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A couple of weeks ago, a math professor and I were discussing the differences between math and management. Both involve problem solving, and budgetary issues require some basic mathematical sense. But in math, problems often start with “givens,” or statements taken as undisputed fact. In management (or politics), the givens themselves are often at issue. When the givens are in dispute, the nature of problem solving changes.

I was reminded of that this week when a couple of articles bumped into each other in my Twitter feed. The first, by Melissa Korn writing in The Wall Street Journal, addresses ways to “fix college admissions.” The second, from Inside Philanthropy (and paywalled, ironically enough), asks “What Does It Take for Community Colleges to Raise More Money?” Read together, they suggest that we need to look hard at what we take as given.

Korn’s piece acknowledges that hyperselective institutions are a small slice of higher education, but it’s written with that small slice entirely in mind. She notes correctly that the Varsity Blues scandal is a symptom of a much more widespread anxiety about college admissions, and that much of the competition for slots at that level has become silly. And several of her suggestions are eminently sensible: ending legacy admissions, for example, is hard to dispute. I particularly liked the idea of a spontaneous one-hour essay written in a proctored setting, rather than the (frequently outsourced) essay that many places require now. That’s a variation on a plagiarism check I used to use when I taught writing classes: if a student who turned in elegant papers couldn’t compose a coherent paragraph in class, I started asking questions. I’ll admit some bias here, though; as a deadline writer, I appreciate the acknowledgment that decent writing to a deadline is a specific and undervalued skill. I certainly like to think it is.

Some of the other suggestions are less successful. Ending college rankings is literally impossible in the face of the First Amendment. Yes, college rankings are destructive in many ways, but anyone can produce lists of anything at any time. (“Top 10 Wallpaper Patterns for Capricorns …”) There’s no stopping the supply without doing something much worse; any reform has to happen on the demand end. And her cavalier claim that “almost nobody pays sticker price for a college education these days” ignores the staggering overrepresentation of the top 1 percent of incomes at high-end schools. The description would be accurate for many lower-tier schools, but it really isn’t at the schools on which her piece focuses.

But the most striking element, for me, is the dog that didn’t bark. Korn’s piece takes for granted that there is, and will be, a small number of elite places that need to manage demand. Her suggestions take that universe for granted. It never mentions increasing the number of seats at the elite places, or improving the second tier of schools, or strengthening community college transfer programs. It’s about applying distributive justice to the number of elite seats that currently exist; it takes the scarcity of those seats (and their desirability) as given. If you accept that premise, then fairer redistribution of the few plum spots is probably the most we can ask. But why accept the premise?

The Inside Philanthropy piece notes, correctly, that donations that might amount to a drop in the bucket at the Stanfords of the world can change lives at a community college. Yet community colleges remain disproportionately underrepresented in the world of college philanthropy.

There’s no shortage of reasons for that, ranging from the relative youth of community colleges -- about half of them were founded in the 1960s, so planned gifts are only starting to become possible at scale now -- to the frustrating paradox that it takes money to make money. When a college is already bare-bones, it’s difficult to devote significant resources to hiring more fundraising staff and schmoozing donors, even if that would pay off over the long run. And for the first few decades of many community colleges’ existence, alumni associations simply weren’t a priority, so starting new ones requires building alumni databases from scratch. Yale doesn’t have that problem.

Here, too, a minor shift in givens would make a difference. What if states, or major foundations, or both, developed capacity-building grants for community college fundraising? In other words, what we got around the “it takes money to make money” problem by priming the pump? It could be framed as a form of investment, because, in fact, it is. We don’t have trouble thinking of Harvard’s endowment as an investment fund, but we don’t think of spending on community colleges as investing. It is, and according to Raj Chetty’s data, it offers better payoff in social mobility. But we have to rethink the givens.

Givens make problems much easier to solve, but they only work if they’re true. We take it as given that only elite places are worth supporting. That’s simply not true. But until we stop taking that as given, we’ll keep solving the wrong problems.

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