Apr 15, 2021 • 17M

On Common Core Math, Individual Variation, and Things You Can't Teach

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Note: I’m trying out audio narration for at least a few articles to see how much value people get out of it, but it takes a fair amount of time to do. Please don’t be shy with the feedback if it’s something you use - feedback helps.

Isaac Asimov’s Dreaming Is a Private Thing is a short story about a sort of VR tech where the superior daydreams of talented imaginers called Dreamers are piped directly to the brains of less gifted viewers as a form of entertainment. The story’s focus is Jesse Weill, a non-dreaming producer of this kind of media; he’s the sort of talent-wrangling executive who makes things happen behind the scenes.

One of his Weill’s responsibilities is identifying children with the potential to be Dreamers, and at some point in the story he is confronted by the father of one such prospect, who has been guaranteed intense training for the boy by one of Weill’s competitors:

Weill sighed. "Mr. Slutsky, I don't like to talk against a competitor. If they say they'll guarantee training, they'll do as they say, but they can't make a boy a dreamer if he hasn't got it in him, training or not. If they take a plain boy without the proper talent and put him through a development course, they'll ruin him. A dreamer he won't be, that I guarantee you. And a normal human being he won't be, either. Don't take the chance of doing it to your son.

Dreaming is one of Asimov’s best short stories, and I think about this particular quote often because it overlaps with something I believe to be true: not every skill can be taught to every kind of person, and sometimes it’s harmful to try.

As a for-instance, think of sales. Here I’m talking specifically about what’s called hard selling, where a person has a pitch and a short time frame to either make the sale or not (think: door-to-door vacuum salesmen or telemarketers). This is as opposed to soft sales, which focus on building a relationship over time (think: a sales rep servicing corporate accounts at a chemical supplier).

Soft salesmen come in a variety of personality shapes and sizes, but if you spend enough time around hard salespeople, you come to notice they are a pretty specific personality type: usually very motivated, grindy, high-energy people with a exceptionally high ability to read social cues and react to them. Really good salespeople often couple that high level of people-reading empathy with a lack of other kinds of empathy, essentially knowing how you feel but not caring much about it beyond how it applies to their ability to close the sale.

There’s a whole industry of books and paid lectures dedicated to taking people from the opposite personality type and training them up, to converting timid people to real-deal closers. You can drop hundreds of dollars to go to a conference where speaker after speaker pushes sales states-of-mind and techniques on salespeople and bookish librarian-types alike. The salespeople leave hyped and maybe have a few new techniques to try; the librarians leave… pretty much the same guys.

More time doesn’t help; I’ve seen people try to train these guys up in sales environments, giving them pitches, rebuttals, roadmaps to success, etc. and they do get better, but it just doesn’t make enough of a difference to make them effective. There’s exceptions to the rule - I’ve seen a few timid people brute force their way through and be successful, but just a few. It’s something that for the most part you either have or you don’t.

Or we could talk about actors. If you’ve been around community theater long enough, you’ve noticed that occasionally someone is just great; they aren’t perfect or refined but they “get it” on a fundamental level. The opposite person also exists - so clearly bad you know they are missing some important self-awareness component that would allow them to be good - they can see good acting on a screen or stage and recognize it as such but they can’t map it onto their own actions.

I’ve asked committed and professional acting-teacher friends about this and they generally relate that they can make any actor better, perhaps making a good actor great or a terrible actor tolerable. What they can’t usually do is make a bad actor great, even if that actor is dedicated and hard-working. They are improving people within a limited spectrum, a range determined in part by elements of personality and self-awareness that aren’t necessarily changeable.

Or think about writing - especially the parts of writing that fall under the “prose” classification. I know a lot of people who are smarter and better educated than me who just can’t write. They know more about sentence structure and grammar than I do; they’d whup my ass hard in a proofreading competition. They’ve had the English classes and have read the relevant creative writing books. Some of them have practiced writing to a much greater extent, time-wise, than I have. But it doesn’t take. There’s something missing that keeps them from anything more interesting to read than very short, spare declarative sentences, something that a dozen college classes on the subject didn’t and couldn’t fix. (Note: Nick from the RC Proofreader Death Corps would like me to clarify that I’m not talking about him and that he writes just fine.)

None of this of course means that everyone who is currently not-great at something is that way because they are constitutionally incapable of improving. I’m sure a lot of people really do just lack for practice; if you want to do something, try. Heck, even do it if you are bad at it - the whole fun of community theater as mentioned above is that nobody is a professional, and everyone is just showing up to do something they like for the kind of person who likes to watch people try their best. But that doesn’t erase the part where not everyone can excel at the things they’d like to be great at. In the case of theater or writing, training them at least does no harm; in the case of trying to shoehorn a non-sales person into a sales job, it can do a little more but it’s still not necessarily a life and death thing - we’ve all had a job that was a bad fit.

These are all imperfect examples, but they roughly circle around what I want to talk about. Sometimes we have an impulse to think that equal training will get everyone to an equal place as if everyone’s capabilities and skillsets were the same - we see this in our high school system being conspicuously devoid of trade-school alternatives, or when we suggest that a bunch of out-of-work coal miners and factory workers should learn to code. This refusal to look at people as different from each other (sometimes in fundamental, limiting ways) isn’t just unrealistic. In some situations, it’s harmful.


Super-long intro aside, this article is about Common Core math. I’m about ten years too late to the party to pretend to be the first to notice that it appears crazy. To anyone who grew up with the conventional old ways of doing work it does tend tolook insane, but in case anybody needs getting caught up, the meme representations of common core are usually something like this:

Or here, more conspiratorially:

2.3 Common Core Math is Insane

Or here, with a bat-shit-crazy Chick Tract-level illustration that feels mildly racist in a way I can’t adequately explain:

Parents' frustrations with Common Core math: It's insane

That last example is long division, if you can’t tell.

I’ll start by defending Common Core a little bit, which seems fair because I’m going to go after it pretty hard later. Yes, it looks crazy to anyone brought up on more “conventional” math. But that would be necessary of any significantly new method for teaching math - if it’s different enough to matter, it’s going to look drastically different than the rote algorithms we are used to. And since new things aren’t by default bad, you can’t blame them for that in an honest, fair way.

Moving on from that, we have to then look at the substance of what they are trying to do. Common Core people trying to explain the advantages Common Core offers often use the term “number sense”. What they are trying to give a child, they say, is a more intuitive understanding of numbers and how math works, so that the child gets something beyond rote-step following and learns to understand the “why” of how a math problem works.

To understand how they try to do this, think of it this way: what’s 20 * 11? You probably got to the answer really quickly by breaking it down to something like (20 * 10) + 20, which is easier. 25*25 becomes (25 *20) + (25 * 5). These are shortcuts; they are the kind of little tricks reasonably intelligent people develop themselves after spending enough time with the old-style rote math algorithms.

Common Core is the result of developing new teaching techniques after looking at kids with this kind high-comfort-level manipulation. Specifically, it’s what you come up with if you assume those techniques are the cause of being good at rote math algorithms, as opposed to being something that flow out of it.

This left friendly idealistic everyone-can-use-smart-kid-methods line of thought is explained here by Vox, who predictably loves the hell out of it:

Even though you can already tell I don’t really buy the philosophy behind common core, I want to stress that it would be absolutely fabulous if we look and find it works - we’d expect to see a bunch of kids who have an intuitive grasp of math that really would move us one step closer to the everyone-in-STEM Andrew Yang utopia that a certain sector of America dreams about. Luckily, we are now far enough past the implementation of Common Core to answer that Laconic If. Unluckily, it doesn’t look great.

In deciding how critically and closely I need to examine something, I end up using a particular rule of thumb a lot: If there are very few studies available on an issue where you’d expect to see tons of research and discussion, something is probably up. This is doubly true when the field is dominated by a particular political ideology (education: check!) and where studies might disprove a preferred view of that ideology (any difference in outcomes is primarily due to to some government-changeable force external to the student: check!).

So when there’s really only one recent review that itself only can find a few studies actually looking at student outcomes, a suspicious person already knows what’s coming. The study does its best to obscure what’s coming next, first by spending a huge amount of time talking about Bill and Melinda Gates Foundation studies (Common Core is Bill and Melinda’s baby, for reference) of how teachers feel common core is going:

Teachers also reported positive changes in student learning. Even though the CCSS was not fully implemented until the 2013–2014 school year in many states, over half (53%) of the teachers in CCSS adopting states reported in 2014 that they had already seen a positive change in their students’ ability to think critically and use reasoning skills as a results of CCSS implementation, and an even higher percentage (68%) of the teachers in schools where CCSS implementation was fully complete in 2012–13 or earlier reported the same (Scholastic and the Bill & Melinda Gates Foundation, 2014).

Eventually, the authors run out of excuses and get around to talking about their findings on actual student performance:

This paper presents findings about the effects of states’ implementation of the new CCR standards on student achievement as measured by NAEP. Contrary to our expectation, we found that the CCR standards had significant negative effects on 4th graders’ reading achievement during the 7 years after the adoption of the new standards, and had a significant negative effect on 8th graders’ math achievement 7 years after adoption based on analyses of NAEP composite scores. The size of these negative effects, however, was generally small, ranging from -0.10 to -0.06 SDs.

Note here that things are getting worse over time; the authors measured at 1, 3, 5 and 7 years after implementation; each measurement is worse than the last. Making things worse in a way the authors don’t acknowledge is this tidbit:

For states that adopted the CCR standards in 2010, almost half of the states were still in their first year of full implementation when they participated in the 2015 NAEP assessments—5 years after adopting the new standards. Thus, findings from this study largely reflect early effects of states’ implementation of the CCR Standards during the transition period, which may be different from the effects after the new standards became fully implemented.

The authors admirably take the exact wrong lesson from this. Since this is from a section headed by “There are a number of potential reasons for the lack of positive effects that we had hoped to find in this study”, they are using data indicating Common Core caused more harm the more fully implemented it was to say something that boils down to “yes, our own analysis shows this is harmful - it’s a shame it didn’t have more time to work, since we all know eventually it must end up being a good thing”.

The authors are right when they say the effect is small, so this doesn’t really prove Common Core is the worst. But “I guess we don’t have proof it’s hurting people much yet” isn’t really the best thing to hear about an expensive new program.


I don’t really blame Common Core proponents for the type of thinking they did, at least when judging it completely within the mental acceptable-thought ecosystem they’ve built for themselves. If you are absolutely dedicated to the thought that everybody should be in STEM and firmly believe that all student-to-student differences must be the result of things you can fix, the logical solution is to find boxes successful student A ticked that successful student B didn’t, and make them tick the same boxes.

The danger, such as it is, comes around when you won’t believe or even acknowledge the possibility of things outside of that ecosystem. So while “normal” people mostly understand that not everyone should be in STEM and that most people don’t need much past long division in terms of math knowledge to make their way through the world, these guys are stuck.

They need every student to have a deep, non-rote understanding of how math works; they can’t be engineers without it. They need it to be true that math-successful kids’ “math sense” is causing their success rather than stemming from it, because to believe otherwise would mean that some kids can’t be forced to like and excel at math by the kind of interventions the government has plausible access to. And this is even before we get into the Kendi-believer set. Even though I’m talking about individual variation here, to them the suggestion that causes of variation in individual outcome exist beyond the control of policy and resource allocation is racist on its face.

Believe it or not, I’m actually not hostile to things like Common Core; I think there must be better ways to teach that can be discovered and used and that this room for improvement implies an obligation to try to find them. But we can only do that one of two ways. We can approach the search for solutions with an open mind that takes into account individual variation in capability and tastes, the limitation of government action and the importance of resources. Or we could instead allow preferred-reality biases to set the limits on our available options, but that limits our successes to broken-clocks-are-right-twice-a-day scenarios.

“Cheap” forms of experimentation do exist (see: charter schools) but they are subject to the normal limitations - it’s easy to dismiss an experiment that works at one or two schools as an outlier or an intentional manipulation of data. National-level tests like Common Core enjoyed are at least somewhat proof against those weaknesses, but are expensive enough that opportunities for them are rare. I think it’s fair to argue that if the current evidence of Common Core’s failure holds up, we wasted our opportunity this round. Worse, if we wasted it we did so because we let the way we wish the world was color our understanding of how the world might actually be. This is important. Let’s not waste our next chance.