level and Free & Reduced Lunch (FRLunch) were significant (p<.001). Table 15 shows the post-hoc Level and FRLunch tests. Figures 16, 17 and 18 show the average new teacher experience for each school year, at each School Level and at the different FRLunch levels, respectively. It would appear that the class size legislation has so far had no significant effect on the level of experience of newly hired teachers. Independent of the legislation, the average experience of these teachers is not significantly different between elementary and middle schools, but those teachers have significantly less experience than those hired into high schools (Elementary: p=.034, Middle: p<.001). Also independent of the legislation, schools with higher proportions of students eligible for free and reduced lunch (61-80% and 81-100%) hired teachers with less experience than did schools with 21-40% or 41-60% eligible students. Schools with low percentages of free and reduced lunch eligible students appear also to have hired teachers with less experience. 23 Statewide class size reduction staffing impact Table 14. New teacher experience by Level by FRLunch Anova table Source Type III Sum of Squares Tests of Within-Subjects Effects Tr Exp 46.784 Tr Exp * Level 85.859 Tr Exp * FRLunch 141.061 Tr Exp * Level * FRLunch 348.259 Error(Tr Exp) 76304.316 Tests of Between-Subjects Effects Intercept 53683.206 Level 287.471 FRLunch 294.615 Level * FRLunch 168.168 Error 32991.789 df 3 6 12 24 4245 1 2 4 8 1415 Mean Square 15.595 14.310 11.755 14.511 17.975 53683.206 143.735 73.654 21.021 23.316 F 0.868 0.796 0.654 0.807 2302.444 6.165 3.159 0.902 Sig. 0.457 0.573 0.797 0.731 0.000 0.002 0.013 0.514 Partial Eta Squared 0.001 0.001 0.002 0.005 0.619 0.009 0.009 0.005 Table 15. Post Hoc School Level and FRLunch Tukey Honestly Significant Difference tests. Tukey HSD (I) Level School Level Elementary Middle FRLunch 0-20% 21-40% 41-60% 61-80% (J) Level Middle High High 21-40% 41-60% 61-80% 81-100% 41-60% 61-80% 81-100% 61-80% 81-100% 81-100% Mean Difference (I-J) Std. Error Sig. 0.348 -0.414 -0.761 0.158 0.165 0.195 0.072 0.034 0.000 -0.294 -0.428 0.214 0.298 -0.134 0.508 0.592 0.642 0.726 0.084 0.249 0.234 0.234 0.244 0.197 0.196 0.209 0.177 0.190 0.190 0.763 0.358 0.891 0.739 0.961 0.073 0.037 0.003 0.001 0.992 24 Statewide class size reduction staffing impact Figure 16. Average new teacher experience, FY04-FY07 4.5 Average New Teacher Experience 4.4 4.3 4.2 4.1 4.0 Experience FY04 4.396 FY05 4.140 FY06 4.254 FY07 4.067 Figure 17. Average new teacher experience at each school level 4.8 Average New Teacher Experience 4.6 4.4 4.2 4.0 3.8 3.6 Experience Elementary 4.252 Middle 3.781 High 4.609 25 Statewide class size reduction staffing impact Figure 18. Average new teacher experience at each level of student free and reduced lunch eligibility 4.8 Average New Teacher Experience 4.6 4.4 4.2 4.0 3.8 3.6 Experience 0-20% 4.020 21-40% 4.455 41-60% 4.571 61-80% 3.985 81-100% 4.040 Teacher vacancies The vacancy reporting system (VRS) was initiated by the state in the fall of 2006 at the beginning of the FY07 school year. The effect of class size legislation on the number of vacancies per school system cannot be determined from these data. It can be investigated, however, whether school districts with high proportions of students eligible for free or reduced lunch (FRLunch) experienced higher teacher vacancy rates than did those with lower rates. Table 16 presents the data for the 30 and 90 day teacher vacancy rates grouped by four FRLunch categories. At this school district level of analysis there were six districts with FRLunch ratios 20% or below; these were included with the 21-40% group for this analysis. Table 17 shows the Anova table for this analysis. Table 16. Descriptive statistics for FY07 teacher vacancy rates by FRLunch FRLunch 0-40% 41-60% 61-80% 80-100% Total 30 Day Vacancy 90 Day Vacancy Mean SD Mean SD N 0.006 0.008 0.003 0.004 27 0.009 0.015 0.008 0.013 61 0.014 0.027 0.012 0.021 75 0.024 0.042 0.035 0.058 17 0.012 0.024 0.012 0.025 180 26 Statewide class size reduction staffing impact Table 17. Vacancy by FRLunch Anova Tests of Within-Subjects Effects Source Type III Sum of Squares df Vacancy 0.000 Vacancy * FRLunch 0.001 Error(Vacancy) 0.014 Tests of Between-Subjects Effects Intercept 0.049 FRLunch 0.015 Error 0.180 Mean Square F Partial Eta Sig. Squared 1 0.000 1.958 0.163 0.011 3 0.000 5.486 0.001 0.086 176 0.000 1 0.049 47.414 0.000 3 0.005 4.863 0.003 176 0.001 0.212 0.077 Figure 19 displays the Vacancy by FRLunch interaction. School districts with 80% or fewer students eligible for free or reduced lunch appeared to have less difficulty filling vacancies for the school year, although they made no significant progress overall in reducing vacancies between thirty days after the beginning of their school year and the ninety day monitoring. The few systems with more than 80% FRLunch, however, had a significantly greater number of vacancies at the ninety day point than they did during the beginning of the school year. Figure19. Vacancy by FRLunch interaction. 0.040 Average Ratio of Vacancies to Teaching Staff 0.035 80-100% 0.030 0.025 0.020 0.015 0.010 0.005 0.000 0-40% 41-60% 61-80% 80-100% 30 Day Vacancy 0.006 0.009 0.014 0.024 61-80% 41-60% 0-40% 90 Day Vacancy 0.003 0.008 0.012 0.035 27 Statewide class size reduction staffing impact Summary. The Gaussian curvilinear regression model developed to predict future staffing underestimated actual fall staffing by 504, or 0.44% of actual staffing in the fall of the FY07 school year. The model was developed to predict the traditional total staffing measure taken in the spring of the FY07 year. The model will be adjusted each year to incorporate each new year's staffing data. Traditional determination of teacher attrition will not be calculated until the end of the school year; comparison to the attrition estimates cannot be yet known. Like many states, Georgia faces a predicted teacher shortage. Determining the persistence of vacancy rates as well as the ability of traditional and alternative preparation routes to fill those vacancies and new demand from rising attrition and persistent enrollment growth must await future data monitoring. The class size legislation did significantly effect a reduction in average class sizes at the elementary and middle school levels, but the minimal changes in the legislation at the high school produced no significant change. Elementary schools at some levels of free and reduced lunch enrollment did not significantly reduce class sizes, specifically those with 41-60% and 81-100% eligible. At the middle schools all groups were generally successful in reducing class size, although those in the 21-40% would appear to have reduced sizes less than the others. The effect of the legislation on the number of classes over legislated limits was complex, producing a three-way interaction of Overlimit, School Level and Free & Reduced Lunch. At the elementary school level, schools with 40% or fewer students eligible for free or reduced lunch had no significant difficulty with the law, but those with more than 40% eligible saw a significant increase in the average number of classes reported over the legislated limit. At the middle school, those schools with more than 80% of their students eligible for free or reduced lunch saw a significant increase in the incidence of overlimit classes. There were no differences among the various groupings of high schools. Findings from the studies of the California CSR initiative would suggest that Georgia would find notable changes in the age and experience of newly hired teachers as the schools struggled to meet the urgent demands of finding enough teachers to fill the new classrooms required by the sudden requirements for decreased class size. Separate analyses of the average age and experience of newly hired teachers over the past four years did not sow a change in either as a function of the new law, although schools with more than 60% of their students eligible for free or reduced lunch did hire teachers with significantly less experience than schools with more than 20% to 60% eligible. Schools with 20% or fewer students eligible for free or reduced lunch those that from previous research we would expect to have the most success hiring the teachers they need hired teachers with an average experience no different from the schools with high percentages of free and reduced lunch eligible students. 28 Statewide class size reduction staffing impact The new teacher vacancy data, being a collection of data begun only after the implementation of the class size legislation, could not be brought to bear on the law's effect. Schools with more than 80% of their students eligible for free or reduced lunch had significantly more vacancies, and their situation worsened significantly from the 30 day to the 90 day into the school year monitoring. The situation for the schools with 80% or fewer free or reduced lunch eligible students showed no change in their vacancy levels between the 30 and 90 day monitorings. The 180 day collection in the spring of FY07 as well as continued monitoring will tell whether the high proportion free or reduced lunch schools continue to have a more difficult time putting certified teachers with their students. This appears to be the first opportunity since the California initiative to report outcomes and consider implications of a statewide CSR. There were substantial differences between the California and Georgia initiatives, but the conditions appear similar enough to produce some of the same consequences in teacher staffing. It would appear that Georgia schools' effort in responding to the legislation, at least in the short term, was fairly successful. It is clear that schools with high proportions of low socioeconomic status students, as classified by the proxy measure of free and reduced lunch, have had more difficulty in responding to the law. Although this first study was limited to the first year impact, the research effort will continue for multiple years to measure long-term impacts. References Biddle, B. J., & Berliner, D. C. (2002). What research says about small classes and their effects. San Francisco, CA: WestEd. Blatchford, P. (2005). A multi-method approach to the study of school class size differences. International Journal of Social Research Methodology, 8 (3), 195205. Blatchford, P., Bassett, P., & Brown, P. (2005). Teachers' and pupils' behavior in large and small classes: A systematic observation study of pupils aged 10 and 11 years. Journal of Educational Psychology, 97 (3), 454-467. Bohrnstedt, G. W., & Stecher, B. M. (2002 September). What we have learned about class size reduction in California. Capstone Report. Sacramento, CA: California Department of Education. Borland, M. V., Howsen, R. M., & Trawick, M. W. (2005). An investigation of the effect of class size on student academic achievement. Education Economics, 13 (1), 73-83. Dobbelsteen, S., Levin, J., & Oosterbeek, H. (2002). The causal effect of class size on scholastic achievement: Distinguishing the pure class size effect from 29 Statewide class size reduction staffing impact the effect of changes in class composition. Oxford Bulletin of Economics and Statistics, 64, 17-38. Dustmann, C., Rajah, N., & van Soest, A. (2003). Class size, education, and wages. The Economic Journal, 113 (485), F99-F120. Ehrenberg, R. G., Brewer, D. J., Gamoran, A, and Willms, J. D. (2001). Class size and student achievement. Psychological Science in the Public Interest, 2 (1), 1-30. Finn, J. D., Gerber, S. B., & Boyd-Saharias, J. (2005). Small classes in the early grades, academic achievement, and graduating from high school. Journal of Educational Psychology, 97 (2), 214-223. Hanushek, E. A. (1998 February). The evidence on class size. Occasional Paper Number 98-1. Rochester: W. Allen Wallis Institute of Political Economy, University of Rochester. Hanushek, E. A. (2003). The failure of input-based schooling policies. The Economic Journal, 113 (485), F64-F98. Iacovou, M. (2002). Class size in the early years: Is smaller really better? Education Economics, 10 (3), 261-290. Imazeki, J. (2003). Class-Size Reduction and Teacher Quality: Evidence from California. In D. Monk & M. Plecki (Eds.), School Finance and Teacher Quality: Exploring the Connections. (pp. 159-178.). Larchmont, NY: Eye on Education: Yearbook of the American Education Finance Association. Jepsen, C. & Rivkin, S. (2003 September). What is the tradeoff between smaller classes and teacher quality? Paper presented at the eighth annual meeting of The Society of Labor Economists, Toronto, Ontario, Canada. Kreuger, A. B. (2002). Understanding the magnitude and effect of class size on student achievement. In Mishel, L., & Rothstein, R. (Eds.). The class size debate. Washington, DC: Economic Policy Institute. Kreuger, A. B. (2003). Economic considerations and class size. The Economic Journal, 113 (485), F34-F63. Levin, J. (2001). For whom the reductions count: A quantile regression analysis of class size and peer effects on scholastic achievement. Empirical Economics, 26 (1), 221-246. Molnar, A., Smith, P., Zahorik, J., Halbach, A., Ehrle, K., Hoffman, L. M., & Cross, B. (2001). 2000-2001 evaluation results of the Student Achievement Guarantee in Education (SAGE) program. Tempe, AZ: Education Policy Studies Laboratory, Arizona State University. 30 Statewide class size reduction staffing impact Mosteller, F. (1995). The Tennessee study of class size in the early school grades. The Future of Children. Critical issues for children and youths, 5 (2), 113-127. Normore, A. H., & Ilon, L. (2006). Cost-effective school inputs: Is class size reduction the best educational expenditure for Florida? Educational Policy, 20 (2), 429-454. Nye, B., Hedges, L. V., & Konstantopoulos, S. (2001). The long-term effects of small classes in early grades: Lasting benefits in mathematics achievement at grade 9. Journal of Experimental Education, 69 (3), 245-258. Retrieved July 12, 2006 from http://weblinks2.epnet.com.proxy-remote.galib.uga.edu:2048 Nye, B., Hedges, L. V., & Konstantopoulos, S. (2002). Do low-achieving students benefit more from small classes? Evidence from the Tennessee Class Size Experiment. Educational Evaluation and Policy Analysis, 24 (3), 201-217. Nye, B., Hedges, L. V., & Konstantopoulos, S. (2004). Do minorities experience larger lasting benefits from small classes? The Journal of Educational Research, 98 (2), 94-100. Office for Standards in Education. (1995). Class size and the quality of education. London: Office for Standards in Education Pedder, D. (2006). Are small classes better? Understanding relationships between class size, classroom processes and pupils' learning. Oxford Review of Education, 32 (2), 213-234. Reichardt, R. (2000). The cost of class size reduction: Advice for policy makers. Santa Monica, CA: RAND Corporation. Stecher, B. M., McCaffrey, D. F., & Bugliari, D. (2003 November 10). The relationship between exposure to class size reduction and student achievement in California. Education Policy Analysis Archives, 11 (40). Retrieved July 10, 2006 from http://epaa.asu.edu.epaa/v11n40 Stecher, B., Bohrnstedt, G., Kirst, M., McRobbie, J., & Williams, T. (2001). Class size reduction in California: A story of hope, promise, and unintended consequences. Phi Delta Kappan, 82 (9), 670-674. Willms, J. D., Somers, Y. M. (2001). Family, classroom, and school effects on children's educational outcomes in Latin America. School Effectiveness and School Improvement, 12 (4), 409-445. Wilson, V. (2002 June). Does small really make a difference? A review of the literature on the effects of class size on teaching practice and pupils' behaviour and attainment. Glasgow, Scotland: The Scottish Council for Research in Education, University of Glasgow. 31