What if we ban private schools?

In the United States, many of the wealthiest students attend private schools. What if we simply passed a law that made it illegal for such schools to exist on the grounds of promoting education equity, as many people have suggested?

THAT IS DEFINITELY ILLEGAL

The first thing that would happen is that courts would declare the law unconstitutional. We know this would happen, because it already happened. In 1922 the state of Oregon passed the Oregon Compulsory Education Act. The law’s main target was Catholic schools, but it impacted all private academies. The law made it so that one could not fulfill their compulsory education requirement through private school attendance. Unless you had some other exemption (e.g. homeschooling) you had to attend your local public school.

The Ku Klux Klan were really pushing this law in Oregon. At the time they were huge defenders of public education, and this was all part of a national panic about immigration. (The Immigration Act of 1924 was a few years away.) Cited in David Tyack’s piece, here is the statement put forth by the Oregon Klan’s Grand Dragon: “The Klan favors … The American public school, non-partisan, non-sectarian, efficient, democratic, for all the children of all the people, equal educational opportunities for all.”

Here’s the full statement. Sheesh.

Anyway, the state was sued and the case made it to the Supreme Court. The Supreme Court was, like, nah man, this is very unconstitutional. It violates the 14th Amendment, the one that extends the rights of liberty to all citizens:

The fundamental theory of liberty upon which all governments in this Union repose excludes any general power of the state to standardize its children by forcing them to accept instruction from public teachers only. The child is not the mere creature of the state; those who nurture him and direct his destiny have the right, coupled with the high duty, to recognize and prepare him for additional obligations.

The world of 2021 is of course very different from 1922. The people in favor of banning private schools today are absolutely not trying to Americanize immigrants. They are definitely not the KKK. Still, it’s very illegal in this country to ban private schools.

WE DID IT ANYWAY

Oh, I don’t know how. They change the constitution. The Supreme Court reconsiders. We find some weird loophole in the 14th Amendment, and also the 1st Amendment. You reboot the universe with a magic ring. Whatever.

As of 2017, about 10% of the nation’s students are in private schools, which makes 5.7 million students. That percentage has been declining slowly, with the loss mostly felt by Catholic schools. About a quarter of private school students attend nonsectarian schools. The rest attend religious schools.

What sort of religions are we talking about? Mostly Christian. From 2015: “In fall 2015, some 5.8 million students (10.2 percent of all elementary and secondary students) were enrolled in private elementary and secondary schools. Thirty-six percent of private school students were enrolled in Catholic schools, 13 percent were enrolled in conservative Christian schools, 10 percent were enrolled in affiliated religious schools, 16 percent were enrolled in unaffiliated religious schools, and 24 percent were enrolled in nonsectarian schools.”

All of the sudden, public schools would need to change how they handle religious education. To be clear, they wouldn’t have to, or that they should. But I bet there would be pressure to change, and I bet it would succeed.

The United States of America is a bit of a global outlier when it comes to teaching religion. We are the land (supposedly) of the strict separation of Church and State. But in much of Europe some sort of non-doctrinal religious education is compulsory. Granted, if you’re secular you often usually opt-out to take an ethics class instead.

Finland is pretty interesting. A course in religious education is compulsory but you get to choose your flavor depending on your religious beliefs. According to a professional organization for Finnish religion teachers: “In 2012 91.9% of pupils in comprehensive school took part in Evangelical-Lutheran [Religious Education], 1.4% in Orthodox, 1.5% in Islam, 0.5% in other religions and 4% in secular Ethics.” Seems like most people just go with the flow and take the Lutheran course. Still, a nice gesture.

If private schools are banned, the United States is going to have to start letting schools teach religion.

They’re also going to have to make some decisions about whether to actually accommodate religious holidays or dietary restrictions. In New York City providing kosher or halal food in public schools still at the “let’s try this interesting experiment” stage and not “we do this” stage.

ENOUGH ABOUT RELIGIOUS KIDS, WE’RE HERE TO BAN PRIVATE SCHOOL FOR RICH PEOPLE

About 2.5% of private school students are attending non-sectarian schools. I don’t know where this 2.5% falls on the wealth spectrum, but give-or-take special programs and financial aid, yeah, let’s go ahead and assume that these kids are all pretty well-off financially.

What happens if they all go into the public school system?

The first thing is that scores, particularly math scores, will probably go up. Private schools underperform public schools on math tests, as argued in “The Public School Advantage.” This is also maybe confirmed by an international perspective, where Cuba (whose schools are all public, Castro nationalized all education) outperforms its entire region on math.

Of course, there are a lot of different ways that countries handle private schools. In this graph the red parts are truly private; the grey parts are dependent on government funding but privately operated, so sort of like charters in the US:

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Japan has a lot of private schools. So does Mexico.

At least in the US, I don’t think it’s particularly mysterious why scores would go up. The government surveys schools to see how much time they spend on various subjects. With the autonomy that private school purchases, these schools spend less time on math.

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Also ELA. I made this chart.

So one thing that would probably happen if private schools were banned is that these wealthier students would score better on math.

But I think the big change would have to do with segregation.

Julie Halpert wrote a really phenomenal piece about public and private schools that catalogs some of what you might expect in a pure public system. The problem is that schools in the US are assigned by neighborhood, and wealthy people can pay to live in wealthy neighborhoods:

Wealthier families tend to buy homes in more expensive areas where the steep taxes result in greater school funding—and are often correlated with higher-quality schools. A study by the Brookings Institution of the country’s 100 largest metro areas found that housing costs tend to correspond with schools’ test scores: On average, home prices near high-performing schools were $205,000 more expensive than they were in areas with low-performing ones. This suggests that in an all-public-school world, those with means would likely buy real estate in well-resourced districts—removing their resources from needier school communities and diluting from those poorer areas the pool of high achievers who experts say can benefit lower-performing students.

If you put wealthy students from powerful families back in the public school system, the main thing you’d get is more wealthy public schools.

And if that doesn’t work, wealthy parents who are sharing a district with poorer ones have another tool in their kit: they can secede, forming a newer, “higher performing” district:

Between 2000 and 2016, 63 communities split off from their existing school districts to form new ones. In just the last two years, 10 more communities have followed. Most of the new districts are more affluent, and less racially diverse, than those they left behind. Another 16 communities are actively exploring efforts to form their own school districts, according to the report.

But would this be widespread? Would there be some benefits for poorer students on the margins?

I don’t know. It’s hard for me to say.

But it’s important to remember that educational inequality in this country is primarily a product of wealth inequality, especially for younger students. The advantages of wealth don’t primarily play out in the 2.5% of students attending non-sectarian private school. The advantages of wealth are (necessarily, really) mostly playing out among the other 97.5%.

Educational inequality is a big deal, but the fantasy of eliminating private schools totally misunderstands the problem.

In short: it’s definitely illegal to ban private schools for wealthy students, but even if you could all it would do is increase their math scores and spur the creation of new wealthy schools and school districts.

What it’s like to not know something

I’ve been reading the book “Metazoa” by Peter Goddfrey-Smith, and I was struck by his description of the “molecular storm,” the setting for cellular life:

“Inside a cell, events occur on the nanoscale, the scale at which objects are measured in millionths of a millimeter, and the medium in which things happen is one of water. Matter in this environment behaves differently from anything in our midsize, dry-land world. At this scale, activity arises spontaneously, without having to be made to happen. In a phrase due to the biophysicist Peter Hoffmann, within any cell is a “molecular storm,” a ceaseless turmoil of collisions, attractions, and repulsions.”

Peter Hoffmann wrote a book that looks just as fascinating, titled “Life’s Ratchet: How Molecular Machines Extract Order from Chaos.” More on the molecular storm, from the description of his book:

“The secret of life, he says, is not some “vital force,” but the unique operations of the second law of thermodynamics at the nanoscale, where molecular machines from kinesins to DNA synthase, fueled by ATP, can harness the energy of the “molecular storm”—the random bombardment of water molecules at jet-plane speeds—to move and work. Hoffman convincingly demonstrates how such “motors” could have evolved from simpler self-assembling structures, but admits that how all these cellular components came to regulate one another so precisely is still a mystery.”

Later, Goddfrey-Smith points to the storm as a crucial difference between the functioning of a biological system like a cell and a computer:

“In the days of ubiquitous computers and AI, it is natural, almost inevitable, to ask about the relationships between living systems and these artifacts. Do organisms and computers do essentially the same thing with different materials? Similarities between the two do arise, often unexpectedly, but it’s also important to recognize dissimilarities. One difference is that much of what a cell does, its main business, is something a computer never has to do. A great deal of the activity in a cell is concerned with maintaining itself, keeping energy coming in, keeping a pattern of activity going despite decay and turnover in materials. Within living systems, the activities that look like the things computers also do — electrical switching and “information processing” — are always embedded within a sea, a mini-ecology, of other chemical processes. In cells, everything that happens takes place in a liquid medium, subject to the vicissitudes of the molecular storm and all the chemical digressions that living systems engage in. When we build a computer, we build something whose operation is more regular and uniform; we build something that will be distracted as little as possible by the undirected ruminations of its chemistry.”

All of this has me thinking about knowledge and its absence. Just as cells are constantly bombarded with molecules, we exist in a storm of images, sounds, smells, and thoughts. Of course we don’t experience it this way — thank you brains! — and instead experience it in a reasonably orderly manner. This order is thanks to two things: the biological structure of our minds, and the structure provided by what we learn.

But the chaos is still lurking beneath the surface. I think you can see this when people make mistakes, especially when they are experiencing cognitive overload. In those moments the structure of knowledge seems to bend under the stress of the challenge, and we get to see some of the random dynamic churning of association.

You can see this at times when students are pushed to apply numerical skills to a new context. You could maybe, maybe, find a way to explain how a student multiplied 0.8 by 1.6 and got 8.0. But to me, that misses the point. The point is that there is no explanation. It’s just the intellectual storm of experience and association bubbling across the mind.

CR parallelogram

Mistakes in math are usually like this: the result of having insufficient structure, not of having the wrong structure. Whatever structures are present are not strong enough to withstand the storm of experience.

This is why I bristle when people talk about student misconceptions. Not because I’m sheepish about judging student ideas as right or wrong. (I’m not into “alternate conceptions.”) And I’m not totally skeptical that misconceptions matter for learning, particularly in science or history. But with math, I think the situation is different. There aren’t a lot of ways to have conceptions about some of these abstract topics. There aren’t a lot of “folk theories” in math, I don’t think.

And when I personally don’t understand something in mathematics, it usually feels like the storm to me. Undifferentiated thoughts, slipping and sliding between different intellectual currents. I’m searching for something to hold on to! And I think our students often feel similarly.

A lot of math teachers feel that every mistake needs to be addressed and explained. If every mistake were a misconception — a faulty or limited mental structure — then I think this would make sense. But mistakes aren’t usually like this. They are chaotic, a snapshot of the storm. And because of this, they can only be addressed is by learning, which is to say building something new.

Making Long Problems Shorter

Some math questions have long complicated answers. This is a problem for teachers, because students get lost in the middle of complex stuff. They end up not learning and feeling bad about it. This is not good.

This past year I taught calculus for the first time. There’s no way around it: some of those solutions take a lot of steps. Moreover, my class was a sort of intro to calc for people who aren’t especially enthusiastic about algebra. This was a class where kids apologized for being bad at math on the first day of school.

What could I, an award-winning* worked example enthusiast, do to help these students?

* Correction 6/15/2021: I have not won any awards.

One approach, one I don’t favor, is to break a complex problem up into many mini-problems. That way, students only have to think about a smaller part at any one moment. This is called “scaffolding.” It’s the approach Active Calculus takes for some of their problems:

Look, that’s still a lot of words and questions. And you can’t forget part (c) once you solve it — you haven’t learned anything until you take all five parts and make sense of them together. I do not like this, it is bad.

What I’ve started to think is that good teaching sometimes involves turning long ideas into a series of shorter ones. But in a way so that after each relatively short task you have learned something complete, gotten a full meal. The pieces add up to something greater, but each part is a meaningfully whole thought. You can breathe in between each piece without the entire structure falling apart.

For longer calculus problems this year, here was my routine for doing that.

Obviously you should not teach young kids how to multiply like this. That is not actually a complex procedure, splitting apart by place value is a powerful idea but it is not long. Let’s be real, I picked it precisely because it’s short and could fit on the image.

First, I would warm up students to the lesson with any skills they’d need for the day’s learning. I was just hoping to help them notice and remember anything they’d need for what was coming next. For this related rates lesson, I knew that the chain rule was going to be important, so we started with that.

Does this look a bit sloppy? Sure it does, it was produced during the glorious 2020-2021 schoolyear.

Then, I would slowly develop the problem, making sure everyone understood the question. “If we’re inflating a spherical balloon, what happens to the volume as it inflates? What happens to the radius?”

“Imagine we inflate the balloon with a constant flow of air, maybe using a pump or something? Will the volume change constantly? What about the radius?”

If I want to make sure students get it, I’ll ask them to take a guess as to what the answer will be. “Will the radius grow at a constant rate? Will it grow faster at first and then slow down? Or slower, then fast? What’s your guess?” (There is a lovely animation somebody made to go along with this problem. I projected it while collecting guesses.)

When it was time to dive into the solution, I would first give a “headline news” version of it. I’d project it on the board, and then talk through it.

The plan of attack. Calculus, attack!

“Here’s the plan of attack for this problem. We can write a function that connects the radius to the volume. But we’re going to turn that into an equation that connects the rate of change of volume to the rate of change of the radius. How? The derivative! We’ll treat volume and the radius as if they are not constants but functions of time, and we’ll use the chain rule to differentiate in terms of time. Then we’ll sub in all the given info from the problem — which rate of change do we already know? that’s right! — and solve for dr/dt.”

This approach is cribbed directly from Richard Catrambone’s research on “subgoal learning.”

Then I start revealing steps in the solution, filling in the empty spaces. What function do we have that connects the volume of a sphere to the radius? How do we differentiate? etc.

I often revealed just one section at a time. If I could prepare this ahead of time, I would. Otherwise I’d produce it on the board in class. Oh, also there’s a mistake in here. I fixed it in class, but will not fix it here. LAZINESS.

I would give students time to study this, time to explain it to a partner, and time to answer some self-explanation questions about it. I had previously explained in the abstract why we’d need to use the chain rule in the second step — I’d ask students to articulate that principle on their own. And I would ask students what if the diameter were 16 inches instead of 12 — what would the answer be then?

Their job now is to understand the details of this particular solution and connect it to the generalized outline I had already presented.

And once we’re comfortable with this solution, we’ll develop another question and ask students to solve just a bit of it on their own. In doing this we’re giving them something short to think about in the context of a much larger problem. These are “completion problems,” a type of task identified and studied by van Merrienboer (for example, here).

And it keeps going:

And so on:

Anyway, I think a lot of what I do as a teacher is I make shorter cycles of learning compared to a lot of other people. I’ll do inquiry, but for a few minutes. I’ll do worked examples, but I structure it so that it’s made of several self-contained tasks that (mostly) stand on their own. Is that just what we in the biz call “scaffolding”? I guess, but it’s not “scaffolding” in the sense of giving kids lots of help to climb up a very tall structure. More like just building a bunch of smaller structures that are just as valuable as the big tall one.

I don’t know what to call it, but it seemed to work well for some of my highly anxious, algebraphobic calculus students.