Heroic of Kelsey not to go for the obvious quip "Freddie complains that some kids can't be expected to read, and evidentially Freddie can't be expected to read where I specifically said that we are talking about top students incoming as freshman to California colleges".
Not just California colleges. We are talking about a flagship UC campus that is known for its STEM work. We are not even talking about lower tier Cal State system schools, I would expect UCSD admissions to be somewhat competitive even in state, especially given location + academic reputation.
Not just "Cal" schools. The pool that Cal universities fish in, isn't very impressive compared to the nation as a whole.
Virtually every non-selective college and university in the nation has large, well funded remedial reading and math programs struggling to yank incoming freshpeople up to grade. It's no surprise that Cal schools do likewise.
He says he’s a Marxist. It’s not hidden. Shorter Cult of Smart: these problems are intractable until we have a communist revolution. How the future communist society is to be organized to produce goods and services is not specified, and he resents it when people ask.
He blocked me when I pointed out how ironic it was that he was complaining bitterly that Substack had invented Notes since he is one of its most prolific users and profits from using it financially.
Honestly maybe it’s best just not to engage with Freddie about this anymore. I don’t think he’s doing it in bad faith - he absolutely 100% believes what he’s saying - but as you note in your piece, he says the same things over and over.
It doesn’t matter what kind of point you’re trying to make. To him, everything is explained by “some kids are just dumb,” and he won’t be satisfied until we accept this and stop trying to teach them.
This is The Argument we're talking about - engaging with people who are demonstrably wrong (and, ahem, making the argument) is basically this magazine's founding principle!
Great article and very much agreed. Freddie is right that if everyone got a great education there would still be differences based on innate ability, but he's dead wrong that we are already providing everyone a great education.
Looking at NEAP test scores where only 30% of kids score proficient at reading it's quite clear that we have a LONG ways to go.
I generally appreciate Freddie deBoer's writing and I believe Ms. Piper's charitable interpretation of his motives is correct: he's trying to combat an actual defect in what he sees as the dominant educational ideology. But everything Ms. Piper writes here concerning the oversimplification of deBoer's arguments seems right to me.
But I want to focus on the positive implications of one of Ms. Piper's points, concerning learning multiplication tables, a process others who have commented describe well as training "automaticity." The underlying issue here seems to me to be the value of rote learning and ways it might in some ways level the educational playing field.
In some other cultures (I'm thinking of East Asian cultures, with which I have some experience) there is a very strong reliance on rote learning in pre-college education. This is a cultural inheritance that Westerners sometimes view as stifling -- the amount of rote learning can be truly astounding (and in traditional times it would approximate memorization of the textual equivalent of, say, the Hebrew Bible). What such extensive memorization stifles tends to be creativity and originality. But it can also provide certain tremendous benefits, the ability to memorize prodigiously being an obvious factor, but also the ability to "know" what other people have to reason to or look up. To use the multiplication tables as an example, it is the difference between being able to *calculate* 12x11=132 and *knowing* that 12x11=132. Not just in math but in all school skill areas, rote learning (and its result, "automaticity") is essential to efficient practice.
When we learn our native language adults require that we do prodigious amounts of rote learning. They do not generally give us phonetic rules and grammatical templates, they encourage us to imitate, over and over. Kids who are eighteen months to about three or four have wonderfully plastic neural capacities and the complex templates laid down through imitation shape the developing brain. By the ages of 3-4 kids are able to convey complex thoughts through language without hesitation: it's automatic. In this sort of context, rote learning doesn't stifle creative expression, it enables it.
Early use of rote learning for reading, arithmetic, geography, historical narratives, etc., if not stressed to the point of devaluing creative thinking and analytic practice, provides a basic toolkit that I believe kids with most levels of intelligence can benefit from, and raises the floor for kids whose natural aptitude for complex thinking may not be strong (and who may most benefit from an increased ability to memorize per se).
I think one of the problems of contemporary education, especially as technology has increasingly allowed us to access "prosthetic memory" instead of our own at a relatively low cost in time and effort, has been the devaluation of rote learning. And I'd speculate that the students most disadvantaged in this would likely be those who either through intrinsic gifts or family/social environments find it harder to do well in school.
I remember an anecdote which I cannot place at the moment, about a group of programmers who had worked in a high security environment where they could not use internet resources like StackOverflow, and so they had to memorize not just the mechanics but the APIs for everything they were writing.
They had become strangely effective programmers, able to bring loops which previously had gone out to the internet and back directly into their own heads.
This has inspired me to make flash cards to memorize things. I would usually look up. One thing that LLMs are excellent for is generating flash cards.
My kid (8, in 2nd grade) cried at night being asked to add 25 plus 25 in a word problem and asked, can't I just do my best? He expected to be able to guess.
Is he just dumb ? No, he was IQ tested at school and was 98% percentile in a couple of categories, notably visual spatial, so we showed him to count larger numbers on your fingers and use coins. With tangible options, he got it ASAP.
Poor instruction plus lots of iPad learning is a disservice. And he goes to a blue ribbon school in a well funded district!
Thank you - I think it's from using apps like iReady where you can guess and just finish without doing tangible work. Math is something you often have to work on, and he's the kind of smart kid who doesn't like things he isn't instantly good at. It's important to learn perseverance, so if school isn't teaching math effectively, I'll have him do an outside program, but I don't think I should have to do that!
I'm exactly that kind of former gifted kid; It took a lot to shift the mindset from smart being something I was inherently born with to a muscle that you have to work.
It may or may not land for your kid, but the idea that being smart just means that you learn more you the same amount of work, not that you Just Know More, really helped me.
That, and practicing persevering through problems I couldn't solve quickly. I did Art of Problem Solving, but I'm sure there's something suitable for every level. The point for me was to practice sticking with it.
There’s one thought people sometimes have, that all kids have the same abilities, and all different outcomes must be the result of different teaching methods. This is wrong, but it’s a natural thought to come to.
Freddie seems to have come to the opposite conclusion, that all teaching methods are equally effective, and all different outcomes must be the result of differences in abilities of the kids. This is also wrong.
When we see different outcomes, they are the result of some interaction of the innate factors and the teaching methods (and presumably various other external factors, like household nutrition and the availability of short format addictive video). Population level variability in outcomes is the result of population level variability in these factors. I don’t believe that the population level distribution of innate ability is that different between 2020s Mississippi and 1990s California (or 1660s Germany for that matter), so I think a large part of the different in outcomes of how many people learn algebra and calculus in these times and places must be the result of variation in instruction. (I expect everyone will agree with me that the reason why not a single teenager in 1660s Germany knew calculus is somehow related to the fact that no one had come up with a way to teach calculus yet.)
This article is definitely why I’m subscribing to the Argument! I have enjoyed almost all of Kelsey’s articles but this one and the original really hit home. I was not a natural at math and without some great teachers and a tutor for a Dad I probably would have given up.
Reading about the curriculum and expectations for students these days is scary but I’d rather have this information now than discover it when my kids are in middle school.
I agree the some kids are just dumb argument is just tone deft isn’t the point of teaching developing skills in all students?
Some kids probably shouldn’t take higher level English or math classes but that doesn’t mean every kid shouldn’t be given the same high level instruction.
There's an excellent model for learning that Justin Skycak writes about in "The Math Academy Way"; you learn a skill by practicing it until it's automatic, and once that happens, you can start practicing skills which rely on it. If something seems like it's too hard for you, it's because your foundations are weak, and you need to practice them.
The concept is "automaticity"; here's a worked example using "compute 4³" as an example.
Here, innate ability solely shows up as how much effort or how many examples it takes to achieve that automaticity.
This is unpopular for a lot of reasons; it's hard to evaluate kids at this granularity, this involves doing a lot of hard work that you can't just take the royal road to avoid, most people have weak foundations somewhere and it's hard on the ego, etc. But if you manage to do it, you can get very, very strong.
Seems like Freddie is trying to jam the square peg of the "there will always be differing levels of academic proficiency" retort into the round hole of "we are not allowing scores of students to reach their academic potential" problem. His dismissal has no answer to the fact that the *highest performing* students are now doing *worse* on exams, a glaring problem that has nothing to do with achievement gaps between students.
It's too bad, because his work on education is, I believe, a valuable contribution to discourse and policymaking, but if he wants to be taken seriously he's eventually going to have to engage with ideas that don't relate to trying to close achievement gaps.
Continually hammering that students have different levels of innate ability tells us nothing about best practices in terms of pedagogy, grading, sorting, etc. There are extremely important concepts in education policy that I'd genuinely like him to weigh in on!
" His dismissal has no answer to the fact that the *highest performing* students are now doing *worse* on exams, a glaring problem that has nothing to do with achievement gaps between students."
I agree that not teaching multiplication facts to automaticity is a policy choice.
We absolutely know how to do it, and absolutely can. It just feels icky to a lot of people, so we don’t mandate it.
I would say there are additional reasons why students may not be adequately taught in math, though.
Sometimes the teacher is great, but the student is absent too much.
Sometimes the teacher knows the math, but student behavior is allowed to grind learning to a halt by discipline policies that prioritize anything but learning.
Sometimes the math teacher is doing a great job, but takes a job in another field that pays more, because they are a rational human being with bills to pay and talents to offer.
But yeah, this is a fixable problem and we need some societal urgency behind it.
This is a fantastic post of course. But I'd like to push you a little harder on this Kelsey: I think you're eliding the question of what exactly the purpose is of teaching these kids who _can but don't_ learn algebra. Freddie propped up a strawman: the purpose, he claims, is putatively so that they can all go to Stanford and work at Google; this is impossible, hence we shouldn't bother teaching them.
So what is that purpose? There are several perfectly reasonable answers here, but all of them depend on some assumptions and are contingent on the specific child or the way specific skills theoretically add value in industry. Rather than spelling them out myself, I'd really like to hear your answer to the following question: why should we invest heavily into teaching a child in the bottom 20th percentile of the innate math talent distribution algebra? Suppose they can learn it (I certainly grant that they can): at what point does the cost outweigh the benefit?
(To reiterate, one answer can be: "never, every child is entitled to learn algebra, and it is universally edifying. You'd never ask a Muslim where the cost-benefit mid-point is for teaching kids Qur'an - similarly you shouldn't ask where the mid-point is for algebra.")
I think it improves peoples' lives to be able to navigate situations like "the apartment complex is offering two months' rent free if you sign a lease; what's the true rent over the next year?" or "Uber pays $15/hour but I'm spending an extra $80 week on gas, is it worth it?" and that even people who are pretty low innate aptitude should learn enough math that they're competent to answer these questions for themselves. I'm fine with not pushing further than that if a kid is experiencing a really shitty return on their efforts, but I think the above are just skills it's worth tons of drill and experimentation and work to inculcate in everybody or their lives are going to be much harder for them to navigate.
Similarly I think the minimum for literacy is "when the doctor's office asks you to fill out and sign a form, you can" and "you can answer a question like 'is this health complaint important enough to go to the doctor about?' with either Google or an LLM and "you can look up the candidates for an election, read their candidate summaries, and decide who you like". This isn't really about economic productivity, it's about being equipped to make your own life decisions.
I think Freddie has this idea that, in some social organizations, the top 10% of performers are many times wealthier than the others, and the bottom 10% performers are impoverished. If you have this social organization, it doesn’t matter whether the top 10% do a bit of linear algebra and the bottom 10% are struggling with high school algebra, or if the top 10% are doing trig and the bottom 10% are struggling with fractions, or if the top 10% are doing differential geometry of Hilbert spaces while the bottom 10% are merely solving differential equations. On this picture, better teaching does nothing for material conditions - it just changes what math gets you the same material conditions. In this picture, the only thing that matters is changing the social organization so everyone can have a good life.
I don’t believe this picture. I believe that regardless of how the rest of society is, the ability to add fractions will help you make some kinds of decisions more quickly and effectively, and the ability to think in terms of calculus, or in terms of Hilbert spaces, will enable you to solve other issues. They can make your life better even if they don’t move you up in the percentiles.
And living in a society where more people have more of these skills will mean that much more human time and effort can be directed to making lots of things better, giving more people more absolute wealth, even if we don’t fix the distributional issues. And absolute quality of life matters - not just relative position.
Freddie is a Marxist. He is, as others have noted, a zero-sum thinker in every respect. The idea that a nation might be generally more prosperous if people know more things on average never even occurs to him. Prosperity and wealth just sort of happen, and all the education system is about is allocating positional goods.
Good, this is the heart of the issue and I don't think Kelsey adequately uplevels the conversation to diagnose that their disagreement is really over political ideology. I think that's a miss for the Argument, because this magazine is supposed to be dedicated to defending liberalism.
If we're to believe that political goods should be allocated "from each according to his abilities, to each according to his needs" then any attempt to equalize abilities threatens to destabilize the justification for differential distribution based on need. The Marxist needs us to believe that the bottom quintile is just going to be needier _no matter what_ and so any question about raising their floor is just a distract and delay tactic meant to forestall our redistributive obligations.
They will certainly concede that we _can_ raise the floor, but what they object to is the assumption which has been implicit in liberalism's educational philosophy — that raising the floor is basically sufficient for justice. That improvements in quality of life and collective output outweigh questions of relative distributional status.
Freddie's contributions to this debate have actually been really helpful in this regard. He, and others like Prof. Kate Harden, have helped break the grip of blank slate reasoning among egalitarian liberals. What this should do is re-focus the conversation on practical tradeoffs like "how do the marginal returns of diminishing investment in educating the bottom quintile compare to using those resources on the top quintile?" "how can we tighten the distribution without lowering the ceiling?" "how do elites structure institutions to care for unlucky losers without treating them like malformed elites?"
There are genuine tradeoffs involved in balancing distributional outcomes with absolute outcomes. Those should be the focus of conversation, unmuddied by bad assumptions about genetic equality or the irrelevance of achievement levels. Focusing on the actual outcomes in education without attending to these ideological disagreements just perpetuates a dialogue where the interlocutors talk past one another.
It is, I think, beyond the median American to compare the risk of getting myocarditis from a COVID vaccine to other, comparable risks. Or to understand, for example, that "most people who experience unintended pregnancy were using contraception" isn't automatically evidence that contraception doesn't work, given that most sexually active people use contraception.
Or to understand that the dose makes the poison, and to understand the concentrations of things that people are worried about, and how we know when something is "toxic".
These are live issues, and innumeracy harms us. Especially since we don't generally accept outsourcing these decisions to a cadre of elite experts any more. That cones with responsibilities. I've seen these people on Facebook. They're curious about how the world works. They've just been misled because they didn't have the strength to understand how they were being fooled.
I'll note that the students going to UCSD are not the bottom 20% but the top 10% or even top 5% in the state. Which makes this all the more shameful.
That being said, I do think you raise an interesting question.
I think realistically, just having a really good handle on multiplication, division, percentages and fractions should be good enough for most people.
That being said a couple of things to keep in mind. I failed high school geometry due to a lack of interest and not doing the work. The teacher wasn't that great either, but I was the bigger factor.
Then later I went to a community college for remedial math and later UCSB where I did calculus. I now have a CPA and an MBA. So some of the people in that bottom 20% might still actually be smart.
But move past the fact that it can be hard to tell which is which.
There still are probably instances where algebra can be helpful in things like construction. Or making sure you add the right amount of ingredients in recipe's (I've worked in food manufacturing and definitely seen this).
So I agree that after a certain point the cost will outweigh the benefit. But I think generally trying to teach kids algebra makes sense, even in the bottom distribution. Trig and calculus much less.
I had a huge crush on my high school geometry teacher. She was about 5’10” tall, had played tennis in college, and had literally just finished her student teaching. Also, she could do this weird thing with her wrist and elbow that allowed her to draw an almost perfect circle on a blackboard. She thought I was a math genius (which was not true). I don’t think I missed a question the entire year.
While I agree with most everything in this article, I think it is incredibly generous. I think it is incredibly generous to Freddie and incredibly generous to math instruction.
(btw: I originally intended to be a math teacher and never found any math that I couldn't handle. My concern as a young adult was that I could not make math interesting to people who were not already interested in it. That's why I switched to a subject that I was *not* as good in.)
1) Folks like Freddie deBoer should be very explicitly clear about how many kids they think cannot handle subjects like 5th grade basic reading and more advanced high school reading skills. Really. Exactly how much of the population are you are talking about. With how much support? Like...ever? With the level of support usually available to them? With additional reasonable support? With perhaps unreasonable support? What are you ACTUALLY saying, Freddie? And do the same for 4th grade calculation skills—including true proficiency with those important basic math facts—and "9th grade algebra." How many kids, Freddie.
If folks like Freddie are not being *very* specific, they are just hand waving and not even describing what *they* think the problem is, let along considering solutions.
2) Yeah. Math instruction. When I was 19 and 23, I didn't understand how to make math instruction work for kids who didn't get it. I didn't have the perspective to understand that kids really can understand these concept, but we cannot teach them like we've been doing so for so long. Sure, this is more efficient—for the kids it works for. But it leaves a *HUGE* share of kids behind. In reality, we see kids (and adults) understanding and applying so many of these principles they they didn't understand in math class when they are relevant to interesting to them. We see them diving in and caring about details and precision. We see them abstracting relationships and applying them elsewhere.
As a real math person—and I am VERY VERY deeply a real math person—I understand that math truly is not about numbers. Arithmetic is just one small piece of mathematics, and the ideas and principle of mathematics rarely require numbers. For folks like me, numbers are the easiest way to think about them and communicate those principles. Far better algebra instruction for people who struggle with how we have long taught math would not be grounded in numbers. We could get to numbers later, of course. But we start elsewhere, with another language for the ideas and skills of abstraction that are so key to algebra. We would apply them differently, perhaps more concretely. Numbers and codes could be later lessons once the real principles have been taught in ways more understandable to...well, to an awful lot of people.
3) Frankly, at lot of the ways that we teach a LOT of things are based in the most efficient (i.e, easiest) way to teach them to learners who are decently good at that subject. Not designed for average learners. And certainly not designed for the smartest learners of those subjects. But for like...I don't know...the 75th percentile? That's no accident. That's a result of intentional decisions about the nature and purpose of schooling. Thomas Jefferson wanted universal education that culminated in a state university system (i.e., UVA), but he his vision was ruthless about cutting lower ability learners off every couple of years. The idea of universal secondary (i.e, high school education)—something beyond basic literacy and numeracy—is not something that most people have considered deeply. It is not something we have changed our approaches to teaching enough to really embrace.
(As for how many examples the smartest math kids need? The best math kids don't need one to two examples to figure out all the variants. No, the best math kids will then make the next few steps themselves—because for them math is just obvious. Show them one spot and they won't just see the various views from it unprompted, but will actually understand where the next (few) spot(s) are and race ahead of you. This is why teaching real math prodigies is both so easy and so challenging. As my great computer science teacher in school, Don Hyatt, said, "On there go my students over the next hill. I need to race to catch up so I can lead them." He was great enough to lead as a truly incredibly teacher. Teaching such students is an entirely different set of skills and demands.)
Every day I'm slightly more tempted to write a browser plugin for automating the process of writing "I think you should read what Kelsey wrote about this" comments.
After DeBoer's string of straw men, I think we should all be making the obvious reading comprehension joke and moving on.
I have to ask whether anyone is really listening to him on education policy. Seems like an awful lot of his posts are full of people arguing his points.
I sense/hope we are approaching the end of the need to respond to a contrarian out on an intellectually faulty limb. (I say that as someone who jumped to pen my own response when I saw his dismissive straw man about the Southern Surge.)
In that spirit, I suggest reading this for the elephant in the room:
It’s the foundational skills, stupid.
We are failing to give kids math and reading foundations then arguing about inequitable access to advanced academics in high school.
That is a clear lesson from the UCSD debacle and Kelsey's classroom stories, alike.
I think actually it's best to understand his critique as that Freddie does not believe learning math in of itself matters. He believes learning math is only a signalling mechanism to show that you are smarter than other students, and regardless of the quality of the instruction, the signalling mechanism has approximately the same fidelity. This seems obviously false to me, but all of his arguments more of less only make sense with this frame, and I do see a lot of the chattering class say something similar.
Heroic of Kelsey not to go for the obvious quip "Freddie complains that some kids can't be expected to read, and evidentially Freddie can't be expected to read where I specifically said that we are talking about top students incoming as freshman to California colleges".
Not just California colleges. We are talking about a flagship UC campus that is known for its STEM work. We are not even talking about lower tier Cal State system schools, I would expect UCSD admissions to be somewhat competitive even in state, especially given location + academic reputation.
Not just "Cal" schools. The pool that Cal universities fish in, isn't very impressive compared to the nation as a whole.
Virtually every non-selective college and university in the nation has large, well funded remedial reading and math programs struggling to yank incoming freshpeople up to grade. It's no surprise that Cal schools do likewise.
I wish Freddie didn't lead so much with rage. It wears me out.
He’s a Marxist. Marxism is motivated by rage and envy. It’s who he is.
Is that so? I really wouldn’t know. I know he’s suffered a lot in his life and has triumphed over a lot of adversity.
He says he’s a Marxist. It’s not hidden. Shorter Cult of Smart: these problems are intractable until we have a communist revolution. How the future communist society is to be organized to produce goods and services is not specified, and he resents it when people ask.
He blocked me when I pointed out how ironic it was that he was complaining bitterly that Substack had invented Notes since he is one of its most prolific users and profits from using it financially.
Honestly maybe it’s best just not to engage with Freddie about this anymore. I don’t think he’s doing it in bad faith - he absolutely 100% believes what he’s saying - but as you note in your piece, he says the same things over and over.
It doesn’t matter what kind of point you’re trying to make. To him, everything is explained by “some kids are just dumb,” and he won’t be satisfied until we accept this and stop trying to teach them.
This is The Argument we're talking about - engaging with people who are demonstrably wrong (and, ahem, making the argument) is basically this magazine's founding principle!
Yes, maybe wait a few years when Freddie's own kid is in school and he's like hey what's with all these iPads ?!
Great article and very much agreed. Freddie is right that if everyone got a great education there would still be differences based on innate ability, but he's dead wrong that we are already providing everyone a great education.
Looking at NEAP test scores where only 30% of kids score proficient at reading it's quite clear that we have a LONG ways to go.
I generally appreciate Freddie deBoer's writing and I believe Ms. Piper's charitable interpretation of his motives is correct: he's trying to combat an actual defect in what he sees as the dominant educational ideology. But everything Ms. Piper writes here concerning the oversimplification of deBoer's arguments seems right to me.
But I want to focus on the positive implications of one of Ms. Piper's points, concerning learning multiplication tables, a process others who have commented describe well as training "automaticity." The underlying issue here seems to me to be the value of rote learning and ways it might in some ways level the educational playing field.
In some other cultures (I'm thinking of East Asian cultures, with which I have some experience) there is a very strong reliance on rote learning in pre-college education. This is a cultural inheritance that Westerners sometimes view as stifling -- the amount of rote learning can be truly astounding (and in traditional times it would approximate memorization of the textual equivalent of, say, the Hebrew Bible). What such extensive memorization stifles tends to be creativity and originality. But it can also provide certain tremendous benefits, the ability to memorize prodigiously being an obvious factor, but also the ability to "know" what other people have to reason to or look up. To use the multiplication tables as an example, it is the difference between being able to *calculate* 12x11=132 and *knowing* that 12x11=132. Not just in math but in all school skill areas, rote learning (and its result, "automaticity") is essential to efficient practice.
When we learn our native language adults require that we do prodigious amounts of rote learning. They do not generally give us phonetic rules and grammatical templates, they encourage us to imitate, over and over. Kids who are eighteen months to about three or four have wonderfully plastic neural capacities and the complex templates laid down through imitation shape the developing brain. By the ages of 3-4 kids are able to convey complex thoughts through language without hesitation: it's automatic. In this sort of context, rote learning doesn't stifle creative expression, it enables it.
Early use of rote learning for reading, arithmetic, geography, historical narratives, etc., if not stressed to the point of devaluing creative thinking and analytic practice, provides a basic toolkit that I believe kids with most levels of intelligence can benefit from, and raises the floor for kids whose natural aptitude for complex thinking may not be strong (and who may most benefit from an increased ability to memorize per se).
I think one of the problems of contemporary education, especially as technology has increasingly allowed us to access "prosthetic memory" instead of our own at a relatively low cost in time and effort, has been the devaluation of rote learning. And I'd speculate that the students most disadvantaged in this would likely be those who either through intrinsic gifts or family/social environments find it harder to do well in school.
I remember an anecdote which I cannot place at the moment, about a group of programmers who had worked in a high security environment where they could not use internet resources like StackOverflow, and so they had to memorize not just the mechanics but the APIs for everything they were writing.
They had become strangely effective programmers, able to bring loops which previously had gone out to the internet and back directly into their own heads.
This has inspired me to make flash cards to memorize things. I would usually look up. One thing that LLMs are excellent for is generating flash cards.
My kid (8, in 2nd grade) cried at night being asked to add 25 plus 25 in a word problem and asked, can't I just do my best? He expected to be able to guess.
Is he just dumb ? No, he was IQ tested at school and was 98% percentile in a couple of categories, notably visual spatial, so we showed him to count larger numbers on your fingers and use coins. With tangible options, he got it ASAP.
Poor instruction plus lots of iPad learning is a disservice. And he goes to a blue ribbon school in a well funded district!
That is _heartbreaking_. I'm glad you found a way to work the problem, but that's such sad approach to being presented with a hard problem.
Thank you - I think it's from using apps like iReady where you can guess and just finish without doing tangible work. Math is something you often have to work on, and he's the kind of smart kid who doesn't like things he isn't instantly good at. It's important to learn perseverance, so if school isn't teaching math effectively, I'll have him do an outside program, but I don't think I should have to do that!
I'm exactly that kind of former gifted kid; It took a lot to shift the mindset from smart being something I was inherently born with to a muscle that you have to work.
It may or may not land for your kid, but the idea that being smart just means that you learn more you the same amount of work, not that you Just Know More, really helped me.
That, and practicing persevering through problems I couldn't solve quickly. I did Art of Problem Solving, but I'm sure there's something suitable for every level. The point for me was to practice sticking with it.
yeah, I'm not opposed to computer guided learning. But you still need to do most of the work on paper.
There’s one thought people sometimes have, that all kids have the same abilities, and all different outcomes must be the result of different teaching methods. This is wrong, but it’s a natural thought to come to.
Freddie seems to have come to the opposite conclusion, that all teaching methods are equally effective, and all different outcomes must be the result of differences in abilities of the kids. This is also wrong.
When we see different outcomes, they are the result of some interaction of the innate factors and the teaching methods (and presumably various other external factors, like household nutrition and the availability of short format addictive video). Population level variability in outcomes is the result of population level variability in these factors. I don’t believe that the population level distribution of innate ability is that different between 2020s Mississippi and 1990s California (or 1660s Germany for that matter), so I think a large part of the different in outcomes of how many people learn algebra and calculus in these times and places must be the result of variation in instruction. (I expect everyone will agree with me that the reason why not a single teenager in 1660s Germany knew calculus is somehow related to the fact that no one had come up with a way to teach calculus yet.)
This article is definitely why I’m subscribing to the Argument! I have enjoyed almost all of Kelsey’s articles but this one and the original really hit home. I was not a natural at math and without some great teachers and a tutor for a Dad I probably would have given up.
Reading about the curriculum and expectations for students these days is scary but I’d rather have this information now than discover it when my kids are in middle school.
I agree the some kids are just dumb argument is just tone deft isn’t the point of teaching developing skills in all students?
Some kids probably shouldn’t take higher level English or math classes but that doesn’t mean every kid shouldn’t be given the same high level instruction.
Frankly, Kelsey is the only reason I subscribe, since MattY doesn't write often (if at all) and Jerusalem became a corporate manager sellout.
Interesting.
I don’t enjoy every article published but I think almost all of them are interesting.
I enjoy Jerusalems articles and the podcasts. I’m not sure why you think that but I’m sure she will still take your subscription money.
There's an excellent model for learning that Justin Skycak writes about in "The Math Academy Way"; you learn a skill by practicing it until it's automatic, and once that happens, you can start practicing skills which rely on it. If something seems like it's too hard for you, it's because your foundations are weak, and you need to practice them.
The concept is "automaticity"; here's a worked example using "compute 4³" as an example.
https://matheducators.stackexchange.com/a/27786
Here, innate ability solely shows up as how much effort or how many examples it takes to achieve that automaticity.
This is unpopular for a lot of reasons; it's hard to evaluate kids at this granularity, this involves doing a lot of hard work that you can't just take the royal road to avoid, most people have weak foundations somewhere and it's hard on the ego, etc. But if you manage to do it, you can get very, very strong.
Seems like Freddie is trying to jam the square peg of the "there will always be differing levels of academic proficiency" retort into the round hole of "we are not allowing scores of students to reach their academic potential" problem. His dismissal has no answer to the fact that the *highest performing* students are now doing *worse* on exams, a glaring problem that has nothing to do with achievement gaps between students.
It's too bad, because his work on education is, I believe, a valuable contribution to discourse and policymaking, but if he wants to be taken seriously he's eventually going to have to engage with ideas that don't relate to trying to close achievement gaps.
Continually hammering that students have different levels of innate ability tells us nothing about best practices in terms of pedagogy, grading, sorting, etc. There are extremely important concepts in education policy that I'd genuinely like him to weigh in on!
" His dismissal has no answer to the fact that the *highest performing* students are now doing *worse* on exams, a glaring problem that has nothing to do with achievement gaps between students."
exactly
Another banger. Beautifully argued.
I agree that not teaching multiplication facts to automaticity is a policy choice.
We absolutely know how to do it, and absolutely can. It just feels icky to a lot of people, so we don’t mandate it.
I would say there are additional reasons why students may not be adequately taught in math, though.
Sometimes the teacher is great, but the student is absent too much.
Sometimes the teacher knows the math, but student behavior is allowed to grind learning to a halt by discipline policies that prioritize anything but learning.
Sometimes the math teacher is doing a great job, but takes a job in another field that pays more, because they are a rational human being with bills to pay and talents to offer.
But yeah, this is a fixable problem and we need some societal urgency behind it.
"We absolutely know how to do it, and absolutely can. It just feels icky to a lot of people, so we don’t mandate it."
Yep, seems very similar to the arguments against phonics. It's boring practice that kids might want to do. But crucial to getting good at the subject
This is a fantastic post of course. But I'd like to push you a little harder on this Kelsey: I think you're eliding the question of what exactly the purpose is of teaching these kids who _can but don't_ learn algebra. Freddie propped up a strawman: the purpose, he claims, is putatively so that they can all go to Stanford and work at Google; this is impossible, hence we shouldn't bother teaching them.
So what is that purpose? There are several perfectly reasonable answers here, but all of them depend on some assumptions and are contingent on the specific child or the way specific skills theoretically add value in industry. Rather than spelling them out myself, I'd really like to hear your answer to the following question: why should we invest heavily into teaching a child in the bottom 20th percentile of the innate math talent distribution algebra? Suppose they can learn it (I certainly grant that they can): at what point does the cost outweigh the benefit?
(To reiterate, one answer can be: "never, every child is entitled to learn algebra, and it is universally edifying. You'd never ask a Muslim where the cost-benefit mid-point is for teaching kids Qur'an - similarly you shouldn't ask where the mid-point is for algebra.")
I think it improves peoples' lives to be able to navigate situations like "the apartment complex is offering two months' rent free if you sign a lease; what's the true rent over the next year?" or "Uber pays $15/hour but I'm spending an extra $80 week on gas, is it worth it?" and that even people who are pretty low innate aptitude should learn enough math that they're competent to answer these questions for themselves. I'm fine with not pushing further than that if a kid is experiencing a really shitty return on their efforts, but I think the above are just skills it's worth tons of drill and experimentation and work to inculcate in everybody or their lives are going to be much harder for them to navigate.
Similarly I think the minimum for literacy is "when the doctor's office asks you to fill out and sign a form, you can" and "you can answer a question like 'is this health complaint important enough to go to the doctor about?' with either Google or an LLM and "you can look up the candidates for an election, read their candidate summaries, and decide who you like". This isn't really about economic productivity, it's about being equipped to make your own life decisions.
I think Freddie has this idea that, in some social organizations, the top 10% of performers are many times wealthier than the others, and the bottom 10% performers are impoverished. If you have this social organization, it doesn’t matter whether the top 10% do a bit of linear algebra and the bottom 10% are struggling with high school algebra, or if the top 10% are doing trig and the bottom 10% are struggling with fractions, or if the top 10% are doing differential geometry of Hilbert spaces while the bottom 10% are merely solving differential equations. On this picture, better teaching does nothing for material conditions - it just changes what math gets you the same material conditions. In this picture, the only thing that matters is changing the social organization so everyone can have a good life.
I don’t believe this picture. I believe that regardless of how the rest of society is, the ability to add fractions will help you make some kinds of decisions more quickly and effectively, and the ability to think in terms of calculus, or in terms of Hilbert spaces, will enable you to solve other issues. They can make your life better even if they don’t move you up in the percentiles.
And living in a society where more people have more of these skills will mean that much more human time and effort can be directed to making lots of things better, giving more people more absolute wealth, even if we don’t fix the distributional issues. And absolute quality of life matters - not just relative position.
Freddie is a Marxist. He is, as others have noted, a zero-sum thinker in every respect. The idea that a nation might be generally more prosperous if people know more things on average never even occurs to him. Prosperity and wealth just sort of happen, and all the education system is about is allocating positional goods.
Good, this is the heart of the issue and I don't think Kelsey adequately uplevels the conversation to diagnose that their disagreement is really over political ideology. I think that's a miss for the Argument, because this magazine is supposed to be dedicated to defending liberalism.
If we're to believe that political goods should be allocated "from each according to his abilities, to each according to his needs" then any attempt to equalize abilities threatens to destabilize the justification for differential distribution based on need. The Marxist needs us to believe that the bottom quintile is just going to be needier _no matter what_ and so any question about raising their floor is just a distract and delay tactic meant to forestall our redistributive obligations.
They will certainly concede that we _can_ raise the floor, but what they object to is the assumption which has been implicit in liberalism's educational philosophy — that raising the floor is basically sufficient for justice. That improvements in quality of life and collective output outweigh questions of relative distributional status.
Freddie's contributions to this debate have actually been really helpful in this regard. He, and others like Prof. Kate Harden, have helped break the grip of blank slate reasoning among egalitarian liberals. What this should do is re-focus the conversation on practical tradeoffs like "how do the marginal returns of diminishing investment in educating the bottom quintile compare to using those resources on the top quintile?" "how can we tighten the distribution without lowering the ceiling?" "how do elites structure institutions to care for unlucky losers without treating them like malformed elites?"
There are genuine tradeoffs involved in balancing distributional outcomes with absolute outcomes. Those should be the focus of conversation, unmuddied by bad assumptions about genetic equality or the irrelevance of achievement levels. Focusing on the actual outcomes in education without attending to these ideological disagreements just perpetuates a dialogue where the interlocutors talk past one another.
Yeah, Freddie very much lives in a zero sum world. But there really is value in education even if you aren't changing your relative position.
It is, I think, beyond the median American to compare the risk of getting myocarditis from a COVID vaccine to other, comparable risks. Or to understand, for example, that "most people who experience unintended pregnancy were using contraception" isn't automatically evidence that contraception doesn't work, given that most sexually active people use contraception.
Or to understand that the dose makes the poison, and to understand the concentrations of things that people are worried about, and how we know when something is "toxic".
These are live issues, and innumeracy harms us. Especially since we don't generally accept outsourcing these decisions to a cadre of elite experts any more. That cones with responsibilities. I've seen these people on Facebook. They're curious about how the world works. They've just been misled because they didn't have the strength to understand how they were being fooled.
I'll note that the students going to UCSD are not the bottom 20% but the top 10% or even top 5% in the state. Which makes this all the more shameful.
That being said, I do think you raise an interesting question.
I think realistically, just having a really good handle on multiplication, division, percentages and fractions should be good enough for most people.
That being said a couple of things to keep in mind. I failed high school geometry due to a lack of interest and not doing the work. The teacher wasn't that great either, but I was the bigger factor.
Then later I went to a community college for remedial math and later UCSB where I did calculus. I now have a CPA and an MBA. So some of the people in that bottom 20% might still actually be smart.
But move past the fact that it can be hard to tell which is which.
There still are probably instances where algebra can be helpful in things like construction. Or making sure you add the right amount of ingredients in recipe's (I've worked in food manufacturing and definitely seen this).
So I agree that after a certain point the cost will outweigh the benefit. But I think generally trying to teach kids algebra makes sense, even in the bottom distribution. Trig and calculus much less.
I had a huge crush on my high school geometry teacher. She was about 5’10” tall, had played tennis in college, and had literally just finished her student teaching. Also, she could do this weird thing with her wrist and elbow that allowed her to draw an almost perfect circle on a blackboard. She thought I was a math genius (which was not true). I don’t think I missed a question the entire year.
While I agree with most everything in this article, I think it is incredibly generous. I think it is incredibly generous to Freddie and incredibly generous to math instruction.
(btw: I originally intended to be a math teacher and never found any math that I couldn't handle. My concern as a young adult was that I could not make math interesting to people who were not already interested in it. That's why I switched to a subject that I was *not* as good in.)
1) Folks like Freddie deBoer should be very explicitly clear about how many kids they think cannot handle subjects like 5th grade basic reading and more advanced high school reading skills. Really. Exactly how much of the population are you are talking about. With how much support? Like...ever? With the level of support usually available to them? With additional reasonable support? With perhaps unreasonable support? What are you ACTUALLY saying, Freddie? And do the same for 4th grade calculation skills—including true proficiency with those important basic math facts—and "9th grade algebra." How many kids, Freddie.
If folks like Freddie are not being *very* specific, they are just hand waving and not even describing what *they* think the problem is, let along considering solutions.
2) Yeah. Math instruction. When I was 19 and 23, I didn't understand how to make math instruction work for kids who didn't get it. I didn't have the perspective to understand that kids really can understand these concept, but we cannot teach them like we've been doing so for so long. Sure, this is more efficient—for the kids it works for. But it leaves a *HUGE* share of kids behind. In reality, we see kids (and adults) understanding and applying so many of these principles they they didn't understand in math class when they are relevant to interesting to them. We see them diving in and caring about details and precision. We see them abstracting relationships and applying them elsewhere.
As a real math person—and I am VERY VERY deeply a real math person—I understand that math truly is not about numbers. Arithmetic is just one small piece of mathematics, and the ideas and principle of mathematics rarely require numbers. For folks like me, numbers are the easiest way to think about them and communicate those principles. Far better algebra instruction for people who struggle with how we have long taught math would not be grounded in numbers. We could get to numbers later, of course. But we start elsewhere, with another language for the ideas and skills of abstraction that are so key to algebra. We would apply them differently, perhaps more concretely. Numbers and codes could be later lessons once the real principles have been taught in ways more understandable to...well, to an awful lot of people.
3) Frankly, at lot of the ways that we teach a LOT of things are based in the most efficient (i.e, easiest) way to teach them to learners who are decently good at that subject. Not designed for average learners. And certainly not designed for the smartest learners of those subjects. But for like...I don't know...the 75th percentile? That's no accident. That's a result of intentional decisions about the nature and purpose of schooling. Thomas Jefferson wanted universal education that culminated in a state university system (i.e., UVA), but he his vision was ruthless about cutting lower ability learners off every couple of years. The idea of universal secondary (i.e, high school education)—something beyond basic literacy and numeracy—is not something that most people have considered deeply. It is not something we have changed our approaches to teaching enough to really embrace.
(As for how many examples the smartest math kids need? The best math kids don't need one to two examples to figure out all the variants. No, the best math kids will then make the next few steps themselves—because for them math is just obvious. Show them one spot and they won't just see the various views from it unprompted, but will actually understand where the next (few) spot(s) are and race ahead of you. This is why teaching real math prodigies is both so easy and so challenging. As my great computer science teacher in school, Don Hyatt, said, "On there go my students over the next hill. I need to race to catch up so I can lead them." He was great enough to lead as a truly incredibly teacher. Teaching such students is an entirely different set of skills and demands.)
Every day I'm slightly more tempted to write a browser plugin for automating the process of writing "I think you should read what Kelsey wrote about this" comments.
After DeBoer's string of straw men, I think we should all be making the obvious reading comprehension joke and moving on.
I have to ask whether anyone is really listening to him on education policy. Seems like an awful lot of his posts are full of people arguing his points.
I sense/hope we are approaching the end of the need to respond to a contrarian out on an intellectually faulty limb. (I say that as someone who jumped to pen my own response when I saw his dismissive straw man about the Southern Surge.)
In that spirit, I suggest reading this for the elephant in the room:
It’s the foundational skills, stupid.
We are failing to give kids math and reading foundations then arguing about inequitable access to advanced academics in high school.
That is a clear lesson from the UCSD debacle and Kelsey's classroom stories, alike.
I think actually it's best to understand his critique as that Freddie does not believe learning math in of itself matters. He believes learning math is only a signalling mechanism to show that you are smarter than other students, and regardless of the quality of the instruction, the signalling mechanism has approximately the same fidelity. This seems obviously false to me, but all of his arguments more of less only make sense with this frame, and I do see a lot of the chattering class say something similar.