Equal or Fair? A Study of Revenues and Expenditures in American Charter Schools

A new study finds that charter schools typically get less funding than traditional public schools. And it also reveals that the primary reason charters tend to get less funding is because traditional public schools must offer far more special education, transportation and student support services. Spending on those programs and services -- often not available in charter schools -- accounts for much or all of the difference in funding each receives. This finding is one of several that Professor Gary Miron and his co-author Jessica Urschel make in Equal or Fair? A Study of Revenues and Expenditures in American Charter Schools, released today by the Great Lakes Center for Education Research and Practice. The study comes amid a growing debate over the question of whether charter schools are inadequately funded compared with traditional public schools. In recent years, numerous charter school advocates have cited the purported funding gap to help explain charter schools' achievement results compared with traditional public schools. Miron and Urshel point out that, compared with traditional public schools, charter schools spend proportionally more on administration -- in the percentage of overall spending that goes to administrative costs, as well as in the salaries they pay administrative personnel. Overall, however, charter schools spend less than traditional public schools: less on instruction, less on student support services and less on teacher salaries and benefits. Equal or Fair? is the most comprehensive study to date on the question. It uses data from the U.S. Department of Education on revenue sources and spending patterns of charter schools and traditional public schools and districts across the nation. It also examines patterns across nine different comparison groups, ranging from traditional public schools to various sub-groups of charter schools. "On first appearance, charter schools receive less revenue per pupil ($9,883) than traditional public schools ($12,863)," Miron and Urschel find. Yet, they add, this direct comparison "may be misleading." States vary considerably in the way they channel funds to charter schools. Moreover, public schools provide -- and receive funds for -- certain services that most charter schools do not provide (or spend far less on) including special education, student support services and transportation and food services. This largely explains the differences in revenues and expenditures for charters compared with traditional schools. "When charter schools and traditional public schools have similar programs and services and when they serve similar students, funding levels should be equal in order to be considered fair," they write. "However, as long as traditional public schools are delivering more programs, serving wider ranges of grades, and enrolling a higher proportion of students with special needs, they will require relatively higher levels of financial support. Under these circumstances, differences or inequality in funding can be seen as reasonable and fair.

Nodal decompositions of a symmetric matrix

Analyzing nodal domains is a way to discern the structure of eigenvectors of operators on a graph. We give a new definition extending the concept of nodal domains to arbitrary signed graphs, and therefore to arbitrary symmetric matrices. We show that for an arbitrary symmetric matrix, a positive fraction of eigenbases satisfy a generalized version of known nodal bounds for un-signed (that is classical) graphs. We do this through an explicit decomposition. Moreover, we show that with high probability, the number of nodal domains of a bulk eigenvector of the adjacency matrix of signed a Erd\H{o}s-R\'enyi graph is $\Omega(n/\log n)$ and $o(n)$.Comment: 38 pages 1 figur