New York algebra fact of the day

Take here in New York, where in 2016 the passing rate for the Regents Examination in Algebra I test was 72 percent. Unfortunately, this (relatively) higher rate of success does not indicate some sort of revolutionary pedagogy on the part of New York state educators. As the New York Post complained in 2017, passing rates were so high in large measure because the cutoff for passing was absurdly low — so low that students needed only to answer 31.4 percent of the questions correctly to pass the 2017 exam.

That is from Freddie deBoer, who has returned to writing, and who argues lower standards and higher graduation rates are a good thing, all matters considered.

And here is another education result of note: “We estimate a dynamic model of schooling on two cohorts of the NLSY and find that, contrary to conventional wisdom, the effects of real (as opposed to relative) family income on education have practically vanished between the early 1980’s and the early 2000’s.”


Easy: Streaming is the answer, with vocational or commercial training, rather than academic training alone as choices for High School. Many years ago we were already there. Then college as signal took over.

Schools don't do much vocational training, and you can't teach a vocation on line.

Watch as much online as you want on welding, then prove it works by passing the welding tests needed to build submarines, carriers, or even Budweiser brewery plumbing, chemical reactors producing petroleum products, plastics, corn oil, ...

Or hell the frame of a 2nd hand go cart

Excellent post. I certainly appreciate this website.
Keep writing!

I agree that America needs a lot more vocational training. Most jobs do not require algebra. People who are not good at algebra should learn something else that is useful.

The college track worked great for me as an engineer, and I enjoyed algebra. But my friends thought I was weird. They were bored by school because it was not teaching them skills that they would use later.

Most people won’t graduate from college and we should not prepare them for college in high school. For the 60% of people who won’t get a university degree, the last 2 years of high school should be vocational training for a job that the student is interested in doing.

This would be an effective way to reduce income inequality, grow our economy, and give more people a sense of purpose in their life.

I have a BS in Computer Science which required enough high level math to have gotten a math degree. I retired 20 years ago. Used algebra very little and calculus not at all. I have never even heard any of the higher level math being mentioned once I graduated. Math for 99% of the population is over rated.

Mathematical reasoning is basically logical reasoning, and studying math helps that part of your brain. So even if you never have to calculate the area under a curve, studying math helps develop the logical, reasoning part of the brain, as well as comfort with abstractions.

Prove it! I suspect at best it is the other way around. That is people who are likely to look for answers and are curious are attracted to math. I was attracted to math and honestly when I was young I believed exactly what you have said. But the simple truth is in life and work you almost never use it. Exceptions of course for engineers etc.

I've seen a VR welding-training rig, and while it wasn't off-the-shelf tech it may be the case the VR can do welding.

If not VR can definitely augment training in other disciplines. I mean hell, "job simulator" is a bestselling VR game on steam right now.

our local school district has a quite good technical+vocational

You can type "2x +3y = 72 solve for y" into Wolfram Alpha. It works so all is well.

If lower standards and higher graduation rates are a good thing, then why doesn't New York simply issue high school diplomas with their birth certificates? Who knows, they might even save aarge chunk of the $22,300 (!) they spend per student let year.

I always think of this solution as the scarecrow solution since it worked for the scarecrow in the movie version of the Wizard of Ox.

+1, clearly it's one of those arguments that can only be taken in moderation. Does the author quantify at what level lowering standards is acceptable and where the break point is for it to become not acceptable?

the effects of real (as opposed to relative) family income on education have practically vanished
Why all the null hypothesis in education? Simple, one axis dominated parental involvement. Active parents skew the distribution of effects, dominate the positive effects and leave barely observable activity for the other Godot theories. Watch the percentage of parental involvement relative to students.

Matt Young---

I might go even further than you. Take 10 high IQ kids and place them randomly in families and see how they perform. Pretty well, i would bet.

Public schools should teach civics, the basics, and try to give it a chance to everybody. On the other hand, many graduate schools should be folded into the four-year education. Such as, why not an AB at law and then pass the bar exam?

Pretty obvious conclusion to draw.

As the signals get weaker, the returns go down. More resources are spent in a zero sum signalIng game, with the only winner the education industry rent seekers

And why they have such low GRE scores.

Algebra is overrated. Texas dropped it for a reason.

Texans decided that math goodies like solving systems of linear equations, quadratic/cubic/logarithmic/exponential functions, and interpreting a regression line just isn't worth it.

I mean, there is an argument that in today's world, something like statistics is way more important than algebra and geometry.

Statistics is largely algebra.

Learning how to reject a null hypothesis is not algebra. I think learning to think that way—identifying what the null hypothesis is and the strict requirements for rejecting it—was one of the greatest life-tools I learned from all of my education.

Okay there is a slight bit of confusion that needs to be cleared up. GWB you are referring to algebra 2 (usually 10th or often 11th grade) but the post Tyler shared is saying students can’t even pass algebra 1 in High school. I’m a HS math teacher and I am all for waving Algebra 2 as it is often an albatross around Struggling student’s necks. But algebra I measures whether they can solve a two step equation, solve a proportion, and understand the basics of linear and exponential functions. I would argue they should need to be able to master the basics of that to earn a diploma.

Matt indeed that is true which makes me think the stats course being used a substitute is not very rigorous.

Requiring (seriously) passing Algebra II to graduate from high school is just cruelty to lower IQ students.

My theory is we should have an Associate's High School diploma for 16 year olds after 2 years of high school who aren't juvenile delinquents but who wouldn't learn much in their last two years of high school.

I think you've re-invented the distinction between the English GCSE and 'A'-level. Presumably many other countries have some equivalent.

I may be a bit out of date on this: I try to avert my eyes from progressive reforms in the schools which seem to be universally intended to bugger up schools as places of education.

Steve, I think the real question is how much education it makes sense for different sections of students to pursue. The system as it is setup obviously makes sense for high achievers. You somewhere between 4-8 years after high school of additional education to become a skilled professional (years vary by profession). But not everyone can achieve that certification. Should they just drop out early? Or does it make sense to keep teaching them, just with a lower, more realistic bar? I don't have the answer to this question, but I also don't anticipate any reform in this area is going to try to answer this question. As I see it, our society is pushing for at least a HS degree. Fine, lower the standards. Then we have variability quality diplomas depending on the higher education path you pursue. Also fine. The current situation doesn't seem too terrible, in my opinion.

I'm guessing that this is prior_approval, who once again, didn't read his own source .

"Algebra is overrated. Texas dropped it for a reason."

Then he posts a link that indicates that Texas still requires 1 year of Algebra but dropped the requirement for a 2nd year of Algebra as a state minimum requirement for a HS diploma.

we are betting you are correct

Is that why Wall Street banks fail every decade? They can't handle a little algebra.

Actually, they can handle the Algebra. They usually mess upon the stuff in the "easy" Statistics course De Boer advocates.

What if high graduation + low standards is a gimmick, the idea being that now you need a graduate degree to have actual, certifiable, skills? Could that mean more money for more educators, without more actual education overall?

Well, our tether to reality has regressed from actual violence is violence, to speech is violence, to silence is violence, so a failing grade is violence is probably on the way.

Coming to a med school near you soon.

I'm guessing that the undermining of efficient institutions will stop just short of medical schools and airline pilot training. :-)

Don't know about pilots, but the med schools started caving to diversity initiatives (including affirmative action) some time ago, so we are already well on our way to compromising standard of care to avoid hurting people's feelings.

Of course, as our engineering friend above will likely agree, most of these professions could easily be taught on the job with an apprenticeship model. So if we have to kill a few surgery patients and crash a few planes to finally rid ourselves of Marxist universities and their near-compulsory leftist funding racket, perhaps that's an acceptable price to pay.

Here’s a similar article on med school

I was aware of the med school problem. But they ain't graduated from residency yet! There will be intense statistical discrimination by all races. Apologies. Reality sucks. Especially scarcity.

Sorry to tell you I had a meeting recently with the senior surgeon at a prestigious cardiac surgery program and he told me his current graduates aren’t ready to do cases alone d/t the accumulated changes in residency training over the last 10+ years. He said they need training beyond their fellowship to work independently

Immigration restrictions are a much bigger obstacle to meritocracy in medicine than affirmative action. I know people who were accepted into top residency programs and then couldn’t get visas at all. At least people who lose a spot to affirmative action would probably end up attending a slightly lower-ranked program and make it up later in their career.

Need a Doctor?
Medical school admission is uncommonly competitive, there being many more applicants than slots. The competition is so intense that if black applicants were held to the same admission standards as whites and Asians, we would turn out almost no black physicians.

We now have a double standard for admission to medical school brought about by affirmative action. As a result, two tiers of American physicians have emerged separated by race and ability.
We have seen that law students admitted under affirmative action do not measure up to their white and Asian peers as law-school graduates. Can we say the same for doctors? We will quantify the performance gap for physicians.

A benchmark for medical competence is the National Board of Medical Examiners (NBME) Exam Part I. Every medical student in the US must pass it to become a physician. Students take the exam two years before graduation. It is one of several ways the profession keeps itself honest. The most comprehensive study of NBME pass rates was published in 1994 by Beth Dawson et al (JAMA 1994 272:9 674-9). The authors examined the performance of every medical student in the US taking the June exam for the first time over the years 1986, 1987 and 1988. Dawson and her colleagues found that white medical students passed the NBME test at a rate of 87.7 percent and blacks at 48.9 percent. Again, using methods described in Appendix A, we found these pass rates equivalent to a black-white mean difference of 1.19 SD. Mean differences for the bar and NBME exams are conspicuously similar. The one-plus SD gap does not yield easily.

Notably, when Dawson's study looked at entering students with similar academic credentials, the pass rates on the NBME exam were independent of race, pointing an accusing finger directly at affirmative action. For all its good intentions, affirmative action has created two levels of competence in American medicine, separated by a bit more than one standard deviation. When you are wheeled into the ER at 2:00 a.m., if you pray, pray that the black doctor who greets you entered medical school through the front door.

well its obvious that the text itself is racist, right?

according to leftist wingnuts Science is racist

“according to leftist wingnuts Science is racist”

Reality is racist.

leftist wingnuttery is not reality

If the NBME eliminates unqualified medical school students, and we know the black doctor in the DR passed it, why should we be concerned? Blacks with high IQs are just as smart as whites with high IQs. I've worked and gone to school with some.

+1, Good point, as long as the requirement for the NBME isn't being bypassed or relaxed, then it would appear that the downside is limited to a lot of younger med students who aren't qualified taking up slots in the program.

“If the NBME eliminates unqualified medical school students, and we know the black doctor in the DR passed it, why should we be concerned?”

Just barely passing the exam on the second try is just as good as easily passing it on the first try? Right.

“Blacks with high IQs are just as smart as whites with high IQs.”

Do you know anything about the tail behavior of normal distributions?

In law, black associate attorneys are much more likely to make partner than Asians though (although still less likely than whites). There is a lot more than affirmative action going on—it’s hard to say whether blacks really do not measure up in later career performance or whether forms of racial bias carry over into evaluations of career performance.

Is there any evidence that the intelligence of your above the level of black MD's matters much?
I doubt it. It's not a math problem.

“It's not a math problem.”

The NBME is not a math test, either. I suspect that someone who has trouble passing it will not be as good at diagnosing medical problems as someone who passed it easily.

Feel free to believe that all MDs are equally skilled.

Cultural affirmative action is still allowing Trump-authoritarianism supporting doctors like Sure to practice medicine. Terrifying, that people completely divorced from Science and Reality are allowed to practice medicine.

Revoking medical licenses and imprisonment of Trump supporting anti-science doctors would be a good first step towards truth and reconciliation once we overthrow the Russian puppet

That was funny. Someone is angry-nice try at the status lower.....


I didn't know they were still adding words to the newspeak dictionary.

" supporting doctors like Sure to practice medicine. "

That's pretty much the definition of an ad hominem attack.

if we get rolled into the e.d.
we actually sorta hope Sure is working there

professional government experts know best... no matter what the field,

the education field is totally dominated by federal/state/local educators, administarators, staff, and politicians ... because the private sector lacks the expertise & high motivation to properly educate the young.

pay your taxes and be silent /S

Wouldn't it be better for Tyler to indicate why it one should pay attention to this guy -- or is it just some random piece of flotsam on the internet?

Pretty inane of deBoer to argue that diluting the value of marks of accomplishment is something to celebrate. We should get revenge by discharging humanities faculties and putting him back in the unemployment line.

What we should be doing is replacing the high school diploma with a book of certificates which indicates the bearer's level of accomplishment in each of a set of courses of study as measured in annual regents examinations. As for students in secondary school, about a third should be improving their literacy and arithmetic to accomplish to a level their peers managed in primary school. Another third should be taking VoTech courses. Of those taking academics and the arts, some might take courses in five subjects and some just work on one or two. Any thing that can reduce the number of English teachers is to be welcomed.

1. First they dumbed down high school to improve graduation rate. The problems bubbled up to college, now we have to push everyone through to the end of college. Next step, graduate school, where GRE scores are already being questioned (as if the GRE is anything but an entry level test)

Not everyone gets to start at the same line in life. But keep on correcting at every stage of the process, and eventually even runners in the olympics will be given a handicap pass to run against U. Bolt

2. Statistics easier than algebra ? That truly must be a ridiculous course, not worthy of the name. First, trying to do "statistics" without algebra is like trying to eat water with a fork -- technically impossible. Bit hard to explain why removal of a prerequisite as opposed to its partial provision gives better results. And as for abstract complexity and subtlety, probability is much harder than algebra -- which is why probability questions are commonly used to weed out graduate students and job candidates in job interviews -- even today there is debate about Marilyn Vos Savant and the Monthy-Hall problem.

So yes, agreed, teach 'Statistics' rather than 'Algebra' is just a fancy way of saying 'don't teach'

3. Finally, the massive discrepancy between performance in eg Singapore and in the US shows algebra is likely not the issue, so much as the fact that the education specialists and text book industry in the US have made a mess of algebra and math teaching, and evaluation. No doubt whatever 'simple' course is prescribed, will be turned into a thicket of thorns once selected as 'core'

Why not deal with core issue: if we are to educate, do it well, if we cannot, pass. But don't pretend there is a middle way.

Yes this is exactly correct. I’m a HS math teacher So I teach these subjects. Replacing algebra with a statistics course means that it is a remarkably Watered down stats course. A reasonably rigorous and appropriate stats course is not easier for students than algebra. This really is just meant to water down any math requirement.

But is not a watered-down statistics course more useful as preparation for citizenship more valuable than an Algebra 2 course that a poor math student would flunk or just barely pass?

The question is irrelevant. We should hold our citizens to the highest standards and recognize and reward differences in achievement to these standards.

Anything less promotes mediocrity.

All things being equal, if you want a high passing rate, it's better to make easier test than lower the passing grade. Students feel the hypocrisy and will feel like a fraud even if they pass. Of course then a ridiculous easy test makes the administrators look bad.

School diplomas should be handed out automatically to all. It doesn't matter in the slightest in life, so why make a big deal out of "graduating" or not?

No shit.

Tyler would be happiest if we just handed out cards saying "Congratulations on turning 18. You are now a High School Graduate!!"

Regarding the second article, my initial reaction was that the US became sufficiently wealthy, and higher education became sufficiently available (a strong majority of high school graduates attend at least some college nowadays), that education to a good extent is available to anybody who's motivated enough and smart enough to go get it. Sort of like how cell phones initially were a good bought mainly by the elite, whereas now they are widespread regardless of income level.

Income is not a strong determinant of whether you have a cell phone (except for the very lowest levels of income), and according to that article it's not a strong determinant of your education level.

And then the rest of the differences in education level are due to social sorting i.e. relative income rather than absolute income.

But my second thought was given the stagnation in real incomes for most Americans since 1980 and the sharp rise in the cost of public colleges (and the relative decline in state funding for those colleges), is college really less scarce than it used to be? In 1980, an 18-year old could still hope to work their way through college by working part-time and attending a low-cost public college. That's a lot more difficult now. Maybe student loans are filling the gap? That is after all their purpose but in recent years pundits and policymakers have been decrying the growth in student loans.

So I'm not sure what to make of that article; how plausible are it results, and if they are valid then what is the explanation?

For 100% passing rate, those with low g factors should just be terminated. We must improve the population.

That's probably the fastest and most effective way to get to Tyler's morally-mandated rapid growth rates. It's a ghastly crime against future well-being to not do this.

I find it even more shocking that about 1/4 of the students still couldn't even pass with a 31.4% the cutoff.

The reason that it's shocking you is that you're trying to directly compare a fraction and a percent, which is impossible. If you write it properly, then you'll see that actually 1/4 of students couldn't pass with a 31/4 cutoff, which clearly makes a lot more sense. You can trust me because I graduated from Frederick deBoer University with a major in mathematics and a minor in internet trolling.

That had better be 31.4159% of the questions -- can Freddie please check? If NY lower it any further, they should go straight to 27.1828%.

Your comment is irrational.

On the contrary, the wisdom in Richard T's comment transcends human understanding.

Oh wait, my bad, not rule. Suck.

University degrees are like belts in martial arts.
They don't mean as much as you think they do.

I wonder how many libertarians here bemoan the lowering of standards. Shouldn't they be happy?

Why would libertarians have any particular position on how rigorous testing standards should be?

Without knowing how hard the questions are, the required rate of correct answers tell us nothing abot how difficult the exam is.

Finally we have a winner!
Pretty much every poster so far has assumed constant difficulty of the questions. We have no evidence of that. Further, if you want to test to truly discern difference in ability, you want to be sure there is a spread of results. Everybody getting a perfect grade tells you almost nothing.

If one every wants to determine how realistic anyone's education plans and proposals are, just ask them what percentage of high school students are capable of doing calculus. If someone answer that all high school student or even most high school students can learn calculus, then one knows to ignore everything that person says about education.

In all my discussions re: public education, I’ve never heard a single person suggest all 18 year olds are “capable of doing” calculus.

Nobody is saying that. But every kid should be able to “Pass” remedial calculus with just effort and memorization. Some semblance of AP BC calculus should be the highest standard, with A+ students being the most capable at the subject while anyone earning a D in remedial calculus should still be allowed to graduate.

Effort makes a ton of difference in high school success (academics, sports, dating, video games, whatever).

I had the “privilege” of going to one of the toughest-grading public schools in the country (highest SAT scores, second-lowest GPAs in the state). You could *easily* earn half the credit on a test just through memorization. I suspect the non-top-track classes were even more heavily weighted towards memorization (and had less material to memorize).

While not perfect, I like the idea that grades are weighted towards intangible student qualities (natural aptitude, effort, dedication) while standardized tests capture student mastery.

Judging student quality becomes impossible when grades become relative and standardized tests are abolished.

Now, if my goal was to eliminate any ability to independently objectively compare students and instead have “blind” admission panels do our sorting... well then sure, let’s replace calc II with stats, pass everybody, and make the SATs optional.

Go ask any high school math teacher if 90% of the students can be taught to look at a math problem, correctly identify which rule/algorithm to apply, and them have the student apply the algorithm. The teacher will look at you like you are crazy. Too many teacher have stories of how student learn fractions by rote on month and then cannot do them the next most because some other memorization has taken the place of the rules they memorized for fractions.

Memorization is integral to learning. It’s not the only thing though.

Additionally, when kids cheat or cram, they’re not actually memorizing... even if they can pass off success for a while, they’ll ultimately be too far behind.

I washed out of piano lessons because I could memorize patterns and play be ear, but didn’t actually spend the time to memorize how to read sheet music (and practice hand-eye coordination in sync with reading).

I deserved to flunk out of lessons, which I did (and regret). Kids deserve to flunk out of school when they don’t do the work. My piano teacher simply telling me I *could* play piano doesn’t change the fact that I *couldn’t* anymore than changing high school math requirements doesn’t change the fact that 90% (by your estimate) don’t know high school math.

If we believe high school math is important to graduating from high school, then this kids... shouldn’t graduate.

I did not say that 90% of students could not learn. I use the 90% lee to determine how unrealistic people are when it comes to education.

There are many people who believe if the teachers are good enough, if enough resources are spent of the students, if the students are properly motivated, then all of the students can learn calculus (or Mandarin Chinese, play the piano, etc).

What ever high school math teach knows is that some students have a real aptitude for math and some students have no aptitude. Tyler Cowen knows this and shows it when he ask all of his academic podcast guest how they spot talented students.

Public schools used to spend as much time trying to identify students with academic aptitude as they would spend on sports. However, since the schools were embarrassed about the demographics of their talented students, many of them work hard now to not notice talented students.

I read some points around the time of the housing meltdown in 2008 that have stuck with me.

The government tends to confuse levels of success and markers of success. That is, people who achieve a certain level of productivity can buy a house. But to the government, the goal isn't to ensure that you have achieved a certain level of productivity. No, their goal is to get you in a house regardless of how productive you are. Of course, when things to south, you are much more likely to lose that house, ruin your credit record and screw your life in the process.

Education is like this too. College should be set up for the top 10-20% of society. Make college hard so that for every 10 you admit, you are flunking out 2-3. Because the goal with college is to create future leaders for society. We don't want our leaders to have simply gone through the motions. We especially understand this with engineering--nobody wants to drive on a bridge designed by a person who doesn't really understand statics and dynamic.

But as is typical with government, they look around and say "Why do some people have so much money? Ah ha! It's because they went to college!" and like some cargo cult medicine man, the gov decides everyone should go to college. And then, they will have more money. But when people struggle, you're only real choice is to dumb-down the curriculum. But that's hurting the original goal of college: To build better/smarter/well-rounded leaders that are steeped in the successes and failures of history.

A high school diploma is now worthless because this exact activity. Because idiots in gov saw high school graduates earned more, and so they decided to give everyone a degree, even if they couldn't read. Wrongly assuming that it will help people earn more. It won't.

And now, we're seeing the cry that black people need to be given easier grades in STEM and much of college. How embarrassing for black people. How racist of those making this case. It's almost like it's designed to humiliate black people in the most overt way possible. You can almost hear the well-meaning racist from the Jim Crow era arguing the exact same thing.

Sadly, schools are going backwards in that way. In the 1960s C's were normal grades at Stanford and Harvard. In the 1980s Caltech was the only top school where that was normal and where one third couldn't graduate. Today all top schools fight to make sure all their admitted students can finish. And almost none have minimal tough course requirements for all students that can guarantee some degree of minimal knowledge upon graduation. You need to rely on markers like finishing in STEM or engineering, with their being a wide range in rigor from bio to physics. And of course virtually no humanities majors are tough and have high standards anymore.

Someone in Government, above the school level, decided that students would need to pass algebra II to graduate from my son's high school. So someone at the school level created a class I call, algebra II in name only. It work out OK for my not good at school son.

Med school, or other school, completion is only one step in a process.
Getting hired, then hired again and again, is another one.
Visualize, if you will, that interview panel peppering you, or your kid, with questions designed to ferret out any non-PC thinking.
At least you made it that far.
Other candidates got weeded out, say, upon discovery of their social media posts, embarrassing photos, retweets or similar marginalia.
When you've seen it happen, your trust in that institution tends to decline.
Lower-trust societies seem less appealing.

Wow. So, why exactly did we fail the other 28% if such a low bar is a "good thing". Why not pass all 100%?

I am completely open to the idea that algebra is a skill you won't use the rest of your adult life, and so shouldn't matter for getting a high school degree or advancing, but the answer isn't to pass so many people with such poor skills in algebra.

I don't think they necessarily explained to us very clearly what the jump from doing math with numbers versus doing it with symbols represented - perhaps it seemed too obvious to adults. But as far as the rules of algebra went, my teacher - whose name I've forgotten but I can hazily remember her face, and the way she never seemed stressed out, which communicated itself to her nearly-all-white "honors" class (though schools were of course desegregated in Houston, TX by then, throughout I tended to have more African-American teachers than classmates) - explicated the subject unusually clearly. She also had a gift for organization and order, and what is rare in a teacher, a lovely hand when she wrote on her well-scrubbed board. (Seeing math written messily is so painful.) I think it was partly her beautiful chalkboard, but also the restrained but emphatic way she rewarded effort, that made us all so eagerly competitive to see our names on that board, under our scores (she would list the top finishers by score - 110, say, because there was a bonus; 108, and so on to 100).

Algebra may be superfluous for most kids, but I can't imagine statistics being easier.

I can't really imagine algebra being the significant problem with school at all, but it's a novel take I guess.

Certainly I can agree it's ridiculous that anyone should be penalized by having their diploma withheld for failure to grasp algebra, however. A cruel notion that would only occur to a thoroughgoing egalitarian.

"1980’s and the early 2000’s."
Brought to You by the Committee to Save the Apostrophe from Abuse

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