total number of dollars that each district (or perhaps even at the level of each school) must have in order to deliver its pupils an adequate education (see Guthrie and Rothstein, Chapter 7 in this volume). (Interestingly enough, once they determine the total per-pupil amount, Guthrie and Rothstein do not insist that schools be required to spend precisely in the way implied by the building blocks that were used in determining the school's total revenue. Instead, schools are to have flexibility in how they use their funds. But they are to be held accountable in some way if the performance of their pupils is not up to par.)

John Augenblick has developed a different approach (Augenblick, 1997). His strategy is to identify the cost structures of districts that are successful. After excluding the outlier districts, both rich and poor, in terms of wealth and per-pupil expenditure, Augenblick scours the remaining districts to see which have been successful in terms of student performance (e.g., 75 percent or more of the pupils meet state minimum competency standards). Then Augenblick looks to see how much was spent per pupil in these successful districts. The basic idea is that if a group of districts with a variety of pupil characteristics can succeed with $X per pupil, then other districts should also be able to do so.

William Duncombe and John Yinger have offered further insights (see Chapter 8 in this volume). They are highly skeptical about whether schools with concentrations of low-income children, especially in urban areas, can realistically succeed with an amount of money that Augenblick's model would provide, and they find arbitrary Guthrie and Rothstein's reliance on the professional model to determine how much extra money those schools should have. Instead, Duncombe and Yinger have developed very sophisticated analytical techniques to determine empirically how much extra money schools (or school districts) should be provided when they face high-cost problems that are beyond their control—like needy pupils and high wage costs. For example, if using the Guthrie and Rothstein approach, it was determined that, say, $6,000 per pupil was needed in an ordinary district or school, the Duncombe and Yinger methodology might then suggest that, say, $12,000 per pupil is needed in a district with a great concentration of low-income children—if those children are to perform, on average, as well as children living in the ordinary district. While these numbers are just hypothetical, it is important to note that Duncombe and Yinger do claim that in New York, for example, many upstate urban communities will need more than twice as much money as New York City suburban schools if they are to have any chance of matching the educational outcomes of those suburbs. Moreover, New York City itself, they say, would need perhaps three times what Scarsdale spends. Given the complexity of the Duncombe and Yinger methodology, many will wonder to what extent they really have taken into account only costs that are beyond the school or district's control and not allowed past spending inefficiencies to determine how much future revenue a school or district ought fairly have.

These examples illustrate the sorts of testimony that might be brought forward by the parties. Of course, these various approaches to determining adequacy

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