Isegoria

More than 1 million fewer students are enrolled in college now than before the pandemic began:

Compared with the fall of 2019, the last fall semester before the coronavirus pandemic, undergraduate enrollment has fallen a total of 6.6%. That represents the largest two-year decrease in more than 50 years, Shapiro says.

The nation’s community colleges are continuing to feel the bulk of the decline, with a 13% enrollment drop over the course of the pandemic. But the fall 2021 numbers show that bachelor’s degree-seeking students at four-year colleges are making up about half of the shrinkage in undergraduate students, a big shift from the fall of 2020, when the vast majority of the declines were among associate degree seekers.

“The phenomenon of students sitting out of college seems to be more widespread. It’s not just the community colleges anymore,” says Shapiro. “That could be the beginning of a whole generation of students rethinking the value of college itself. I think if that were the case, this is much more serious than just a temporary pandemic-related disruption.”

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“The easiest assumption is that they’re out there working,” says Shapiro. “Unemployment is down. The labor market is good. Wages are rising for workers in low-skilled jobs. So if you have a high school diploma, this seems like a pretty good time to be out there making some money.”

Five-year-olds whose pretest performance showed that they had not mastered number conservation were presented four training sessions:

Some were just given feedback on their number conservation performance; others were given feedback and asked to explain their reasoning; yet others were given feedback and asked to explain the reasoning that led to the experimenter’s judgment. Being asked to explain the experimenter’s reasoning produced considerably more learning than either of the other two procedures.

Number conservation is kind of hard:

The Bulletproof Musician summarizes the results:

The kids who were asked to imagine what the expert’s perspective might be ultimately got 62 percent of the questions correct over the course of their four testing sessions. Whereas the group that provided their own reasoning for the answer only got 48 percent of the problems correct. And those who provided no rationale got 49 percent correct.

Although error avoidance during learning appears to be the rule in American classrooms, Janet Metcalfe says, laboratory studies suggest that it may be a counterproductive strategy, at least for neurologically typical students:

Experimental investigations indicate that errorful learning followed by corrective feedback is beneficial to learning. Interestingly, the beneficial effects are particularly salient when individuals strongly believe that their error is correct: Errors committed with high confidence are corrected more readily than low-confidence errors. Corrective feedback, including analysis of the reasoning leading up to the mistake, is crucial. Aside from the direct benefit to learners, teachers gain valuable information from errors, and error tolerance encourages students’ active, exploratory, generative engagement. If the goal is optimal performance in high-stakes situations, it may be worthwhile to allow and even encourage students to commit and correct errors while they are in low-stakes learning situations rather than to assiduously avoid errors at all costs.

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It might seem intuitive that if one does not want errors on the test that counts, then one should avoid errors at all stages of learning. In this view, committing errors should make those errors more salient and entrench them into both the memory and the operating procedures of the person who makes them. Exercising the errors should make the errors themselves stronger, thus increasing their probability of recurrence. Such a view, which is consistent with a number of the oldest and most well established theories of learning and memory (Bandura 1986, Barnes & Underwood 1959, Skinner 1953), suggests that errors are bad and should be avoided at all costs.

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However, Stevenson & Stigler (1994; see also Stigler & Hiebert 2009) and their colleagues conducted a landmark study in which they were able to videotape lessons in grade 8 mathematics classrooms in a variety of countries, including the United States, Taiwan, China, and Japan. Of most interest, given that Japan is by far outstripping the United States in math scores, is the striking difference in the teaching methods used in those two countries. Although there may be many other reasons for the differences in math scores, one highly salient difference is whether or not teachers engage with students’ errors. Videotapes show that, in the United States, set procedures for doing particular kinds of problems are explicitly taught. These correct procedures are rehearsed and emphasized; errors are avoided or ignored. The students are not passive in American classrooms. A teacher may ask for student participation in repeating, for example, a procedure for borrowing when subtracting. When asking a question such as, “Can you subtract 9 from 5?” to prompt students to answer, “No, you have to borrow to make the 5 a 15,” the teacher may fail to even acknowledge the deviant child who says, “Yes. It’s negative 4.” If the response does not fit with the procedure being exercised, it is not reinforced. Errors (as well as deviant correct answers) are neither punished nor discussed but are disregarded. Praise is given, but only for the “correct” answer.

As Stevenson & Stigler (1994) pointed out, praise curtails discussion and serves mainly to reinforce the teacher’s role as the authority who bestows rewards. It does not empower students to think, criticize, reconsider, evaluate, and explore their own thought processes. By way of contrast, in Japan praise is rarely given. There, the norm is extended discussion of errors, including the reasons for them and the ways in which they may seem plausible but nevertheless lead to the incorrect answer, as well as discussion of the route and reasons to the correct answer. Such in-depth discussion of the thought processes underlying both actual and potential errors encourages exploratory approaches by students.

Instead of beginning with teacher-directed classwork and explication, Japanese students first try to solve problems on their own, a process that is likely to be filled with false starts. Only after these (usually failed) attempts by students does teacher-directed discussion — interactively involving students and targeting students’ initial efforts and core mathematical principles — occur. It is expected that students will struggle and make errors, insofar as they rarely have available a fluent procedure that allows them to solve the problems. Nor are students expected to find the process of learning easy. But the time spent struggling on their own to work out a solution is considered a crucial part of the learning process, as is the discussion with the class when it reconvenes to share the methods, to describe the difficulties and pitfalls as well as the insights, and to provide feedback on the principles at stake as well as the solutions.

As Stevenson & Stigler (1994, p. 193) note, “Perhaps because of the strong influence of behavioristic teaching, which says conditions should be arranged so that the learner avoids errors and makes only a reinforceable response, American teachers place little emphasis on the constructive use of errors as a teaching technique. Learning about what is wrong may hasten understanding of why the correct procedures are appropriate, but errors may also be interpreted as failure. And Americans, reluctant to have such interpretations made of their children’s performance, strive to avoid situations where this might happen.”

The Japanese active learning approach well reflects the fundamental ideas of a learning-from-errors approach. Engaging with errors is difficult, but difficulty can be desirable for learning (Bjork 2012). In comparison with approaches that stress error avoidance, making training more challenging by allowing false starts and errors followed by feedback, discussion, and correction may ultimately lead to better and more flexible transfer of skills to later critical situations.

Considerable research now indicates that engagement with errors fosters the secondary benefits of deep discussion of thought processes and exploratory active learning and that the view that the commission of errors hurts learning of the correct response is incorrect. Indeed, many tightly controlled experimental investigations have now shown that in comparison with error-free study, the generation of errors, as long as it is followed by corrective feedback, results in better memory for the correct response.

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Early studies by Izawa (1967, 1970) showed that multiple unsuccessful retrieval attempts led to better memory for the correct feedback than did a procedure producing fewer incorrect responses. Kane & Anderson (1978) showed similar results: Attempting the generation of the last word of the sentence, even if what was generated was wrong, led to enhanced correct performance compared to reading the sentence correctly from the outset. Slamecka & Fevreiski (1983) asked people to remember near antonyms, such as trivial-vital or oscillate-settle. Even failed attempts (followed by feedback containing the correct answer) improved later recall of the correct answers over simply reading the correct answer. Kornell et al. (2015) have conducted a recent investigation of the same issue and have reached similar conclusions.

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It appears that to be beneficial, the guess needs to be somewhat informed rather than a shot in the dark.
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Interestingly, in the related-pair case in which a large beneficial effect of committing errors was found, the participants were metacognitively unaware of the benefit. Even immediately after they had experienced the task and had evidenced a benefit of 20 percent (i.e., roughly the difference between a C-minus and an A, if it had been a course grade), participants thought that the error-free condition had resulted in better recall (Huelser & Metcalfe 2012). This lack of awareness of the benefits of error generation may contribute to the aversion to errors in the American teaching style evinced in Stigler’s work.

Pano Kanelos has left his post as president of St. John’s College in Annapolis (the Great Books school) to build the University of Austin, dedicated to the fearless pursuit of truth.

Arnold Kling wishes them luck, but he doesn’t think that this is how start-ups work:

You don’t begin with a manifesto and a top-heavy board of advisors. You begin with a few very energetic founders trying to put together a prototype. I say get some proof-of-concept work done, then go after endorsements. Yes, it’s hard to do “proof-of-concept” if your mental model is to be a better version of Harvard. But that means you should have a different mental model.

Physics professor Chad Orzel’s child (“SteelyKid”) started school in 2013, which was close to the peak of the freakout over Common Core Math:

The inscrutability of the new standards for elementary school math was an endlessly recurring topic in late-night talk show monologues and frustrated Facebook rants from high-school classmates whose kids are a bit older than mine. Nobody seemed able to understand what was now deemed to be third-grade math, and everybody was pissed about it.

As is often the case with issues touching on STEM in schools, I found this a little puzzling. As SteelyKid started to get into the math curriculum, I thought it was great — not just the endless algorithmic chugging I dimly remembered from my own childhood, but something much closer to actual math. Students were being asked to get answers by multiple methods, check them against each other, and explain how they knew their final answers were right. These are all things I struggle to get college frosh to do in intro physics, and here it was built right into the elementary school math curriculum.

So, on reflection, I guess it’s pretty obvious why everybody else hated it…

Social scientists distinguish between what are known as treatment effects and selection effects:

The Marine Corps, for instance, is largely a treatment-effect institution. It doesn’t have an enormous admissions office grading applicants along four separate dimensions of toughness and intelligence. It’s confident that the experience of undergoing Marine Corps basic training will turn you into a formidable soldier. A modelling agency, by contrast, is a selection-effect institution. You don’t become beautiful by signing up with an agency. You get signed up by an agency because you’re beautiful.

At the heart of the American obsession with the Ivy League is the belief that schools like Harvard provide the social and intellectual equivalent of Marine Corps basic training—that being taught by all those brilliant professors and meeting all those other motivated students and getting a degree with that powerful name on it will confer advantages that no local state university can provide. Fuelling the treatment-effect idea are studies showing that if you take two students with the same S.A.T. scores and grades, one of whom goes to a school like Harvard and one of whom goes to a less selective college, the Ivy Leaguer will make far more money ten or twenty years down the road.

The extraordinary emphasis the Ivy League places on admissions policies, though, makes it seem more like a modelling agency than like the Marine Corps, and, sure enough, the studies based on those two apparently equivalent students turn out to be flawed. How do we know that two students who have the same S.A.T. scores and grades really are equivalent? It’s quite possible that the student who goes to Harvard is more ambitious and energetic and personable than the student who wasn’t let in, and that those same intangibles are what account for his better career success. To assess the effect of the Ivies, it makes more sense to compare the student who got into a top school with the student who got into that same school but chose to go to a less selective one. Three years ago, the economists Alan Krueger and Stacy Dale published just such a study. And they found that when you compare apples and apples the income bonus from selective schools disappears.

“As a hypothetical example, take the University of Pennsylvania and Penn State, which are two schools a lot of students choose between,” Krueger said. “One is Ivy, one is a state school. Penn is much more highly selective. If you compare the students who go to those two schools, the ones who go to Penn have higher incomes. But let’s look at those who got into both types of schools, some of whom chose Penn and some of whom chose Penn State. Within that set it doesn’t seem to matter whether you go to the more selective school. Now, you would think that the more ambitious student is the one who would choose to go to Penn, and the ones choosing to go to Penn State might be a little less confident in their abilities or have a little lower family income, and both of those factors would point to people doing worse later on. But they don’t.”

(I’ve cited Malcolm Gladwell’s Getting In before.)

Bryan Caplan explains his family’s homeschooling Odyssey:

Six years ago, I began homeschooling my elder sons, Aidan and Tristan.  They attended Fairfax County Public Schools for K-6, becoming more disgruntled with every passing year.  Even though they went to an alleged “honors” school for grades 4-6, they were bored out of their minds.  The academic material was too easy and moved far too slowly.  The non-academic material was humiliatingly infantile.  And non-academics — music, dance, chorus, art, poster projects — consumed a majority of their day.  As elementary school graduation approached, my sons were hungry for a change.

So what did we do? In consultation with my pupils, I prepared an ultra-academic curriculum. Hours of math every day. Reading serious books. Writing serious essays. Taking college classes. And mastering bodies of knowledge.

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While my sons’ objective performance and subjective satisfaction in middle school were both sky-high, my wife insisted that they try regular high school. Back in those days, the political brainwashing at FCPS was modest, but the anti-intellectual pedagogical philosophy was already overwhelming. I never liked high school, but at least in my day teachers actually taught their subjects. Not so at FCPS. With the noble exception of their calculus teacher, my sons’ high school teachers just showed videos and treated teens like babies. After three weeks, my wife gave a green light to resume homeschooling.

Silver lining: Since comedy is tragedy plus time, we’ll be laughing about those three weeks of regular high school for the rest of our lives. Yes, a kid in their Spanish class really did raise his hand and say, “Spain’s in… South America, right?”

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I hired an excellent Spanish tutor to give them Spanish five days a week year-round. And I asked their tutor to use the immersion method: ¡No Inglés!

The results were phenomenal. In months, the twins started speaking exclusively Spanish to each other. The wishful thinking of, “You hate it now, but work hard and you’ll come to love it” came true for them.

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In 12th grade, the college application process took over my sons’ lives. While they still prepared themselves for AP Statistics and Physics C: Electricity and Magnetism, filling out applications consumed almost the entire first semester. Despite everything we’d accomplished, I was nervous. The most reliable researchers I cornered told me that discrimination against homeschoolers was now mild, but short of a major lawsuit, how can anyone really find out?

To cope, I gave my sons the same advice I give everyone in this situation: Not only is admission random; funding is random as well. So throw a big pile of dice.

In response, my sons maxed out the Common App, which allows you to apply to up to 20 schools. (They also applied to Georgetown, which stubbornly refuses to join the Common App).

The college application weighed heavily on my students. I raised them to think clearly and speak bluntly. They knew to pull their punches on AP essays, but the whole college admission process is simply drenched in Social Desirability Bias. If you write a personal statement that admits, “I want to attend your school because I need a strong signal to advance my career, and you’re selling the thirteenth-best signal on the market,” you won’t be getting in. This was the one time I had to push them to do their work. Tristan averred that the academic refereeing process (four rounds of revisions!) was easy by comparison. My many pep talks largely fell on deaf ears. Still, they soldiered on, and finally resumed their actual studies. Intellectually, the highlight of their year was probably auditing my Ph.D. Microeconomics class.

Soon, college acceptances started to come in. Once the University of Virginia admitted them to their honors program, I stopped worrying. Johns Hopkins, by far the highest-ranked school in the DC area, took them as well. Then in early February, Vanderbilt offered both of them full merit scholarships. No one else came close to that deal, so that’s where they decided to go. And that’s where they are this very day. (Hi, sons!) If you see Aidan or Tristan on campus, be sure to introduce yourself. They’re not attention hogs like me, but they have much to say about anything of substance, and are hilarious once you put them at ease.

My general read: I think the median school probably did discriminate against my sons for being homeschooled. Their SATs were 99%+, their AP performance was off the charts, they ran an impressive podcast, and they had a refereed history publication. (At many schools, five such pubs would buy an assistant professor tenure!) Yet they were waitlisted by Harvard and Columbia, and rejected by all the lesser Ivies. All public schools accepted them; I don’t know if this stems from lower discrimination or just lower standards. Nevertheless, the net effect of homeschooling was almost certainly highly positive. My sons used their immense educational freedom to go above and beyond, and several top schools were suitably impressed. The critical factor at Vanderbilt, I suspect, was that their faculty, not their admissions committees, hand out academic merit scholarships.

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Yes, they missed their chance to have a normal high school experience. They had something much better instead. At least in their own eyes.