¹ The language used in the United States includes, for example, “principal” rather than “head teacher,” “student” rather than “pupil,” and so on.

² Reardon, Sean, “The Widening Academic Achievement Gap between the Rich and the Poor: New Evidence and Possible Explanations,” in Murnane, Richard and Duncan, Greg, eds., Whither Opportunity (New York: Spencer Foundation and Russell Sage Press, 2011), 91–116.Google Scholar

³ Kaushal, Neeraj, Magnusson, Katherine, and Waldfogel, Jane, “How Is Family Income Related to Investments in Children’s Learning?” in Murnane, Richard and Duncan, Greg, eds., Whither Opportunity, 187–206.Google Scholar The enrichment spending ratio almost doubled from 1972.

⁴ See Payne, Charles, So Much Reform, So Little Change: The Persistence of Failure in Urban Schools (Cambridge, MA: Harvard Education Press, 2008)Google Scholar for a perspicuous account of why urban schools are so difficult to improve.

⁵ For several formulations of educational equality principles, see Jencks, Christopher, “Whom Must We Treat Equally for Educational Opportunity to be Equal?” Ethics 98, no. 3 (1988): 518–33Google Scholar. See also Swift, Adam, How Not to Be A Hypocrite: School Choice for the Morally Perplexed (London: Routledge, 2005)Google Scholar; Burwood, Les, “Equality of Opportunity as a Sensible Educational Ideal,” Journal of Philosophy of Education 26, no. 2 (1992): 257–59Google Scholar; and Norman, Richard, “No End to Equality,” Journal of Philosophy of Education 29, no. 3 (1995): 421–31.Google Scholar

⁶ See Curren, Randall, “Justice and the Threshold of Educational Equality,” in Katz, Michael, ed., Philosophy of Education 1994, (Urbana, IL: Philosophy of Education Society, 1995), 239–48Google Scholar; Tooley, James, Education Without the State (London: Institute of Economic Affairs, 1995 Google Scholar); Gutmann, Amy, Democratic Education (Princeton, NJ: Princeton University Press, 1989)Google Scholar; Anderson, Elizabeth, “Fair Opportunity in Education: A Democratic Equality Perspective.” Ethics 117, no. 4 (2007): 595–622 CrossRefGoogle Scholar; Satz, Debra, “Equality, Adequacy, and Education for Citizenship,” Ethics 117, no. 4 (2007): 623–48.CrossRefGoogle Scholar

⁷ For an explicit formulation along these lines see Schouten, Gina, “Fair Educational Opportunity and the Distribution of Natural Ability: Toward a Prioritarian Principle of Educational Justice,” Journal of Philosophy of Education 46, no. 3, (2012): 472–91CrossRefGoogle Scholar. See also Bou-Habib, Paul, “Who Should Pay for Higher Education?” Journal of Philosophy of Education 44, no. 4, (2010): 479–95.Google Scholar

⁸ The theories within category vary by metric, as we shall see later.

⁹ We say “currently” because we are alert to the role that high quality software has come to play in inducing learning at all levels, and that this role might increase in the future.

¹⁰ The case of Jaime Escalante is instructive here. His mostly Hispanic students in an East Los Angeles, California school consistently attained spectacular results in Advanced Placement Calculus. When he moved to a school in Sacramento, California, even though it had a similar population, he was unable to replicate the success.

¹¹ Harry Brighouse and Gina Schouten, “Understanding the Context for Existing Reform and Research Proposals,” in Richard Murnane and Greg Duncan, eds., Whither Opportunity, 507–22.

¹² These schools are described in detail in Mathews, Jay, Work Hard. Be Nice: How Two Inspired Teachers Created the Most Promising Schools in America (Chapel Hill, NC: Algonquin, 2009).Google Scholar

¹³ Tuttle, Christina Clark, Gleason, Philip, and Clark, Melissa, “Using Lotteries to Evaluate Schools of Choice: Evidence from a National Study of Charter Schools,” Economics of Education Review 31, no. 3 (2012): 237–53Google Scholar and Tuttle, Christina Clark, Gill, Brian, Gleason, Philip, Knechtel, Virginia, Nichols–Barrer, Ira, and Resch, Alexandra, “KIPP Middle Schools: Impacts on Achievement and Other Outcomes,” Mathematica Policy Research (2013). (Can be accessed at http://www.mathematica-mpr.com/publications/redirect_PubsDB.asp?strSite=PDFs/education/KIPP_middle.pdf).Google Scholar

¹⁴ Ibid., xiii.

¹⁵ Typically fifth through eighth grades. (Those students who leave before completing their fourth year in the KIPP school remain a part of the treatment group for the duration of the four years after enrollment. By including students even when they fail to persist in the KIPP school, the report avoids artificially inflating the positive impacts of enrollment.)

¹⁶ The study also examines survey responses regarding student attitudes and behaviors. These responses suggest that KIPP may influence behaviors and attitudes in ways that enhance students’ prospects for long-term academic achievement. For example, the data suggest that students who enrolled in KIPP schools spent 35 to 53 minutes more on homework each night than they would have if they had remained in their neighborhood schools. Other effects on attitude or behavior were either negative or not significant.

¹⁷ Dobbie, Will and Fryer, Roland G. Jr. “Are High-Quality Schools Enough to Close the Achievement Gap?: Evidence from a Bold Social Experiment in Harlem,” National Bureau of Educational Research, Working Paper No. 15473 (Cambridge, MA: National Bureau of Educational Research: 2009).Google Scholar

¹⁸ However, the external-to-schools programs may more decisively account for the improvement in outcomes other than test score gains, such as absenteeism (ibid., 24–27).

¹⁹ In most states, regular, nonchartered, public schools are allowed to expel students as a last resort, but the school district still has a legal obligation to educate the students, the cost of which is nontrivial once they are not in a school.

²⁰ We should emphasize that we do not have evidence either way on this — it is not something that, as far as we know, social scientists have even tried to estimate. The conjecture, however, seems reasonable, and is widely shared, including by supporters of charter schools.

²¹ Because their business models are so different, KIPP and similar charter schools do not compete directly with local schools for teachers and managers; but if the presence of a KIPP school worsens the working conditions in a local school, that school is less able to compete with other schools (and school districts) for teachers and managers.

²² Harry Brighouse and Gina Schouten, “To Charter or not to Charter: What Questions Should We Ask, and What Will the Answers Tell Us?” forthcoming in Harvard Educational Review.

²³ Jencks refers to Equality of Educational Resources as “Democratic Equality.” See Jencks, Christopher, “Whom Must We Treat Equally for Educational Opportunity to be Equal?” Ethics 98, no. 3 (1988): 518–33.Google Scholar

²⁴ For reasons why this might be, see Richard Rothstein, Class and Schools (Washington, DC: Economic Policy Institute, 2004).

²⁵ See, for example, the discussion of Weak and Strong Humane Justice in Jencks, “Whom Must We Treat Equally for Educational Opportunity to be Equal?” 518–33. Jencks’s meritocratic conception — “Weak Humane Justice” — corresponds to John Rawls’s principle of fair equality of opportunity in rejecting inequalities of educational achievement caused by social class background differences ( Rawls, John, A Theory of Justice (Cambridge, MA: Harvard University Press, 1971)CrossRefGoogle Scholar), and is assumed for the sake of argument by Swift, Adam, How Not to Be A Hypocrite: School Choice for the Morally Perplexed (London: Routledge, 2005)Google Scholar. See also Burwood, Les, “Equality of Opportunity as a Sensible Educational Ideal,” Journal of Philosophy of Education 26, no. 2 (1992): 257–59Google Scholar; and Norman, Richard, “No End to Equality,” Journal of Philosophy of Education 29, no. 3 (1995): 421–31CrossRefGoogle Scholar. Jencks’s more demanding variant — “Strong Humane Justice” — rejects, in addition, inequalities of achievement caused by natural differences. Jencks considers both variants, as if they are stand-alone principles constituting the whole of justice (whereas most egalitarians are pluralists about justice). He rejects both variants of humane justice. For further discussion, see Brighouse, Harry, “Education” in Gauss, Gerald and Fred D’Agostino, eds., The Routledge Companion to Social and Political Philosophy (New York; Oxford: Routledge, 2013), 721–31.Google Scholar

²⁶ The subgroups need not contain the same students across scenarios.

²⁷ For explanations of priority principles generally, see Parfit, Derek, “Equality and Priority,” Ratio 10, no. 3 (1997): 202–21CrossRefGoogle Scholar; and Arneson, Richard, "Luck Egalitarianism and Prioritarianism,” Ethics 110, no. 2 (2000): 339–49.CrossRefGoogle Scholar

²⁸ For examples of arguments for adequacy as the lone principle of educational justice, see Tooley, James, Education without the State (London: Institute of Economic Affairs, 1995)Google Scholar; Anderson, Elizabeth, “Fair Opportunity in Education: A Democratic Equality Perspective,” Ethics 117, no. 4 (2007): 595–622 CrossRefGoogle Scholar; Satz, Debra, “Equality, Adequacy, and Education for Citizenship,” Ethics 117, no. 4 (2007): 623–48CrossRefGoogle Scholar. Anderson says that “sufficientarian principles do not constrain inequalities in educational access above the sufficiency threshold” (615). For examples of arguments for adequacy as at least one of the principles of justice in education see Curren, Randall, “Justice and the Threshold of Educational Equality,” in Katz, Michael, ed., Philosophy of Education 1994, (Urbana: Philosophy of Education Society, 1995), 239–48Google Scholar and Gutmann, Amy, Democratic Education (Princeton, NJ: Princeton University Press, 1989)Google Scholar. For each of the mentioned theorists, exactly what education must be adequate for is somewhat different.

²⁹ Anderson, Elizabeth, “Fair Opportunity in Education: A Democratic Equality Perspective,” Ethics 117, no. 4 (2007): 595–622.Google Scholar

³⁰ Satz, Debra, “Equality, Adequacy, and Education for Citizenship,” Ethics 117, no. 4 (2007): 623–48.Google Scholar

³¹ As Elizabeth Anderson puts it, “I use Rawls’s insights to different ends than Rawls himself did, because my concern lies with non-ideal theory—that is, with constructing workable criteria of justice in educational opportunity for our currently unjust world, rather than for a well-ordered society.” See Anderson, Elizabeth, “Fair Opportunity in Education: A Democratic Equality Perspective,” Ethics 117, no 4 (2007): 595–622 at 621.Google Scholar

³² Similarly, adequacy principles provide no guidance when all constituents exceed the adequacy threshold on either alternative, and when the same number meet the threshold on either alternative, but the distributions are otherwise nonidentical. And yet, in many of these cases, it seems that principles of justice should render a verdict.

³³ This is the adequacy threshold defended in Anderson, Elizabeth, “Fair Opportunity in Education: A Democratic Equality Perspective,” Ethics 117, no. 4 (2007): 595–622.CrossRefGoogle Scholar

³⁴ Devah Pager’s random controlled study, conducted in Milwaukee, Wisconsin, suggests that knowing that a male candidate is African American has the same effect on an employer’s decision as knowing, if the candidate is Caucasian, that he has a criminal record. See Pager, Devah, Marked: Race, Crime, and Finding Work in an Era of Mass Incarceration (Chicago: University of Chicago Press, 2006).Google Scholar