پاداش یا تنبیه؟ اندازه کلاس و کیفیت معلم

The high stakes testing and school accountability components of our K-12 education system create an incentive for principals to behave strategically to maximize school performance. One possible approach is the adjustment of class sizes based on observed teacher effectiveness. Conceptually, this relationship may be positive or negative. On one hand, performance-maximizing principals may place more students in the classrooms of more effective teachers. But because administrators may have compensation constraints, it is also plausible that they may reward more effective teachers with fewer students in the classroom. This paper examines whether principals reward effective teachers by decreasing their class size or whether they increase the size of classes of more effective teachers as a means of enhancing the school outcome. Results overall indicate that more effective teachers do have larger classes. This result holds implications for prior policy studies of class size as well as for education policy more generally.

Education policy often seeks to improve student outcomes through broad based initiatives designed at the federal and state levels and implemented through local school districts. By setting standards for student achievement and addressing procedures for the provision of educational inputs, these initiatives create the constraints under which local administrators operate. One of the larger efforts in education policy research has been the study of the effect of resource constraints on student achievement, and within that, one policy studied has been the effect of class size on achievement. From a policy perspective, states typically establish a maximum number of pupils per class for schools. Districts allocate resources to schools based on estimates of the number of students and the resulting number of teachers required to satisfy the state class size mandate. Principals then determine the number of students to place in a classroom. There is a large literature that has examined these policies and the effect of class size on student performance. The assumption is that class size influences student learning because it directly affects the degree to which the teacher can react to individual student learning differences and, thus, alters the effectiveness of the teacher.2 The assumption, of course, is that smaller classes facilitate more effective teaching, ceteris paribus. The Tennessee STAR experiments are the most prominent of positive findings in this research area (Finn et al., 2001, Krueger, 2003 and Nye, 2000). There are also results from numerous studies indicating that class size does not systematically affect achievement, although significant reductions in class size do appear to increase student performance on standardized exams. For example, a reduction in class size of about ten students would lead to gains in student achievement comparable to what could be achieved through the improvement of teacher quality by one standard deviation (Nye, Hedges, & Konstantopoulos, 2001).3 This paper takes a new policy look at class size. For the purpose of this paper, we are not directly interested in whether class size influences student performance. We address whether class size is used as a policy instrument of principals and school administrators in response to demonstrated teaching effectiveness. More explicitly, do principals consider a teacher's prior effectiveness when determining the current class size for that teacher? We argue that theoretically, class size can be reduced as a means of compensating or “rewarding” teachers for good performance or it can be increased by principals in an effort to put more students in the classrooms of effective teachers. This, of course, has the effect of “punishing” the more effective teachers. We empirically examine this question with a data set that matches students to teachers in a longitudinal panel that allows us to measure prior teacher effectiveness. We find that more effective teachers do receive punishment in the form of larger class sizes. Our results hold implications for prior policy studies regarding the effects of class size on student achievement as well as for education policy more generally.

This paper makes an important contribution in that it raises the question of whether principals or other administrators of schools may use class size as a strategic policy variable in influencing their schools’ performance. The findings provide some support to the idea that principals are indeed strategic in choosing class size for teachers. In particular, principals place more students in the classroom of more effective teachers, controlling for all other factors. There are multiple implications for this finding. First, as discussed early in this paper, a great deal of research has examined the relationship between class size and student outcomes and, for the most part, this research has assumed that class size is an exogenous variable. But if the estimates from past models have been biased because class size is endogenous, there is little policy advice that can be made based on prior estimates. The efficiency of public resources devoted to class size reduction should be further addressed. More importantly, this paper holds implications for a current policy issue of high salience: evaluation of teacher performance. The finding that principals appear to behave strategically in assigning numbers of students to a teacher reinforces earlier work that effective principals are ones that know their teachers and exercise their discretion managerially within the school. If the finding of this paper holds across other states or other data sets, then the role of principals in evaluating teachers cannot be understated. While value-added models and other quantitative models of effectiveness may be part of an evaluation system, the subjective judgment of the principal who is both responding to parents and accountable to the state must be a critical piece of a teacher's performance evaluation. Finally, while this paper examined the choice of class size by the administrator, one possible extension of this research is to explore the possibility of a subsequent response by more effective teachers in the long run. Allgood and Rice (2002) found evidence that turnover rates are higher in lower income, lower achieving schools, and as Figlio (1997) finds, higher quality teachers tend to command higher salaries that affluent districts are more willing to pay. Although much needs to be done, one possible explanation is that the larger class sizes of more effective teachers in lower performing schools coupled with lower compensation may motivate exit, particularly if they can command higher salaries in other schools with teachers of similar quality. As always, this paper calls for much more research.