I’m going to stay at a controversial stuff today. I’m going to relay an antidote that is related to the discussion about reading.
About 15 years ago, I was stationed in South Carolina. I had a lot of kids.
Two of my kids were in third grade I believe. And one was maybe in ninth grade, and she was struggling with Algebra 1. I have more kids but they are not germane to the story.
Anyway, my 14-year-old, Was spending every night crying at the dinner table about algebra, as parents were getting frustrated, her grades were bad, it was just a bad situation.
At random, I happened to read this article in the LA Times that floated this hypothesis that the reason so many kids struggle with algebra is because they do not learn their multiplication facts to mastery.
That day, I went home and I actually gave my ninth grader a multiplication fact test. I sat there and watched her struggle with the multiplication facts. I watched her use all these finger tricks, and count by fives, and all these other strategies.
Remember my 2 3rd-graders. Coincidentally at this time they were learning their multiplication facts. I started talking to them, and sure enough they were learning all the same little tricks and short cuts. There was very little memorization.
that night, I ordered this multiplication fact flashcards set from online. It had something like 144 cards. Every multiplication fact from 0 to 12.
When it came, I drilled the fuck out of my kids. Yes, including the ninth grader. It became a game. We would have competitions. We started with the ones and twos, and then went all the way through the deck. Within about four weeks my kids could spit out multiplication facts like nobodies business.
I then started doing reverse multiplication facts with them. I would show them the answer, and have them tell me every combination that multiply to be that number.
See, I had started researching algebra, which I realized was basically all predicated on factoring, which was basically predicated on knowing your multiplication facts the opposite direction as well.
There is a happy ending. My ninth grader ended up getting an a minus in that class.
Every single one of my kids has kicked ass in math since then.
Especially algebra.
For a while I got into educational blogging. In fact my blog is still out there.
I read so much about phonics, and teaching math, and educational theory.
The biggest problem with these fuzzy instructional methods is that middle class kids I have parents that can basically supplement help or a job the schools do. Parents will sort of naturally give phonics lessons at home. Parents will buy math flashcards.
But other kids, who don’t have the same resources at home will struggle, and these critical skills are the backgrounds to education for the rest of their lives.
It’s made me pretty skeptical about the field of education. Go read about the largest educational study ever conducted, called project follow through.
They tested a bunch of teaching methods, and literally only one method showed significant positive affects. I’m not even going to tell you.
Anyway, if you have kids I suggest you buy a good pack of flashcards, and make sure that your kids learn those multiplication facts to mastery.
My kids favorite game was war. You give them half a second to answer the flash card, they get to keep it if they get it right, you keep it if they get it wrong. Then make a big deal about when you lose. Kids love that. The day that they win all those cards, you should see how proud they are.
OK, I got a head to the airport I’m heading to Des Moines Iowa today. Goodbye El Paso.
Yes I dictated this, my eyes don’t work well in the morning so please forgive any grammatical errors.
>>” But other kids, who don’t have the same resources at home will struggle, and these critical skills are the backgrounds to education for the rest of their lives.”
Bingo. And we all too often sweep this under the rug in the name of equity when it is perhaps the greatest cause of inequity. Schools can and should deliver adequate foundational reading and math instruction. Everything else pales in comparison. My years of teaching 9th graders who couldn’t read beyond an elementary school level taught me the importance of a systematic phonics system. What’s so amazing is that, like your flash cards, the actual time needed isn’t that much. 25-30 minutes a day of phonics when elementary schools usually have a literacy block that is three hours long really isn’t a difficult ask.
Actually, I’m of the opinion that highly educated parents are actually bad for our education system as a whole.
They take their influence for granted, so they’re more likely to push all sorts of fuzzy instruction methods like inquiry learning, or project-based learning. Sure their kids might benefit from this, but only because they have learned the basic facts.
The simple fact is kids need to have direct instruction on certain basic skills.
Too many education schools and teachers have mistaken correlation for a causation. They see these high-performing kids who do well with fuzzy curriculum, and then jump to the conclusion that they can use this fuzzy curriculum for all kids.
It's also intimately linked with tracking and gifted classes. If you get the smart kids and their parents out from underfoot you have the leeway to focus on getting the basics taught well to the remainder.
If their kids are stuck with the (to their minds) "dumb kids", then they're going to use their disproportionate influence and time to turn the curriculum into a gifted curriculum that blows off the basics.
When economists looked at this in Chicago they found that adding "gifted" classes lead to substantial gains for the students in the gifted section, with the largest gains among Black and hispanic students. They didn't find any positive (or negative) effects on the students in the non-gifted class https://www.aeaweb.org/articles?id=10.1257/aer.20150484
"If their kids are stuck with the (to their minds) "dumb kids", then they're going to use their disproportionate influence and time to turn the curriculum into a gifted curriculum that blows off the basics."
To be clear, I am pretty sure that this never works well enough for the strong students to end up happy either.
Someone I know works in both education research and tutors k-12 kids in math. While the field is getting better, she describes a real lack of rigor. Focus is on correlations, tiny sample sizes, and not really digging into figuring out if something works or not. As a tutor, she's always focused on hammering in the basics until they're second nature, but that kind of thinking isn't very fashionable in those circles.
> The simple fact is kids need to have direct instruction on certain basic skills.
Another fact is that teachers - that is, people who major in K-12 Education - learn to teach in K-12 from people who only teach college students. So their education in pedagogy comes almost entirely from people who practice pedagogy tuned for instructing professionals in matters of judgement and intellectual synthesis (how to write essays is a good example). There's basically no means by which the lessons learned by experienced K-12 teachers are promulgated back into the academy.
I spent a decade of my spare time tutoring the children of panicked parents fearful their children would not be allowed to attend university. The Province of Ontario had decided that three passed courses of high school math were necessary to be eligible to attend university. My main take away from this work was that high school math teachers suck at their jobs. Every single student I tutored succeeded. They did so because I bothered to analyze what mistakes they consistently made. Aside from the arithmetical skills you drilled your children on you have to understand basic properties of math. You have to understand order of operations and distributive properties and associative properties and commutative properties. The thing I noticed is that students often lacked these insights and constantly made the same errors. This should have been as evident to their teachers as it was to me. And it was all fixable. So I fixed them. Among them are several able professionals. Not STEM students mind you but how much algebra does a lawyer need to know?
Re your last point: more than you’d think. When I was in Iraq in 2008, I attended a briefing on an irrigation water pump conducted by the senior engineer of a US infantry division. He was a civil engineer in civilian life.
As the briefing proceeded, I realized that he was “plotting a slope” and that I now had an answer to an age old question: “when will I ever need to do this stuff?”
I called my kids as soon as the briefing was over and got them to speak with an army brigadier general about how useful math could be.
Excellent point. My thinking is that multiplication is basically the precursor to a division. And fractions are basically a form of division (mixed in with multiplication).
So many things you need to master, that schools just don’t seem to do a good job of.
I did a session or two helping out at a community college remedial algebra class, and the #1 problem was not understanding fractions. This was more than a mechanical problem; the students didn't understand what fractions represent.
Not understanding that 2/17 is bigger than 2/43 is not a matter of knowing multiplication tables. But some of these students would pull out their calculators to add two one-digit numbers.
Algebra is actually very useful for a deal lawyer, bluster and intimidation more important for a trial lawyer. Calculus won’t hurt either of them, but isn’t a critical skill,
It's a lot more difficult to deal with individual mistakes having a class with 30 kids. That said, this is exactly why reading and math groups are important.
Yes! Reduce class sizes. That means having more classrooms and more teachers and paying them. That means increasing taxes. Hope everyone is good with that.
For our son, we used two 10-sided dice. We'd roll them, and he'd have to announce the product of the numbers on the two faces. We'd time it: how many could he do in sixty seconds? He's very competitive and he got very fast in short order. Come to think of it, we could have used 20-sided dice for more facts, but we didn't.
Oh man! As a DnD nerd, I definitely have a few d20 laying around! Gonna write this down for when it's time to start drilling multiplication with my kids!
Rory, I tutored the big STEM weedout courses as a Student Support Services (a Great Society program!) tutor at UConn and you are one million percent correct here. Every time I hit a snag with calculus, I'd start drilling algebra. Hit a snag with algebra, start drilling arithmetic. Each layer of math builds on the last, and you can't do algebra if your arithmetic isn't automatic, and you can't to calculus if your algebra isn't automatic.
General Chemistry was the same way. Big weed out course, and all these kids think they suck at Chemistry, but really their algebra just needed work. All GC is is applied algebra, the entire time.
I was lucky enough to have a first grade teacher who drilled phonics, and a fourth grade teacher who drilled multiplication tables. The single best way to get fundamental skills down like that is to drill baby drill.
Wow... even in College. It was pure luck I discovered it. The 14-year old that I taught is about to finish her Masters degree in Social Work, but she had no issues with College Algebra and Statistics.
Every single one of my kids has kicked ass once I figure out this little secret.
It's such a simple hack that it blows my mind people don't realize it.
Even drilling can be fun. Its not like you have to do it for hours a day. Just 15-30 minutes a day. Make it a game.
I’m at the airport now, I figured I would elaborate what I learned about multiplication facts and algebra.
First of all, what I am talking about here also applies to long division and calculus and all sorts of other things.
The basic premise is that people only have so much working memory. Algebra is sort of a multi step thinking process. You have to take these numbers figure out what products make up each one, then how they add up individually, along with whether it’s going to be positive or negative. Just writing that was tiresome. Human beans are only capable of storing so much knowledge and using it at a single instance.
When you master things like phonics or multiplication, basically becomes like muscle memory. You’re working memory doesn’t have to spend any time trying to figure out what five times six is.
Now imagine trying to factor a problem, Where you have to use your fingers to figure out multiplication facts. And even more than that, you have to do it in reverse.
It’s such a basic concept, but you would be amazed how many schools do not drill multiplication.
Honestly, go check with your kids. Give them a multiplication test. More than a few of you might be shocked.
Yes, many many people have difficulties with advanced calculus because they can't instantly implement in the chain-rule on an arbitrary expression, or because they didn't memorize all of the common trig identities. It's like trying to read Shakespeare when you can't remember how to pronounce half the words.
Basically it's turtles all the way down. When someone is teaching you an extremely non-intuitive concept you need to be able to focus on the mechanism that makes it work... not the mechanics of to go from one step to the next.
Makes me appreciate the rote match drilling I received from the Good Nuns in 40-student classes. When working as a city manager, Finance was always shocked at how quickly I could deal w large numbers. I agree, it's all about basics.
My phone has an alarm setting where I have to do a basic multiplication-and-addition to turn the alarm off (something like "7 x 6 + 4"). I use it because if I'm awake enough to get the right answer, then I won't fall back asleep after turning the alarm off, which is a problem I used to have with other alarms.
But, believe me, if you want to silence a blaring noise and a bright light when you are half-awake, knowing your basic multiplications without thinking too hard becomes really important.
This is an amazing comment which I think has the potential to be made into a feature-length film. Who would you like to play you? Your kids who didn't make it into this version can also be in it and will have minor story arcs.
I taught Pre-Algebra in a Title 1 charter school in New Orleans from 2016-2019. Most students were two or three years behind grade level. There's been a considerable shift away from what opponents describe as "drill-and-kill" pedagogy. I've never been convinced that any student can develop critical thinking skills in numerical analysis without having a rock-solid foundation in multiplication and ratios. Unfortunately, too many in the education space think otherwise. This seems similarly related to the debate about phonics.
I find it quite frustrating and counter intuitive. Anyone who's trained in music or sports knows that you have to have the fundamentals down pat before you can even start doing anything complicated or interesting. Same goes for math and reading. It's not fun, but you have to do it.
I am a full-time musician, drummer, and I agree completely, that you need to have the fundamentals of playing the instrument down ice cold, starting with how you hold the drumsticks correctly. Everything builds from there.
Here's a question for any other musicians who teach: Have you noticed that students that are in the 5th and 6th grade, have a hard time writing out musical notes on staff paper? They don't teach cursive writing in a lot of schools anymore, so you don't get that fine muscle development in their strong hand. Having that fine muscle control in your strong hand, throws a switch in the brain, that allows your weaker hand to develop a certain level of the same fine muscle control. Thoughts?
I mean, one reason you don't see teachers intensively drilling individual students using flash cards is they have a classroom of like 50 kids to teach math to; drilling each one in turn until they got it would take too long. And what would the other kids do while they were waiting their turn, or after?
I suspect the education space, particularly at the academic theorist level, tends to attract people who disproportionately do not love, and sometimes even resent, math.
When I was a first-termer in the Air Force, we used to say, "Those that can do, do. Those that can't do, teach. Those that can't teach, administrate. Those that can't administrate become officers."
I was a musician in the Air Force. The drums. 2 years in a career field band at McGuire AFB in NJ, and 24 years with the premier band, The United States Air Force Band in Washington, DC. I retired as a SMSgt. I tested for Chief, didn't make the cut, and was at top cap, so welcome to retirement and the second career, which was playing music and doing some private teaching. Until Covid, I was playing regularly, and was scaling back the teaching. Once things get back to normal, I'm finally going to sign up for some space-A flights, and just go where the planes go. From there, I'll find another hop to somewhere else. If I want to go to Germany, for example, I don't need to fly into Germany. I can fly to any base on the Continent, and then take a train the rest of the way. I really want to see Berlin again.
Eh, I wouldn't be that harsh. There are lots of great teachers out there at the practitioner level, including math teachers. And it's a pretty diverse (personality-wise) profession. I'm really just talking about *education policy academia* which is dominated by folks within a narrow range of personality types.
Which schools? I have this vague memory that there were some very successful charter schools in New Orleans that utilized direct instruction and were pretty successful.
100% can confirm. My wife has a PhD in Nuclear Engineering. Her Dad drilled her with flash cards growing up and made it a fun game. She would not be where she is today without that.
I’m more of a liberal arts guy, but I still remember my “times tables” from school - I can visualize them.
With my own kids and their assignments I had to figure out what gimmick was being used - often some combination of groups of dots. Some of the methods were clever in a good way, but I thought a lot of it was just crap. We got flash cards too.
At the schools here where I’m at still use simple tests to measure speed and accuracy for the basics.
Speed and accuracy are underrated. I probably should’ve emphasize that I did not consider a kids with mastered anything until he could see it within a split second. In our games, any hesitation was a loss for the kid.
Back in 1960 when I was in first grade, our class was chosen for a new method of teaching math called the Cuisenaire Rod System. Consequently, I struggled through math all the way through high school, barely passing Algebra 1 and Algebra 2. I didn't even attempt Geometry. Out of the colleges that accepted me, I majored in Music Education, I chose the one that allowed you to either take a math or science course, rather than both. I thought I was in the clear after taking a course in Environmental Biology, which had no math, just a bunch of theory about how to make cleaner water.
After 3 years, I left college, because I wasn't sure that I wanted to continue becoming a music teacher. I spent 2 years studying privately with a teacher in New York City, lived at home in my parents' basement (literally, because that's where the drums were set up), practiced 6-7 hours per day, and landed a gig with the Air Force. I spent 2 years in a regional band, and 24 years with the premier band in Washington, DC.
I decided at about age 40 to go back to school. I was accepted by the University Of Maryland as a music major. One of their requirements for a BA in Music, was a course called Finite Mathematics. I knew there was no way that I was going to be able to pass a college-level math course, so I hired a private math teacher.
At at our first meeting, she gave me a math test that started at 1+1, and continued all the way up to some advanced form of Calculus. She said, "stop when you no longer understand what you are doing." It didn't take long. She told me that I had fallen down on the development of basic math skills somewhere between 1st and 2nd grade. No wonder I had struggled all those years. She started me right from the beginning with the basics. Addition and subtraction drills, multiplication and long division, fractions, sets, etc. Once I had the basics down, the rest of it suddenly became fun, rather than my remembrance of 12 years of public school math torture. Yes, I was a victim of the so-called "New Math." Now, they have this Common Core math, where there are at least 10 steps to get from 1+1=2. I maybe be exaggerating, but you catch my drift.
Once I had the basics down, the rest came naturally. It's the same thing when learning a musical instrument. You have to have the basics down cold, or you won't progress anywhere.
my kid got optional homework from Kindergarten with the teacher saying "you can really tell which kids do the homework." And it's like ... are the kids who really need it going to be the ones who do it?
Agreed, beyond phonics and the times tables, every kid is better off in the back yard with his pals sucking up dirt and looking for bugs like EO Wilson.
Me too. We moved here (Colorado) three years ago youngest was in an elementary school with a no homework policy. So refreshing after dealing with the stupid make-work of previous schools. But he started middle school this year which has homework and the adjustment has been….difficult.
Yeah, currently hitting a brick wall with IB algebra with my 15 year old. She has never been great at math, but typically in the "meaty part of the curve" and having helped her through some homework recently the fact she didn't have memorization of times tables and so on drilled back when she was little definitely isn't helping. Also 100% agree on the flashcards although I didn't really use them myself, I pretty much improvised something equivalent with my mother back in the day.
Make sure you get a pack of flashcards that does not duplicate. That means it has 3×4 card, and 4x3 card.
She needs to be able to spit them out with in a split second.
Then, once she can do that 100% of the time. Start showing him cards with the answers. And then make her spit out all the combinations that make up that number.
So for instance. 12 is 1x12, 2x6, and 3x4
She needs to be able to do that by mastery as well.
There are obviously other rules and tricks to learn. But if she doesn’t have to think about these with her work in memory, chicken be more likely to learn the other stuff.
I remember my kids taking exactly that course. After spending money on a tutor (a retired HS teacher), we received the advice you offered here- get your basic math facts down cold.
The argument was always that the basics are not fun. My warped mind also believes that our education system is designed to fail a certain percentage of our population, so that they can become "clients" of the social services industry.
My thinking is its really hard for many people to think outside their priors.
Hardcore partisans have this issue.
I just think a certain number of teachers are either so naive, or so jaded they are unable to consider alternatives to how they "want" the world to be.
I'm of the...play the game with the rules you have, not the rules you wish you had mentality.
My elementary school did the group competition thing with flash cards and really drilled the memorization of arithmetic through the 9s. We learned the theory behind it AFTER so that it could be extrapolated to bigger numbers.
As I'd said earlier, I come from a family of educators and married into a family of educators. My mom taught high school and her biggest frustration was trying to teach literature and writing when so many students lacked even elementary-level reading and writing skills. I think outstanding teachers manage to identify and remedy some of those deficiencies on the fly but it really shouldn't get to that point.
Good story Rory. My grandfather, who rode a horse every day 10 miles to a one-room schoolhouse, memorized the times tables up to 25 and used to practice them in bed as a way to go to sleep. He died at 99, still sharp, 23x19 on his lips as the family legend goes. Your story of what you did for your daughter's math struggles resonated with me, because it so mirrored my experience with my daughter's English struggles. Public schools are important, but there's no substitute for engaged parents paying attention, having flash cards when needed, and the importance of memorizing the basics.
The best way to make reading relevant to a kid is to give them and ipad and make them use google to find the content they want. my second grader reads very well but has almost no interest in books. he prefers articles on whatever interests him at the time
When I was growing up we had a set of encyclopedias. I would spend hours looking up subjects. Cowboys or tanks or how an internal combustion engine works.
It’s amazing how much knowledge we have in our fingertips now.
We had these too. Also an atlas-type thing with two pages on every country in the world. I also clearly remember getting the new Guinness Book of World Records every year at Christmas and reading it cover to cover.
Also, in 3rd grade, every morning we did a "Mad Minute" worksheet of multiplication questions that you could only progress from once you hit a certain score multiple days in a row. We must have stopped at 10s because I'm really not great at multiplying by 12 but have had the rest down since then.
I went to elementary school in Minnesota in the early '90s and could absolutely not learn to read well with the "whole language" instruction given. My sisters kind of intuitively learned phonics, but I wasn't having an luck with that. It took me just a couple months with Hooked On Phonics to catch up the summer before second grade, admittedly because my language comprehension was way above my reading level since my mom read to me so much. If my parents' hadn't invested a lot of time and effort in enrichment activities, I'd probably be slinging a mop at McDonald's and hardly be able to read my bank account app instead of holding down a lucrative position in a STEM field.
So, I don't trust the schools basically at all with my son. He's getting extra home instruction and tutoring right off the bat. I want him to hit the hard stuff and fail before he encounters it in real school and gets a bad grade. I also disagree with the homework policies I've seen with my friends' kids. For me, sitting your butt down and doing some crap you don't want to do is a skill in itself and one you should start building early.
Do you have a link to a good argument for that? Just curious what it is from someone who seems reasonable and thoughtful. I have heard it doesn't increase performance at grade level skills, but that's not particularly why I see it as important.
Call Nell it’s not that I am zero homework. But I feel that the purpose of homework should only be to reinforce what a child has learned in school. For instants in my example above, having a kid come home and do a couple of simple multiplication sheets would be good.
Too often, teachers underestimate the amount of time and effort it takes to do some of these homework assignments. And then I’ll forget the kid has multiple classes here imagine if the teacher games 30 minutes of homework, and four other teachers give 30 minutes. Now your kid is trying to do 2 1/2 hours of homework in the evening when they really should be playing.
Then if you’re like me with a bunch of kids you have seen some just terrible homework assignments. Think… coloring a picture for history class. And every diarama ever.
It got to the point where I would simply tell my kids teachers no.
If they had homework that took more them 20 minutes, I would write a note on it. Include district guidelines.
What’s even more telling is when u have two kids in same class. One has lots of homework. One doesn’t. And the kids learn the same stuff.
My absolute worst moments as a parent have been at the table trying to teach my kids some subject. Kids crying. Me frustrated. I think back and cringe.
But that is preliminary, and maybe it's the case that doing 1 hour of homework every night is great for this, but doing obvious busy work after that is not.
Note that willingness to buckle down and do the work are important life skills, so homework could be helping with this.
I know that college is really punishing to those who haven't learned to just sit down and do the work, since the teachers won't help you with that. Maybe that's good/bad, but (at least when I attended) it's how it was - so being used to doing the homework you're supposed to do is good.
(I agree that 2.5 hours a night seems excessive - what if you're also practicing in band or for sports or whatever)
As a lawyer, the pipeline problem looms huge because firms get beaten up over their racial demographics, but at the end of the day there's very little firms can do to fix it at their end of things because the "pipeline" is so long -- to be a lawyer in most states you have to have passed the bar exam (black and Hispanic law students have lower bar pass rates), to take the bar exam in most states you have to have graduated from law school (black and Hispanic law students have lower graduation rates), to attend a law school you generally have to have graduated from college (black and Hispanic college students have lower graduation rates), and to attend college you generally have to have graduated from high school (black and Hispanic high school students have lower graduation rates).
So, you get proposals to do things like abolish the bar exam or convert law schools to one-year plus apprenticeship type programs, but realistically that isn't going to change the total numbers all that much because you need to significantly boost the numbers coming up from college, which in turn requires boosting the numbers coming up from high school.
We have that issue in medical education too (mostly residency level). We are VERY pro-DEI and strongly recruit applicants from underrepresented groups but that pool of residency applicants is too small. It's hard to win a national recruiting battle against Harvard affiliates, Stanford, etc.
We now aren't allowed to use USMLE scores as a screening tool (which, fine, I understand the argument) but it doesn't fix the underlying pipeline issue that likely has the greatest impact. The real work isn't about recruiting the superstars. It's about diversifying the ranks of the more-average trainees. There's no quick fix for that.
I vote for science as having the most intractable version of this problem, because the pipeline features all of the above but also faces a compounding problem related to alternative endpoints. To get a top-tier scientist job you need to do the college, master’s, phd, postdoc thing, but throughout that process there are always options to offramp to a middle tier job that pays well but not nearly as well as one for someone who goes the distance. A law school grad doesn’t have a ton of options other than pressing on or giving up completely.
In practice personal wealth plays a key role in scientific advancement, because talented people from a poor family are under enormous pressure to cash in without reaching their full potential throughout the whole process.
At least anecdotally, it seems even worse than you say: those jobs at the end of the offramp tend to pay far better than their academic counterparts, which only adds to the appeal of cashing in for those who aren't already comfortably off.
I’m going to stay at a controversial stuff today. I’m going to relay an antidote that is related to the discussion about reading.
About 15 years ago, I was stationed in South Carolina. I had a lot of kids.
Two of my kids were in third grade I believe. And one was maybe in ninth grade, and she was struggling with Algebra 1. I have more kids but they are not germane to the story.
Anyway, my 14-year-old, Was spending every night crying at the dinner table about algebra, as parents were getting frustrated, her grades were bad, it was just a bad situation.
At random, I happened to read this article in the LA Times that floated this hypothesis that the reason so many kids struggle with algebra is because they do not learn their multiplication facts to mastery.
That day, I went home and I actually gave my ninth grader a multiplication fact test. I sat there and watched her struggle with the multiplication facts. I watched her use all these finger tricks, and count by fives, and all these other strategies.
Remember my 2 3rd-graders. Coincidentally at this time they were learning their multiplication facts. I started talking to them, and sure enough they were learning all the same little tricks and short cuts. There was very little memorization.
that night, I ordered this multiplication fact flashcards set from online. It had something like 144 cards. Every multiplication fact from 0 to 12.
When it came, I drilled the fuck out of my kids. Yes, including the ninth grader. It became a game. We would have competitions. We started with the ones and twos, and then went all the way through the deck. Within about four weeks my kids could spit out multiplication facts like nobodies business.
I then started doing reverse multiplication facts with them. I would show them the answer, and have them tell me every combination that multiply to be that number.
See, I had started researching algebra, which I realized was basically all predicated on factoring, which was basically predicated on knowing your multiplication facts the opposite direction as well.
There is a happy ending. My ninth grader ended up getting an a minus in that class.
Every single one of my kids has kicked ass in math since then.
Especially algebra.
For a while I got into educational blogging. In fact my blog is still out there.
I read so much about phonics, and teaching math, and educational theory.
The biggest problem with these fuzzy instructional methods is that middle class kids I have parents that can basically supplement help or a job the schools do. Parents will sort of naturally give phonics lessons at home. Parents will buy math flashcards.
But other kids, who don’t have the same resources at home will struggle, and these critical skills are the backgrounds to education for the rest of their lives.
It’s made me pretty skeptical about the field of education. Go read about the largest educational study ever conducted, called project follow through.
They tested a bunch of teaching methods, and literally only one method showed significant positive affects. I’m not even going to tell you.
Anyway, if you have kids I suggest you buy a good pack of flashcards, and make sure that your kids learn those multiplication facts to mastery.
My kids favorite game was war. You give them half a second to answer the flash card, they get to keep it if they get it right, you keep it if they get it wrong. Then make a big deal about when you lose. Kids love that. The day that they win all those cards, you should see how proud they are.
OK, I got a head to the airport I’m heading to Des Moines Iowa today. Goodbye El Paso.
Yes I dictated this, my eyes don’t work well in the morning so please forgive any grammatical errors.
>>” But other kids, who don’t have the same resources at home will struggle, and these critical skills are the backgrounds to education for the rest of their lives.”
Bingo. And we all too often sweep this under the rug in the name of equity when it is perhaps the greatest cause of inequity. Schools can and should deliver adequate foundational reading and math instruction. Everything else pales in comparison. My years of teaching 9th graders who couldn’t read beyond an elementary school level taught me the importance of a systematic phonics system. What’s so amazing is that, like your flash cards, the actual time needed isn’t that much. 25-30 minutes a day of phonics when elementary schools usually have a literacy block that is three hours long really isn’t a difficult ask.
Actually, I’m of the opinion that highly educated parents are actually bad for our education system as a whole.
They take their influence for granted, so they’re more likely to push all sorts of fuzzy instruction methods like inquiry learning, or project-based learning. Sure their kids might benefit from this, but only because they have learned the basic facts.
The simple fact is kids need to have direct instruction on certain basic skills.
Too many education schools and teachers have mistaken correlation for a causation. They see these high-performing kids who do well with fuzzy curriculum, and then jump to the conclusion that they can use this fuzzy curriculum for all kids.
It's also intimately linked with tracking and gifted classes. If you get the smart kids and their parents out from underfoot you have the leeway to focus on getting the basics taught well to the remainder.
If their kids are stuck with the (to their minds) "dumb kids", then they're going to use their disproportionate influence and time to turn the curriculum into a gifted curriculum that blows off the basics.
Huh, never thought of G&T programs as being useful there.
Makes intuitive sense(doesn't mean it's true!), wonder if it's been studied.
When economists looked at this in Chicago they found that adding "gifted" classes lead to substantial gains for the students in the gifted section, with the largest gains among Black and hispanic students. They didn't find any positive (or negative) effects on the students in the non-gifted class https://www.aeaweb.org/articles?id=10.1257/aer.20150484
"If their kids are stuck with the (to their minds) "dumb kids", then they're going to use their disproportionate influence and time to turn the curriculum into a gifted curriculum that blows off the basics."
To be clear, I am pretty sure that this never works well enough for the strong students to end up happy either.
I would not argue with that.
One of those situations where, if they're in the tent, they're going to piss in it.
If you boot them out politely and give them a pat on the head, they'll dig a fucking latrine over in their own space.
Someone I know works in both education research and tutors k-12 kids in math. While the field is getting better, she describes a real lack of rigor. Focus is on correlations, tiny sample sizes, and not really digging into figuring out if something works or not. As a tutor, she's always focused on hammering in the basics until they're second nature, but that kind of thinking isn't very fashionable in those circles.
Not fashionable at all.
> The simple fact is kids need to have direct instruction on certain basic skills.
Another fact is that teachers - that is, people who major in K-12 Education - learn to teach in K-12 from people who only teach college students. So their education in pedagogy comes almost entirely from people who practice pedagogy tuned for instructing professionals in matters of judgement and intellectual synthesis (how to write essays is a good example). There's basically no means by which the lessons learned by experienced K-12 teachers are promulgated back into the academy.
true. plus in their mind, direct instruction is boring and not cool. It has no fancy words... therefore its beneath them.
I spent a decade of my spare time tutoring the children of panicked parents fearful their children would not be allowed to attend university. The Province of Ontario had decided that three passed courses of high school math were necessary to be eligible to attend university. My main take away from this work was that high school math teachers suck at their jobs. Every single student I tutored succeeded. They did so because I bothered to analyze what mistakes they consistently made. Aside from the arithmetical skills you drilled your children on you have to understand basic properties of math. You have to understand order of operations and distributive properties and associative properties and commutative properties. The thing I noticed is that students often lacked these insights and constantly made the same errors. This should have been as evident to their teachers as it was to me. And it was all fixable. So I fixed them. Among them are several able professionals. Not STEM students mind you but how much algebra does a lawyer need to know?
Yes. That is the next step. Order of operations.
It’s not as glamorous as multiplication facts.
Math is nothing but a bunch of small rules that you add up.
We have to master each and every rule.
Sounds like you do an awesome job.
Re your last point: more than you’d think. When I was in Iraq in 2008, I attended a briefing on an irrigation water pump conducted by the senior engineer of a US infantry division. He was a civil engineer in civilian life.
As the briefing proceeded, I realized that he was “plotting a slope” and that I now had an answer to an age old question: “when will I ever need to do this stuff?”
I called my kids as soon as the briefing was over and got them to speak with an army brigadier general about how useful math could be.
That Army Brigadier General might actually have only 1 arm!
Another problem high school students have is not understanding how fractions work. You cannot learn algebra if you don't understand fractions.
Excellent point. My thinking is that multiplication is basically the precursor to a division. And fractions are basically a form of division (mixed in with multiplication).
So many things you need to master, that schools just don’t seem to do a good job of.
I did a session or two helping out at a community college remedial algebra class, and the #1 problem was not understanding fractions. This was more than a mechanical problem; the students didn't understand what fractions represent.
I wonder how many of them also didn’t know their multiplication tables to mastery.
Not understanding that 2/17 is bigger than 2/43 is not a matter of knowing multiplication tables. But some of these students would pull out their calculators to add two one-digit numbers.
Algebra is actually very useful for a deal lawyer, bluster and intimidation more important for a trial lawyer. Calculus won’t hurt either of them, but isn’t a critical skill,
It's a lot more difficult to deal with individual mistakes having a class with 30 kids. That said, this is exactly why reading and math groups are important.
Yes! Reduce class sizes. That means having more classrooms and more teachers and paying them. That means increasing taxes. Hope everyone is good with that.
For our son, we used two 10-sided dice. We'd roll them, and he'd have to announce the product of the numbers on the two faces. We'd time it: how many could he do in sixty seconds? He's very competitive and he got very fast in short order. Come to think of it, we could have used 20-sided dice for more facts, but we didn't.
Oh man! As a DnD nerd, I definitely have a few d20 laying around! Gonna write this down for when it's time to start drilling multiplication with my kids!
Nice!
Rory, I tutored the big STEM weedout courses as a Student Support Services (a Great Society program!) tutor at UConn and you are one million percent correct here. Every time I hit a snag with calculus, I'd start drilling algebra. Hit a snag with algebra, start drilling arithmetic. Each layer of math builds on the last, and you can't do algebra if your arithmetic isn't automatic, and you can't to calculus if your algebra isn't automatic.
General Chemistry was the same way. Big weed out course, and all these kids think they suck at Chemistry, but really their algebra just needed work. All GC is is applied algebra, the entire time.
I was lucky enough to have a first grade teacher who drilled phonics, and a fourth grade teacher who drilled multiplication tables. The single best way to get fundamental skills down like that is to drill baby drill.
Wow... even in College. It was pure luck I discovered it. The 14-year old that I taught is about to finish her Masters degree in Social Work, but she had no issues with College Algebra and Statistics.
Every single one of my kids has kicked ass once I figure out this little secret.
It's such a simple hack that it blows my mind people don't realize it.
Even drilling can be fun. Its not like you have to do it for hours a day. Just 15-30 minutes a day. Make it a game.
I’m at the airport now, I figured I would elaborate what I learned about multiplication facts and algebra.
First of all, what I am talking about here also applies to long division and calculus and all sorts of other things.
The basic premise is that people only have so much working memory. Algebra is sort of a multi step thinking process. You have to take these numbers figure out what products make up each one, then how they add up individually, along with whether it’s going to be positive or negative. Just writing that was tiresome. Human beans are only capable of storing so much knowledge and using it at a single instance.
When you master things like phonics or multiplication, basically becomes like muscle memory. You’re working memory doesn’t have to spend any time trying to figure out what five times six is.
Now imagine trying to factor a problem, Where you have to use your fingers to figure out multiplication facts. And even more than that, you have to do it in reverse.
It’s such a basic concept, but you would be amazed how many schools do not drill multiplication.
Honestly, go check with your kids. Give them a multiplication test. More than a few of you might be shocked.
Yes, many many people have difficulties with advanced calculus because they can't instantly implement in the chain-rule on an arbitrary expression, or because they didn't memorize all of the common trig identities. It's like trying to read Shakespeare when you can't remember how to pronounce half the words.
I have no idea what those are. But I will take your word! I never did advanced calculus.
Basically it's turtles all the way down. When someone is teaching you an extremely non-intuitive concept you need to be able to focus on the mechanism that makes it work... not the mechanics of to go from one step to the next.
Makes me appreciate the rote match drilling I received from the Good Nuns in 40-student classes. When working as a city manager, Finance was always shocked at how quickly I could deal w large numbers. I agree, it's all about basics.
It doesn’t even take that much time and effort to teach these facts. 20 minutes a day, for a month or two, and they’re down for life.
My phone has an alarm setting where I have to do a basic multiplication-and-addition to turn the alarm off (something like "7 x 6 + 4"). I use it because if I'm awake enough to get the right answer, then I won't fall back asleep after turning the alarm off, which is a problem I used to have with other alarms.
But, believe me, if you want to silence a blaring noise and a bright light when you are half-awake, knowing your basic multiplications without thinking too hard becomes really important.
I need that app for my kids. They are notorious snoozers.
"Wax on, wax off" basically.
All of that could be true but it doesn’t seem to have a long term impact.
I have a 65 mustang and 65 C20. I’m sitting in seat 4C on my next flight. My shoes are brown.
What is: "Tell me you're an elitist prick without telling me you're an elitist prick"?
:p
Lol. More like… What are facts that aren’t germane to the conversation.
How do you mean? I'm pretty sure having good command of Junior/Senior year math tracks pretty well with getting into an elite college.
You’re assuming failure to master the math is due to a pedagogical failure rather than a lack of elite college level ability.
On some level pedagogy obviously makes a difference. Unless your position is that it is simply not possible to be taught things.
I’ve mentioned many times that my position is that above a fairly low level of competence it won’t have a beneficial long term impact.
This is an amazing comment which I think has the potential to be made into a feature-length film. Who would you like to play you? Your kids who didn't make it into this version can also be in it and will have minor story arcs.
But seriously, that was awesome. Thanks!
Matt Damon! I would say Tom Cruise, but he is my wife’s free pass, and I don’t want to tempt fate.
Ah, good choice. He already has experience playing an unpretentious math whiz in Good Will Hunting, but now he's old enough to have a 9th grader.
Unfortunately I'm not actually a studio executive, but hopefully somebody on here is and will see this and pick it up.
I taught Pre-Algebra in a Title 1 charter school in New Orleans from 2016-2019. Most students were two or three years behind grade level. There's been a considerable shift away from what opponents describe as "drill-and-kill" pedagogy. I've never been convinced that any student can develop critical thinking skills in numerical analysis without having a rock-solid foundation in multiplication and ratios. Unfortunately, too many in the education space think otherwise. This seems similarly related to the debate about phonics.
I find it quite frustrating and counter intuitive. Anyone who's trained in music or sports knows that you have to have the fundamentals down pat before you can even start doing anything complicated or interesting. Same goes for math and reading. It's not fun, but you have to do it.
I am a full-time musician, drummer, and I agree completely, that you need to have the fundamentals of playing the instrument down ice cold, starting with how you hold the drumsticks correctly. Everything builds from there.
Here's a question for any other musicians who teach: Have you noticed that students that are in the 5th and 6th grade, have a hard time writing out musical notes on staff paper? They don't teach cursive writing in a lot of schools anymore, so you don't get that fine muscle development in their strong hand. Having that fine muscle control in your strong hand, throws a switch in the brain, that allows your weaker hand to develop a certain level of the same fine muscle control. Thoughts?
I mean, one reason you don't see teachers intensively drilling individual students using flash cards is they have a classroom of like 50 kids to teach math to; drilling each one in turn until they got it would take too long. And what would the other kids do while they were waiting their turn, or after?
I suspect the education space, particularly at the academic theorist level, tends to attract people who disproportionately do not love, and sometimes even resent, math.
There are a disproportionate number of articles written about why we need more women or POC or anybody in STEM written by people who aren’t in STEM.
The military adage "those who cannot do, teach" comes to mind often when I look at the education space.
When I was a first-termer in the Air Force, we used to say, "Those that can do, do. Those that can't do, teach. Those that can't teach, administrate. Those that can't administrate become officers."
I'm retired Air Force. What did you do?
I was a musician in the Air Force. The drums. 2 years in a career field band at McGuire AFB in NJ, and 24 years with the premier band, The United States Air Force Band in Washington, DC. I retired as a SMSgt. I tested for Chief, didn't make the cut, and was at top cap, so welcome to retirement and the second career, which was playing music and doing some private teaching. Until Covid, I was playing regularly, and was scaling back the teaching. Once things get back to normal, I'm finally going to sign up for some space-A flights, and just go where the planes go. From there, I'll find another hop to somewhere else. If I want to go to Germany, for example, I don't need to fly into Germany. I can fly to any base on the Continent, and then take a train the rest of the way. I really want to see Berlin again.
Eh, I wouldn't be that harsh. There are lots of great teachers out there at the practitioner level, including math teachers. And it's a pretty diverse (personality-wise) profession. I'm really just talking about *education policy academia* which is dominated by folks within a narrow range of personality types.
Which schools? I have this vague memory that there were some very successful charter schools in New Orleans that utilized direct instruction and were pretty successful.
100% can confirm. My wife has a PhD in Nuclear Engineering. Her Dad drilled her with flash cards growing up and made it a fun game. She would not be where she is today without that.
I’m more of a liberal arts guy, but I still remember my “times tables” from school - I can visualize them.
With my own kids and their assignments I had to figure out what gimmick was being used - often some combination of groups of dots. Some of the methods were clever in a good way, but I thought a lot of it was just crap. We got flash cards too.
At the schools here where I’m at still use simple tests to measure speed and accuracy for the basics.
Speed and accuracy are underrated. I probably should’ve emphasize that I did not consider a kids with mastered anything until he could see it within a split second. In our games, any hesitation was a loss for the kid.
Back in 1960 when I was in first grade, our class was chosen for a new method of teaching math called the Cuisenaire Rod System. Consequently, I struggled through math all the way through high school, barely passing Algebra 1 and Algebra 2. I didn't even attempt Geometry. Out of the colleges that accepted me, I majored in Music Education, I chose the one that allowed you to either take a math or science course, rather than both. I thought I was in the clear after taking a course in Environmental Biology, which had no math, just a bunch of theory about how to make cleaner water.
After 3 years, I left college, because I wasn't sure that I wanted to continue becoming a music teacher. I spent 2 years studying privately with a teacher in New York City, lived at home in my parents' basement (literally, because that's where the drums were set up), practiced 6-7 hours per day, and landed a gig with the Air Force. I spent 2 years in a regional band, and 24 years with the premier band in Washington, DC.
I decided at about age 40 to go back to school. I was accepted by the University Of Maryland as a music major. One of their requirements for a BA in Music, was a course called Finite Mathematics. I knew there was no way that I was going to be able to pass a college-level math course, so I hired a private math teacher.
At at our first meeting, she gave me a math test that started at 1+1, and continued all the way up to some advanced form of Calculus. She said, "stop when you no longer understand what you are doing." It didn't take long. She told me that I had fallen down on the development of basic math skills somewhere between 1st and 2nd grade. No wonder I had struggled all those years. She started me right from the beginning with the basics. Addition and subtraction drills, multiplication and long division, fractions, sets, etc. Once I had the basics down, the rest of it suddenly became fun, rather than my remembrance of 12 years of public school math torture. Yes, I was a victim of the so-called "New Math." Now, they have this Common Core math, where there are at least 10 steps to get from 1+1=2. I maybe be exaggerating, but you catch my drift.
Once I had the basics down, the rest came naturally. It's the same thing when learning a musical instrument. You have to have the basics down cold, or you won't progress anywhere.
my kid got optional homework from Kindergarten with the teacher saying "you can really tell which kids do the homework." And it's like ... are the kids who really need it going to be the ones who do it?
I’m actually anti-homework. Except for maybe a small amount of mastery.
Agreed, beyond phonics and the times tables, every kid is better off in the back yard with his pals sucking up dirt and looking for bugs like EO Wilson.
As long as the dirt doesn't have lead dust in it.
Me too. We moved here (Colorado) three years ago youngest was in an elementary school with a no homework policy. So refreshing after dealing with the stupid make-work of previous schools. But he started middle school this year which has homework and the adjustment has been….difficult.
yeah i don't think its massively helpful but i appreciate seeing what she is learning at school anyways.
Yeah, currently hitting a brick wall with IB algebra with my 15 year old. She has never been great at math, but typically in the "meaty part of the curve" and having helped her through some homework recently the fact she didn't have memorization of times tables and so on drilled back when she was little definitely isn't helping. Also 100% agree on the flashcards although I didn't really use them myself, I pretty much improvised something equivalent with my mother back in the day.
Make sure you get a pack of flashcards that does not duplicate. That means it has 3×4 card, and 4x3 card.
She needs to be able to spit them out with in a split second.
Then, once she can do that 100% of the time. Start showing him cards with the answers. And then make her spit out all the combinations that make up that number.
So for instance. 12 is 1x12, 2x6, and 3x4
She needs to be able to do that by mastery as well.
There are obviously other rules and tricks to learn. But if she doesn’t have to think about these with her work in memory, chicken be more likely to learn the other stuff.
Best of luck, I have been there before.
I remember my kids taking exactly that course. After spending money on a tutor (a retired HS teacher), we received the advice you offered here- get your basic math facts down cold.
In hindsight, it seems so simple and obvious. Yet, after decades of mass wars and arguments about education… Kids are still not learning these basics.
The argument was always that the basics are not fun. My warped mind also believes that our education system is designed to fail a certain percentage of our population, so that they can become "clients" of the social services industry.
I am not that cynical.
My thinking is its really hard for many people to think outside their priors.
Hardcore partisans have this issue.
I just think a certain number of teachers are either so naive, or so jaded they are unable to consider alternatives to how they "want" the world to be.
I'm of the...play the game with the rules you have, not the rules you wish you had mentality.
Hell yes. Memorization saved me as a first grader, and I haven't looked back since.
My elementary school did the group competition thing with flash cards and really drilled the memorization of arithmetic through the 9s. We learned the theory behind it AFTER so that it could be extrapolated to bigger numbers.
As I'd said earlier, I come from a family of educators and married into a family of educators. My mom taught high school and her biggest frustration was trying to teach literature and writing when so many students lacked even elementary-level reading and writing skills. I think outstanding teachers manage to identify and remedy some of those deficiencies on the fly but it really shouldn't get to that point.
Good story Rory. My grandfather, who rode a horse every day 10 miles to a one-room schoolhouse, memorized the times tables up to 25 and used to practice them in bed as a way to go to sleep. He died at 99, still sharp, 23x19 on his lips as the family legend goes. Your story of what you did for your daughter's math struggles resonated with me, because it so mirrored my experience with my daughter's English struggles. Public schools are important, but there's no substitute for engaged parents paying attention, having flash cards when needed, and the importance of memorizing the basics.
All day I've been trying to figure out if this story was serious.
The best way to make reading relevant to a kid is to give them and ipad and make them use google to find the content they want. my second grader reads very well but has almost no interest in books. he prefers articles on whatever interests him at the time
When I was growing up we had a set of encyclopedias. I would spend hours looking up subjects. Cowboys or tanks or how an internal combustion engine works.
It’s amazing how much knowledge we have in our fingertips now.
We had these too. Also an atlas-type thing with two pages on every country in the world. I also clearly remember getting the new Guinness Book of World Records every year at Christmas and reading it cover to cover.
Also, in 3rd grade, every morning we did a "Mad Minute" worksheet of multiplication questions that you could only progress from once you hit a certain score multiple days in a row. We must have stopped at 10s because I'm really not great at multiplying by 12 but have had the rest down since then.
I went to elementary school in Minnesota in the early '90s and could absolutely not learn to read well with the "whole language" instruction given. My sisters kind of intuitively learned phonics, but I wasn't having an luck with that. It took me just a couple months with Hooked On Phonics to catch up the summer before second grade, admittedly because my language comprehension was way above my reading level since my mom read to me so much. If my parents' hadn't invested a lot of time and effort in enrichment activities, I'd probably be slinging a mop at McDonald's and hardly be able to read my bank account app instead of holding down a lucrative position in a STEM field.
So, I don't trust the schools basically at all with my son. He's getting extra home instruction and tutoring right off the bat. I want him to hit the hard stuff and fail before he encounters it in real school and gets a bad grade. I also disagree with the homework policies I've seen with my friends' kids. For me, sitting your butt down and doing some crap you don't want to do is a skill in itself and one you should start building early.
I’m anti-homework. But that’s a whole different debate.
Do you have a link to a good argument for that? Just curious what it is from someone who seems reasonable and thoughtful. I have heard it doesn't increase performance at grade level skills, but that's not particularly why I see it as important.
Call Nell it’s not that I am zero homework. But I feel that the purpose of homework should only be to reinforce what a child has learned in school. For instants in my example above, having a kid come home and do a couple of simple multiplication sheets would be good.
Too often, teachers underestimate the amount of time and effort it takes to do some of these homework assignments. And then I’ll forget the kid has multiple classes here imagine if the teacher games 30 minutes of homework, and four other teachers give 30 minutes. Now your kid is trying to do 2 1/2 hours of homework in the evening when they really should be playing.
Then if you’re like me with a bunch of kids you have seen some just terrible homework assignments. Think… coloring a picture for history class. And every diarama ever.
It got to the point where I would simply tell my kids teachers no.
If they had homework that took more them 20 minutes, I would write a note on it. Include district guidelines.
What’s even more telling is when u have two kids in same class. One has lots of homework. One doesn’t. And the kids learn the same stuff.
My absolute worst moments as a parent have been at the table trying to teach my kids some subject. Kids crying. Me frustrated. I think back and cringe.
It’s the teachers job to teach. Not mine.
https://stophomework.com/the-case-against-homework/
Just Google “case against homework”
There's also the question of if it improves conscientousness.
https://www.learningandthebrain.com/blog/homework-improves-conscientiousness/
__Preliminary__ results from this study: yes.
But that is preliminary, and maybe it's the case that doing 1 hour of homework every night is great for this, but doing obvious busy work after that is not.
Note that willingness to buckle down and do the work are important life skills, so homework could be helping with this.
I know that college is really punishing to those who haven't learned to just sit down and do the work, since the teachers won't help you with that. Maybe that's good/bad, but (at least when I attended) it's how it was - so being used to doing the homework you're supposed to do is good.
(I agree that 2.5 hours a night seems excessive - what if you're also practicing in band or for sports or whatever)
Sorry about the grammar. I’m on phone. My eyes suck.
As a lawyer, the pipeline problem looms huge because firms get beaten up over their racial demographics, but at the end of the day there's very little firms can do to fix it at their end of things because the "pipeline" is so long -- to be a lawyer in most states you have to have passed the bar exam (black and Hispanic law students have lower bar pass rates), to take the bar exam in most states you have to have graduated from law school (black and Hispanic law students have lower graduation rates), to attend a law school you generally have to have graduated from college (black and Hispanic college students have lower graduation rates), and to attend college you generally have to have graduated from high school (black and Hispanic high school students have lower graduation rates).
So, you get proposals to do things like abolish the bar exam or convert law schools to one-year plus apprenticeship type programs, but realistically that isn't going to change the total numbers all that much because you need to significantly boost the numbers coming up from college, which in turn requires boosting the numbers coming up from high school.
We have that issue in medical education too (mostly residency level). We are VERY pro-DEI and strongly recruit applicants from underrepresented groups but that pool of residency applicants is too small. It's hard to win a national recruiting battle against Harvard affiliates, Stanford, etc.
We now aren't allowed to use USMLE scores as a screening tool (which, fine, I understand the argument) but it doesn't fix the underlying pipeline issue that likely has the greatest impact. The real work isn't about recruiting the superstars. It's about diversifying the ranks of the more-average trainees. There's no quick fix for that.
I vote for science as having the most intractable version of this problem, because the pipeline features all of the above but also faces a compounding problem related to alternative endpoints. To get a top-tier scientist job you need to do the college, master’s, phd, postdoc thing, but throughout that process there are always options to offramp to a middle tier job that pays well but not nearly as well as one for someone who goes the distance. A law school grad doesn’t have a ton of options other than pressing on or giving up completely.
In practice personal wealth plays a key role in scientific advancement, because talented people from a poor family are under enormous pressure to cash in without reaching their full potential throughout the whole process.
At least anecdotally, it seems even worse than you say: those jobs at the end of the offramp tend to pay far better than their academic counterparts, which only adds to the appeal of cashing in for those who aren't already comfortably off.