This qualitative study explores the process of implementing effective online teaching practices through interviews with thirty exemplary instructors. Emergent themes include providing students with constructive feedback, fostering interaction and involvement, facilitating student learning, and maintaining instructor presence and organization. Analyses of the findings and implications for online instruction are presented.

The density of a general d-dimensional stable random vector X is expressed as an integral over the sphere in R d of a function of the parameters of the one dimensional projections of X. These formulas give insight into the form of multivariate stable densities and are useful for numerical calculations. Corollaries give simplified expressions for symmetric stable and the :=1 strictly stable densities, relations among the densities in different dimensions, and values of the densities at the location parameter for all cases except the :=1, non-strictly stable ones. Expressions for the densities in the multidimensional analog of Zolotarev's (M) parameterization and a discussion of computational versions of the formulas are also given. Academic Press

World Bank Studies are published to communicate the results of the Bank's work to the development community with the least possible delay. The manuscript of this paper therefore has not been prepared in accordance with the procedures appropriate to formally edited texts. This work is a product of the staff of The World Bank with external contributions. The findings, interpretations, and conclusions expressed in this work do not necessarily reflect the views of The World Bank, its Board of Executive Directors, or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. The boundaries, colors, denominations, and other information shown on any map in this work do not imply any judgment on the part of The World Bank concerning the legal status of any territory or the endorsement or acceptance of such boundaries. Nothing herein shall constitute or be considered to be a limitation upon or waiver of the privileges and immunities of The World Bank, all of which are specifically reserved.

This work is a product of the staff of The World Bank with external contributions. The findings, interpretations, and conclusions expressed in this work do not necessarily reflect the views of The World Bank, its Board of Executive Directors, or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. The boundaries, colors, denominations, and other information shown on any map in this work do not imply any judgment on the part of The World Bank concerning the legal status of any territory or the endorsement or acceptance of such boundaries. Nothing herein shall constitute or be considered to be a limitation upon or waiver of the privileges and immunities of The World Bank, all of which are specifically reserved.

Using data from a census of private schools in one of Lagos, Nigeria's administrative jurisdictions, this paper explores the linkages between a heterogeneous sector of private schools and issues of school access, affordability, quality, and ultimately social mobility for households at the bottom of the income distribution. Although a large private education market has buoyed Lagos's growth towards near-universal primary enrolment, this heterogeneous school sector appears to be providing socially stratifying paths towards educational attainment. We apply Lucas's (2001) theory of effectively maintained inequality to assess the extent to which access to higher quality education services within the private sector is determined by cost. We find that higher-cost private schools provide students with greater opportunities to study in institutions with higher quality inputs and increased potential for progression within the educational system. As such, it is highly 2 likely that these schools are primarily accessible to students at the upper ends of the income distribution.