Ten Most Read, Ten You Should Read

Eight years ago, on the second anniversary of my blog, I asked, “Am I a hedgehog or a fox?”  Hilarious, that I could ever be so deluded. I understand why my brain thinks itself a hedgehog, but it will just have to cope with reality.

I am a fox. Even at my lowly level of the word, this is a list only a fox could produce.

Ten Most Read Articles:

1. More than Gotcha: Kamala’s Busing Blunder— June 28, 2019
   The only item past its sell date. Most of my work maintains its relevance. But this article, outdated though it is, has a good number of my strengths on display. First, unlike the entire media class, I know how to search for and use relevant history. No one listening should have thought anything other than “that’s bullshit” when she claimed to have been on the frontlines of segregation in Berkeley, CA. But no journalist bothered to do the research. Next, I understood as no one else seemed to that she was essentially coming out in favor of busing.  At a time when most of the media (and all of Twitter) was wowed, I  pointed out she’d almost certainly have to walk that comment back. The other strength: sometimes I really hate people while many other folks are like, man, why is Ed hating on her and then later they go oh, I get it.
   ignore me, lazy way to space
2. Asian Immigrants and What No One Mentions Aloud–October 8, 2013
   I’ve kind of cornered the market in Asian immigrant criticism–not of the people, but of the culture, which I think is very damaging to American education. I wouldn’t make such a big deal out of it if everyone else weren’t determined not to notice. This was the first time I wrote about it.
   ignore me, lazy way to space
   
3. Functions vs. Equations: f(x) is y and more — May 24, 2015
   A math curriculum piece in third place? Blew me away. But as I mentioned, curriculum searches are specific and get through Google’s recency bias, so they’re the one article category that still gets fed via search engines. I keep meaning to revisit this article because it had a very bimodal reaction. Mathy readers who didn’t teach were aggravated and confused by the article and told me I didn’t understand the math. On the other hand, a number of professors on Twitter understood my point  instantly and were very appreciative (and some later commented as well). I think the mathy folks thought I was confusing a system with a function, whereas the professors understood I was using an example of multiple equations that wasn’t a system to show students a difference they hadn’t seen before.
   ignore me, lazy way to space
4. Homework and grades–February 6, 2012
   I have relatively few strong views about what teachers should do. Homework is the exception. Homework is insane. Grades are fraud.
   ignore me, lazy way to space
5. Algebra and the Pointlessness of The Whole Damn Thing— August 19, 2012
   My first really huge piece, and one I’m still quite fond of. It’s getting harder to find data easily; more states are hiding racial and economic distinctions. But if you look at current data, you’ll see the same pattern: poor whites do about as well as non-poor blacks and Hispanics. Been like that for decades.
   ignore me, lazy way to space
6. Philip Dick, Preschool and Schrödinger’s Cat — April 5, 2013
   Canonical Ed on IQ.
   ignore me, lazy way to space
7. Binomial Multiplication and Factoring Trinomials with The Rectangle— September 14, 2012
   Another curriculum piece. I took a long time to make sure the figures and explanations were thorough. I hope other teachers get good use from it. Still the best way to teach factoring, even if your kids don’t use it.
   ignore me, lazy way to space
8. The myth of “they weren’t ever taught….”— July 1, 2012
   This is one of my favorite pieces. It’s all true, still. Every word. And new teachers have to come to grips with it every year.
   ignore me, lazy way to space
9. The SAT is Corrupt. No One Wants to Know.–December 31, 2014
   I am adamantly opposed to grades-based college admissions. But the College Board is corrupt. The international SAT is corrupt. And they’ve changed it in ways to make it far less useful, all in the hopes of ending the score gap, which was never going to happen.
   ignore me, lazy way to space
10. The Gap in the GRE–January 28, 2012
    Another of my favorite pieces that asks a very good question: why are genuine high achievers in verbal tests so less frequent than in math tests? Note that in the intervening years, the College Board and the ETS have eliminated all the verbal difficulty in the SAT and the GRE.

So there’s my ten most popular.

Then I just looked over all my articles and looked for favorites that also captured my zeitgeist (can people have zeitgeist?). I was particularly looking for self-contained articles–a lot of time I go down one rabbit hole and then get to the main point. (Yes, I’m thinking of those for my rewrite plans.) I also wanted a good sample.

1. Teacher Quality Pseudofacts, Part II–January 15, 2012
   This is a top 20 all-time post and was a steady performer for years. I almost didn’t include it; today it seems kind of old hat. But in fairness, that’s like saying 1933’s 42nd Street is cliché because it uses all the old tropes about movie musicals. It didn’t use them. It invented them. When I wrote this article, it was common wisdom that teachers were low-skilled, low-quality, and not very bright. Only the terminally uninformed, the amateurs and the hacks,  have made that claim in four or five years.  I like to think Pseudofacts has had something to do with that change,  because of the very easily found data I brought to light.
   ignore me, lazy way to space
2. The false god of elementary school test scores–July 30, 2012
   Another one I almost didn’t include because it definitely has the rabbit hole problem about Rocket Ship at the beginning. However, like Pseudofacts, it’s an early example of my actually looking at readily available information and pointing out the obvious. Plus, great title.
   ignore me, lazy way to space
3. The Fallacy at the Heart of All Reform–September 7, 2012
   I wrote a history of modern education reform throughout much of 2020-21. This was a history of earlier policy. But the definition of fallacy I include here holds for the entire era.
   ignore me, lazy way to space
4. The Day of Three Miracles— April 28, 2015
   I don’t often talk about colleagues, mainly because for years my relationship with them was….fraught. Not bad, just…there. But this is not only a colleague story, it captures a conundrum that few people in education policy seem to understand. Access or rigor. Not both.
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5. Citizens, Not Americans— June 16, 2016
   I love this piece. By the way, Dwayne is married, has a kid, and is in the military. Abdul went to a top tier school and majored in pharmacy, and when he told me I want “Gack!” and he said “yeah, I know. Stupid move.” and now he’s getting an MA in nurse practitioner, or whatever it’s called. Haven’t heard from Chuy. Wing and Benny still teach. One of them is now department chair, and I had a lot to do with it.
   ignore me, lazy way to space
6. “Get Out” a scathing satire? Get Out.–January 22, 2018
   I love movies, and I know as much about American diversity as anyone in the country, and I think this is a terrific review that isn’t at all what you’ll expect.
   ignore me, lazy way to space
7. Algebra 2, the Gateway Course–January 28, 2018
   Another story about colleagues, students, and really stupid education policy.
   ignore me, lazy way to space
8. Making Rob Long Uncomfortable–December 24, 2018
   Silly title, but you can listen to the podcast and see what I mean. It’s well-written, and captures a certain mindset among the centrist conservative punditocracy. As I wrote: “You could practically hear Rob’s toenails shrieking against the tiles as he braked to a stop.  This was not the conversation he’d signed up for. He was there to lightly mock feminists and social justice nuts, not crack witty, on-the-nose jokes with Heather about the racial skills deficit.”
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9. The Students of My Christmas Present— December 25, 2018
   I don’t often get sentimental. And I’ve put up Christmas trees most years since.
   ignore me, lazy way to space
10. Idiosyncratic Explanations for Teacher Shortages–May 31, 2019
    Here I raise an issue that seems quite obvious, but isn’t. We have thousands, if not millions, of unemployed PhDs who will never get a tenured job and work as poorly paid adjuncts. Why don’t they become teachers? After all, everyone says we need smarter teachers, right? There’s a cognitive dissonance revealed in the fact that everyone understands that a poorly paid PhD is acting rationally in refusing to take a better-paid, more secure job with great benefits.
    ignore me, lazy way to space
    I thought I was done, but 2017 spoke up, really pissed off. Why nothing? I tried reassurance. It was nothing personal. I wrote some good shit that year. Besides, 2020 and 2021 aren’t represented either. But it would not be assuaged and as my mother isn’t doing well, and this is a not only an ode to American schools but also a lovely story about my mom, an extra…
    ignore me, lazy way to space
11. What the Public Means by “Public Education”–March 19, 2017
    When education reformers wonder why everything went wrong, they should think about the thoughts expressed here.

Thanks for reading.

Five Education Policy Proposals for 2016 Presidential Politics

Every election year, someone bemoans the fact that education is never a major factor in presidential politics. This year might be an exception, because of Common Core. But the reality is, presidential aspirants never talk about the issues that really interest the public at large.

Instead, politicians read from the same Big Book Of Education Shibboleths that pundits do.

To wit: Our public schools are a national disgrace with abysmal international rankings. Our test scores that haven’t budged in 40 years. Unions prevent bad teachers from being fired. Teachers are essential to academic outcomes but they are academically weak and unimpressive, the bottom feeders of college graduates. Administrators are crippled because they can’t fire bad teachers. We know what works in education. Choice will save our country by improving student outcomes. Charters have proven all kids can learn and poverty doesn’t matter. And so on.

All the conventional wisdom I’ve outlined in the previous paragraph is false, or at least complicated by reality. Any education reformer with more than two years experience would certainly agree that the public is mostly unmoved by rhetoric about teacher quality, tenure, curriculum changes, and choice—in fact, when “education reform” is a voting issue, the voters are often going against reform.

Education reformers are very much like Meg Ryan in When Harry Met Sally: All this time I thought he didn’t want to get married. But, the truth is, he didn’t want to marry me.  

Yeah, sorry. Your ideas, reformers, they just don’t do it for the public.

So I put together some policies that a lot of the public would agree with and many would consider important enough to make a voting issue. In each case, the necessary legislation could be introduced at the state or federal level.

There’s a catch, of course. These proposals are nowhere on the horizon. But any serious understanding of these proposals will lead to an understanding of just how very far the acceptable debate is from the reality on the ground.

To understand these proposals, a Reality Primer:

1) Some children cannot learn to the desired standard in an acceptable timeframe or, in the case of high school, in any timeframe.
2) The more rigorous the standard, the greater number of students who will be incapable of learning to that standard.
3) As a result of the first two immutable facts, schools can’t require an unbendable promotion standard.
4) By high school, the range of student understanding in any one classroom is beyond what most outsiders can possibly conceive of.

and somewhat unrelated to the previous four:

5) Education case history suggests that courts care neither about reality or costs.

The primer is important. Read it. Embrace it. In fact, if you read the primer and really get on board, you’ll be able to come up with the proposals all by yourself.

Some additional reading to remind readers of where I’m coming from:

• The Fallacy at the Heart of All Reform
• Not Why This. Just Why Not That
• An Alternative College Admissions System
• Algebra, and the Pointlessness of the Whole Damned Thing
• Jason Richwine, and Goring the Media’s Ox
• Just a Job
• What causes the achievement gap? The Voldemort View

I originally had all the proposals as one huge post, but I’ve been really short on posts lately. Here’s the list as I build it:

1. Ban College-Level Remediation
2. Stop Kneecapping High Schools
3. Repeal IDEA
4. Make K-12 Education Citizen Only
5. End ELL Mandates

Algebra and the Pointlessness of The Whole Damn Thing

The whole algebra debate kicked off by Hacker’s algebra essay has…..well, if not depressed me, then at least enervated me.

A recap:

Hacker:

We shouldn’t make everyone take algebra. No one needs algebra anyway; we never really use it. Statistics would be much more useful. Algebra is the primary obstacle to high school success; millions of kids are failing because they can’t manage this course. If we just allowed students to have an easier time in high school, more of them would graduate successfully and go on to college.

Outraged Opposition:

Algebra is essential to college success and “real life” and one of many obstacles to high school success. No one is happy with the current state of affairs, but it’s clear that kids aren’t learning algebra because their teachers suck, particularly in elementary school. We need to teach math better in the lower grades, rather than lower our standards. Besides, the corollary to “not everyone should take algebra” is “some people should take algebra” and just how are you planning to divide up those teams? (Examples: Dan Willingham, Dropout Nation)

Judicious Analysis:

Sigh. Guys, this is really a debate about tracking, you know? And no one wants to go there. While it’s true that algebra really isn’t necessary for college, colleges use success in advanced math as a convenient sorting mechanism. Besides, once we say algebra isn’t necessary, where do we stop? Literature? Biology? Chemistry? But without doubt, Hacker is right in part. Did I say that no one wants to go there? Or just hint it really, really loudly?
Examples: Dana Goldstein, Justin Baeder Iand II.

Voldemort Support:

Well, of course not everyone should take algebra, trig, or calculus. Or advanced literature. Or science. Not everyone has the cognitive ability or the interest. We should have a richer and more flexible curriculum, allowing anyone with the interest to take whatever classes they like with the understanding that not all choices lead to college and that outcomes probably won’t have the racial distributions we’d all prefer to see. Oh, and while we’re at it, we should be reviewing our immigration policies because it’s pretty clear that our country doesn’t need cheap labor right now.

Hacker, Outraged Opposition and Judicious Analysis to Voldemort Support:

SHUT UP, RACIST!

So really, what else is left to say? The Judicious Analysis essays I linked above were the strongest by far, particularly Justin Baeder II.

Instead, I’m going to revisit a chart I updated from the last time I posted it:

These are California’s math scores by grade and subject, the percentage scoring basic/proficient or higher on the CST. Algebra entry points differ, so the two higher (and slightly longer) of the four short lines are the percentages of “advanced” students with those scores—those who took algebra in 7th or 8th grade. The lower, shortest lines represent the scores of students who began algebra in 9th grade.

Notice that advanced students don’t match the performance of the entire elementary school population through 5th grade. Notice, too, that the percentage of advanced students scoring proficient or higher is just around half of the population. When I just considered algebra students who began in 8th grade (see link above), the percentage never tops 50. Notice that around 40% of the kids who started algebra in 9th grade achieved basic or higher.

NAEP scores show the same thing—4th grade math scores have risen, while 12th grade scores stay flat. In fact, Daniel Willingham, who declares above that we’re doing a bad job at teaching elementary math, was considerably more sanguine about teacher quality back in December, citing the improved elementary school math performance shown in the NAEP. So the strong elementary school performance, coupled with a huge dropoff in advanced math, is not unique to California.

These numbers, on the surface, don’t support the conventional wisdom about math performance: namely, that elementary school teachers need improvement and that the seeds of our students’ failure in higher math starts in the lower grades. Elementary students are doing quite well. It’s only in advanced math, when the teachers are much more knowledgeable, with higher SAT scores and tougher credentialling tests, that student performance starts to decline dramatically.

What these numbers do suggest is that as math gets harder, fewer and fewer students achieve mastery, or anything near it. . What they suggest, really, is that math knowledge doesn’t advance in a linear fashion. Shocking news, I know. We have all forgotten the Great Wisdom of Barbie.

Break it down by race and the percentages vary, but not the pattern. I skipped Asians, because California tracks Asians by subcategory, and life’s too short. I’m going to go right out on a limb and predict that Asians did a bit better than whites.

(Note: I know it’s weird that in all cases, 9th graders in general math have nearly the same percentages as 9th graders in algebra, but it’s easily confirmed: whites, blacks, Hispanics).

Whites in the standard math track perform as well as advanced math blacks and just a bit worse than advanced track Hispanics. Sixty to seventy percent of blacks and Hispanics on the standard track fail to achieve a “basic” score.

Some people are wondering how poverty affects these results, I’m sure. Let’s check.

Hey! Look at that! The achievement gap disappears!

Just kidding. This chart shows the results of blacks and Hispanics who are NOT economically disadvantaged and whites who ARE economically disadvantaged. You can see it on the legend.

So that’s how to make the achievement gap disappear: compare low income whites to middle class or higher blacks and Hispanics and hey, presto.

And that’s all the charts for today. I’m not detail-oriented, and massaged this all in Excel. You can do your own noodling here. Let me know if I made any major errors. The 2012 results should be out in a couple weeks.

Anyway. With numbers like these, it’s hard not to just see this entire debate as insanely pointless. In California, at least, tens of thousands of high school kids are sitting in math classes that they don’t understand, feeling useless, understanding deep in their bones that education has nothing to offer them. Meanwhile, well-meaning people who have never spent an hour of their lives trying to explain advanced math concepts to the lower to middle section of the cognitive scale pontificate about teacher ability, statistics vs. algebra, college for everyone, and other useless fantasies that they are allowed to engage in because until our low performers represent the wide diversity of our country to perfection, no one’s going to ruin a career by pointing out that this a pipe dream. And of course, while they’re engaging in these fantasies, they’ll blame teachers, or poverty, or curriculum, or parents, or the kids, for the fact that their dreams aren’t reality.

If we could just get whites and Asians to do a lot worse, no one would argue about the absurdity of sending everyone to college.

Until then, everyone will divert themselves by engaging in this debate—which, like many kids stuck in the hell of unfair expectations, will go nowhere.

Learning Math

Jessica Lahey’s In Defense of Algebra, in which she describes her adult triumph over math, reminded me of my own experiences learning math and how they might be relevant. This is long, but if I make what I did sound too easy, people will get the wrong idea.

I struggled in math during high school, but was simply too clueless to quit. I got As and Bs algebra in 8th grade, got Cs and Ds in the subsequent courses until senior year, when I held onto a B the entire year in AP Calculus and, in what remains one of the great academic shockers of my life, passed the AP Calc test with a 3. Many years later, I took the GRE for my first master’s. I spent a month slogging through math, relearning enough of it to get by, and was very pleased with my 650 quant score, which was the 65th percentile on the GRE. Good, but not great, which is pretty much how I did on the SAT many years earlier. (Verbal, which I spent no time on, was 790).

My math turnaround began after I started grad school, when my son was failing geometry. After reading his book and working dozens of problems, I was able to help him (he went on to pass both the AP Stats and Calc AB tests, and is stronger in college math than I am). Needing a part time job for grad school, I auditioned for a job at Kaplan.

I originally hired on to teach GRE classes, but within a month I was working close to 40 hours a week teaching the high school tests. Two months later, I was teaching Math 1c and Math 2c, which was ridiculous. I had to learn the SAT math by rote at first, and the SAT Subject math tests required trig and second year algebra. I protested to no avail, and my manager’s decision was prescient—within a few months, parents were emailing me for private homework tutoring in high school math. It turns out I’m very good at explaining things; when I didn’t know how to do a problem in the early days, which was often, I’d go look it up or ask a student who did understand the problem. Ah, that’s the part I missed! Anyone else do that? I could see students nodding. I made the process very transparent, showed students where the glitches in my comprehension were, helped them find their own glitches and, it turns out, students would rather be tutored by someone who knows where the understanding glitches are.

I told parents I didn’t have a clue what a log was if it wasn’t in an Ingalls story, but even after raising my rates as an attempt to scare them off, I was getting lots of work. Still, for my own peace of mind, I decided I needed to learn more math instead of literally learning it while teaching others.

I started with test math, my strength. The REA and Kaplan test prep books served as my educational foundation. Between the two books, I learned how to recognize the subject and how to solve a number of common problems. When I was tutoring students, I would recognize the type of problem it was. Then, using their textbook, I’d help them work problems by example and explain. In explaining the math, I learned a great deal. My students learned and got improved grades, more confidence, and better test scores. Me, I kept getting more clients.

After four years of this, I had an excellent understanding of high school math through pre-calc, and routinely scored 800 when taking practice Math 2c tests (which I did for the first few years to keep me alert to weak spots). I not only knew the material cold, for the most part, but was by this point extremely familiar with the curriculum and sequencing for pre-algebra through algebra II/trig, and somewhat familiar with the same for math analysis (pre-calc) and calculus.

Seven years after my first GRE and untold decades after high school, I aced two of the three teacher math credential tests, and passed the third, in calc, with what can be called a gentleman’s C—the conceptual questions, the trig and the math history questions pulled me through. I scheduled my ed school GRE with two days’ lead, and got an 800 on the quant—by that time I was getting 800s on the practice test without a pencil, sitting around the Kaplan office with 15 minutes to kill. (Verbal: 780, but I was distracted and finished in 12 minutes.)

As I was studying for the calc credential test (which I took twice), I suddenly had an epiphany about why I was now able to learn math, when I’d done so poorly in high school, and for this, boys and girls, I must go back even further, back to the dark old ages of the mainframe and the earliest days of my previous career:

I was unfocused after college, having done well in English lit classes and nothing else. I started as a data entry clerk, but got a contract at IBM using a mainframe product that everyone in its customer base hated, but had to use. While entering the data, I noticed a few short cuts, asked for a manual, and began customizing the product in ways very few people knew was possible. The boss was impressed and made me responsible for product demonstrations, showing my work and explaining how the product could be customized. I got a job from one of the companies that came to the demo, a major brokerage firm. It was my first real job after five years of temping in admin jobs, during and after college. (Irony alert: I’d taken, and nearly flunked, one computer programming course in college and was convinced it wasn’t the career for me. I was three years into my new job before I felt comfortable saying I was an applications programmer, much less a computer programmer.)

And the first day I got to my new job, my boss said to me, “So I need to put you on a different project first. Our systems management application needs to be installed on the NYC machine.We have this automated process that moves the source code out of Panvalet, automatically builds the compile JCL based on the program—you know, if it’s CICS or batch, IDMS or DB2, and so on, and compiles it, linkrefs it, and installs it in the right library. It’s already working here; you just need to transfer all the code, change the libraries, and so on. You know CICS, right?”

“No.”

“Oh, it’s a transaction server environment. We mostly use COBOL here, but we’ve got some assembler routines. You know COBOL or assembler? No problem, I’ll sign you up for a class. The code itself is mostly ISPF calls with EXEC, although I’d like to upgrade to REXX.”

It’s not just that I didn’t know COBOL, and had no idea what CICS was. It’s that I didn’t know what compile meant, or source code, or batch, or JCL, much less IDMS or DB2. And I didn’t have the foggiest clue what REXX or EXEC was, and ISPF to me was an application, not something I programmed with.

Baby, I brought that motherf***er in on time. Two and a half months. I got a bonus, too, because by the time it went live, my director had figured out a small fraction of how much I didn’t know, and was extremely impressed. She never grasped the sum total of my ignorance, thank god. Nor did she ever realize that I still didn’t know what the difference between CICS and batch was and didn’t realize that (at the time) a program couldn’t be both, only vaguely understood that “compile” meant translating code I could read into weird symbols I couldn’t read but presumably the computer could, never did learn COBOL, and only vaguely understood what JCL was or what it did. All that was in my future. The only thing I was pretty confident about after those two and a half months was that I was pretty darn good at EXEC and ISPF dialogs, and that these things weren’t what the brokerage products ran on.

So my epiphany was this: Working with computers had taught me how I learned. How I learned. Which was not like most people. When books don’t work as a learning tool, then I have to learn by a particular type of doing. Explanations won’t help. Learning in a vacuum won’t help. I need to learn by trial and error. And then, I learn like Wile E. Coyote traverses the desert; I just keep on going until something blows up in my face. Go this way? Boom! Okay, that way doesn’t work. File it away. Go that way? Two steps, yes, then BOOM! Okay, the two steps, file away, then don’t go that way because BOOM! how about this way? Tiptoe, tiptoe, try this, ha! It worked! Done. On to the next. Make sense of the chaos, bit by bit, understanding the rules by the reaction.

When I’m learning something, I neither know nor care about why. Understanding will usually come. So just as I ultimately understood CICS only several months after I started making changes to a mission critical CICS transaction, I didn’t bother with understanding what, exactly, trigonometry was. Two years after I first learned how to work trig problems, I read that trigonometry was the study of the ratio of right triangle sides, and I was like Holy Crap, that’s exactly what trig is. What a trip. One day soon I’ll internalize the fundamental theorem of algebra, but give me time. If not, I’ll wave the dead chicken over the problem because that’s what worked the last time. And it usually works again. (Note: Ironically, as a math teacher, I am big on explaining why, but that’s because I’ve realized that most people aren’t like me.)

Of course, theory, whether it be math or computers, is usually beyond me. And yet, in both math and computers, I am capable of occasional insights that please actual mathematicians and computer scientists, even though most of the time I don’t care, as they are working on things that I find utterly incomprehensible.

Why did I struggle with math in high school? The usual reasons don’t apply. I was an A student, and remained one in English and history. Unlike Jessica, I never felt labelled, nor did I give up. I had excellent math teachers, all of whom knew that my intellect was considerable and took the time to reach out—each one sat me down at some point and asked why I wasn’t doing better, given my obvious brains.

I just know that some people are going to read my post, as they read Jessica Lahey’s, and conclude that, by golly, we prove that anyone can learn math, and that labelling kids based on early progress is cruel and wrong and demoralizing. Lahey herself clearly holds this position.

Well, no. Lahey and I are both extremely bright and I know I say this a lot, but that’s because people persist in ignoring the relationship between “smart” and “academic achievement”. Lahey clearly has excellent verbal skills, strong at writing and foreign language (she’s a Latin teacher at an elite middle school), whereas I’m a hybrid who, in addition to excellent verbal skills, tested high on every computer aptitude test that came out back when I was in college. On the other hand, I can’t speak any foreign languages, and I suspect Lahey isn’t as strong on logic and pattern recognition, which is why she needed an algebra teacher to get through first year algebra, whereas I self-taught myself the entire high school curriculum.

What Lahey and I both demonstrate is that it’s possible to be well above average in smarts, yet still struggle in math when later experience proves that we were entirely capable of grasping it.

Why, then, does an otherwise smart person struggle with math?

I have a theory, involving my layman’s understanding of IQ, which I’ll go into briefly.

Two visual aids to categorizing or measuring intelligence: Wechsler Adult Intelligence Scale subscores and subtests and Cattell-Horn-Carroll theory. In both, you can see what most people know on a casual level: intelligence has a verbal component and a visual/spatial component (known as performance in Wechsler). Logic seems to cut across the categories. It’s not terribly controversial to point out that advanced math, even that found in high school, requires more visual spatial and logic ability. I don’t know, specifically, how my intelligence maps to these categories. But I’ve always known that my verbal abilities were very high, my pattern recognition and decision processing equally so, and my visual-spatial relatively weak.

Imagine smart kids who has really strong verbal skills but unknown weaknesses in either logic or visual spatial abilities. These kids would coast easily through elementary school, where the skills needed are almost exclusively verbal—reading and arithmetic. By the end of of 8th grade, they’re bored out of their minds. Most of elementary school is time spent teaching them things they already know and developing social skills.

So for 8 years, this type of smart kid hadn’t ever had to struggle to learn something—in fact, learning itself is pretty alien to smart kids. (This, parents of smart kids, is why you should make sure your kids have to struggle with something—cooking, art, horseback riding, making nice with other people, whatever.)

And then, math. Algebra and beyond can come as a big shock. When school has come easily all your life, it’s hard to even know what “learning” is, much less how it applies to you. I’ve talked to countless people who qualify as Really, Really Smart, and every one of them has agreed that at some point in their lives, they realized that they had no idea how to learn. Some figured it out in high school or college. Some, like me, didn’t figure it out until they got a job that required them to learn something. Others, like Lahey, had access to a math teacher and went back and learned it because they wanted to fill in a gap that they felt was necessary for parenting.

So the otherwise smart kids who struggled with math did so in part because their particular intelligence was strong on verbal, and lighter on the spatial and (probably) visualization skills that are helpful in math. Plus, math was, to quote the Great Barbie, tough. And these kids had never once faced “tough” in a school subject. Many folded.

This was particularly true in the era before we began demanding higher math of all students (say about a decade or fifteen years ago). Before the 90s, math teachers weren’t held responsible for their students’ failures, and we accepted that not everyone was “good at math”. Kids with strong verbal abilities just took less math—in those days, it didn’t end your hopes of college, even of elite college. It was quite normal to get into an excellent school with a strong performance in history or English with little more than second year algebra on a transcript.

Today, of course, any white or Asian kid who wants to go to an elite college has to have advanced math, so the smart verbal kids who don’t have the requisite math skills have a much stronger incentive to either compensate or fake it, with or without a tutor. Moreover, math teachers these days are far more likely to reward effort over ability, so it’s easier for a student to get As in math by religiously doing homework and extra credit, even if they do poorly on tests. And of course, math teachers are also less likely to dismiss the effort involved in teaching math to those who aren’t necessarily strong in the subject. Thus, for many reasons, smart kids today with primarily verbal skills are less likely to have given up on math and are at least willing to fake it. Many learn to compensate, as I did much later in life, by using their other cognitive abilities to make up for their relative weakness.

(Compensation: Picture a circle inscribed in a square. Can you estimate the ratio of the circle’s area to the square’s? Or would you, like me, be completely incapable of a reliable guess and so calculate the difference by creating a radius of length r and work it as an algebra problem? I contend that people who can make an accurate estimate and do the algebra have an easier time in math than the people who can only do it with the algebra.)

Back in the day, the kids whose intelligence was strong in the math aspects but weak in verbal got a similar shock when they were expected to write an analytical essay on Hamlet and offer some original insights. Unfortunately, as has been noted before, our history and English curriculum has never recovered from the dumbing down it suffered through in the interests of multi-culti, giving kids who are strong at math little reason to ever struggle to access their verbal abilities.

This has obvious implications for the big algebra controversy kicked off by Hacker. But it involves recognizing that underlying cognitive ability is a huge determinant when deciding who should, or perhaps shouldn’t, take algebra.