Pasadena public schools has a math academy https://www.mathacademy.us/ that teaches kids up through AP calculus before high school. When thinking about relocating to the bay area I was shocked to see that math acceleration is actively discouraged and even the main math curriculum seems to be decelerated from the standard
The bay area has hundreds of school districts with different math acceleration programs. There's no single standard or even an average approach as far as I can tell. San Francisco was very unusual in refusing to do any acceleration before high school at all.
I can see how to push Calculus down to 8th grade, but you have to drive the elementary school coverage a bit for that. I get my youngest daughter to take calculus - for college credit, in 10th grade. It was taught by one of the math faculty members from a local college. But there was a big problem with the school system - the high school was required to teach students 3 years of math - clock time. She skipped 8th grade so to get her ready for calculus in 10th grade I had her do Geometry by correspondence over the summer before 9th grade, and pre-calculus by correspondence over the summer after 9th grade. She got placement - but no credit for those.
My daughter could not meet the state education requirements, which were time based, not mastery based and the principal was not happy about it. My daughter solved the high school education requirements by dropping out after 10th grade and doing early admissions to the University, where she did her engineering degree.
Some of the methods taught were ridiculous - so I taught my kids the standard approaches - "you have to know it the teacher's way, AND my way". It turned our that the standard way of multiplication and division works just fine with complex numbers, polynomials, and other mathematical objects.
I work 25 hours a week at a Mathnasium in Oregon (franchise drop-in teaching - parents pay to be able to drop their kids off for an hour a day ten times a month) and I'm proud of what I do. I go home every day having helped about forty kids get about an hour better at math.
Our teaching is effective (we're mastery based; kids repeat topics as often as they need to), but it doesn't scale. We maintain ratios of one instructor per four students and I don't think the job can be properly done with much less. So it's a "solution" that only can work for kids with affluent parents.
I don't know what the solution is for public school. I have a couple teacher friends in my book clubs (not math, but the issues generalize) and hear enough horror stories to be glad I'm not there.
Sometimes public schools have a math interventionist, and sometimes they're good, but it's something like one interventionist to 600 children, so they can't help, for instance, students who are at grade level but far behind their potential.
My partner has both tutored and substitute taught k-12 math in Sonoma / Marin counties for the past 4 years. The level of malpractice and bad methodologies should be considered negligent at best and possibly criminal.
Most classes do not have books. Teachers give (sometimes ok, often very bad) notes on how to do a specific operation or problem, and then give out questions on homework. If your notes were bad or you didn't understand it exactly, you are often screwed. No book to go look into, so the kids are often left not learning a thing.
Past this, things are often taught in online "discovery" modules. And these should just be considered awful. They are math problems on subjects that the teachers haven't even taught, as a way to have the kids "teach themselves" how to solve these problems with no outside references.... UHHHH WHAT?
Then, most of the class is just taught on a Chromebook, with access to the internet? Meaning that these kids have the choice of either doing hard math, or messing around on the internet. Almost all the kids are going to choose to mess around on the internet as opposed to doing hard things.
Then, somehow the teachers tend towards awful? There is definitely some selection bias here, but almost all the kids who get tutored by my partner wish she was their math teacher for the full classes, because she actually sits down and takes the time to explain how the math works and work with them. This is bias towards one on one teaching, which is obviously superior but not scaleable, but the amount of teachers just phoning it in and not caring about the individual kids learning math is way too high.
And again, this is despite teaching and tutoring at some of the best districts in the Bay Area (and to be fair, some of the less good ones too).
Baffles me how some districts can be so bad. Who the hell decides not to have a text book at all? Or to allow internet access from chrome books during class?
But again I am stuck with my "does not jive with my experience" problem. We're in San Mateo county, but not an especially special district. My kids have textbooks. Their school network only has very limited internet access. How is it that these accute problems exist in multiple districts in Marin and Sonoma and not in San Mateo?
California has a weird thing where every few thousand kids is a completely separate school district. So while you say "not a problem in San Mateo", you might mean "not a problem in the 2 or 3 districts my kids go to", as San Mateo County has 23 different school districts. This means 23 different standards of using math textbooks versus not using textbooks, etc. Marin county has 15 or so districts. Sonoma County has 30 school districts. This means massive bloat in the administration and paperwork and taxes and teaching standards, since everything is different in each and every separate school district. And each district only has about 2000 students on average.
It's very confusing overall to me, as I grew up in the Denver metro area, where there is 1 district for every ~75,000 - 100,000 kids, meaning general alignment in an area. Having these tiny school districts in the bay creates an incredibly vast amount of duplicate work in administration, contracts, etc (and certainly bloats the costs of actually running the schools).
That was kind of what I was thinking. It’s hard to generalize because every district is different and they’re so small, especially elementary districts. Even within our elementary district we have had big differences for instance in ‘phone use policy. But people make these big sweeping generalizations about California or the Bay Area that can’t apply with so much generality
I do kind of agree that the small districts are expensive. My wife is a trustee so I see some of the cost more closely than most people do.
But I’m also pretty happy not to be part of SFUSD or LAUSD, which both seem pretty bad in different ways.
There is a reason why the bay area suburbs don't have all the problems that San Francisco Oakland and San Jose have. That's because each one of them is their own little city.And they don't have to find consensus. That is why the bay area does not have the problem that Los Angeles does.
Now it is true that declining enrollment is gonna hit them hard.But on the other hand that's something los angeles isn't escaping, either.
There’s already a noticeable trend where there are cities people move to to have kids because they have good elementary schools, and cities people move to when their kids leave home, because they’re cheaper, and then you have noticeable clusters of young families. Then the other districts need to close schools, and the administration has accelerated this by yanking federal subsidies. Very likely this just gets more and more exaggerated, but that’s not great because there are lots of families that can’t afford to live in Cupertino.
California doesn't have a weird thing. California simply has school districts based on cities rather than on counties. San Mateo county has twenty three school districts because it has twenty cities. California always defines its school district by cities not by county. And it also has something that's fairly rare, which is high school only districts and these do cross city boundaries.
The peninsula and south bay are very different from San Francisco and Marin. Both the latter have a huge number of private schools, therefore, their public schools tend to be overwhelmingly centered on the extremely low-income students who are also low achievers. Outside of the cities, the rest of the bay area has exceptionally good schools.
It's extremely weird for anybody to talk about California county like it has any meaning whatsoever. About the only time I can think of in the past 40 years that county distinctions have mattered is during COVID when San Mateo County was considerably less hawkish than Santa Clara and Alameda county.
In any event, it 's bizarre that you would think that counties have any meaning in California schools particularly in the Bay Area. And given the Bay Area public schools outside of the cities are extraordinarily good they wouldn't want to be like Denver.
There is no greater obligation a nation (or species for that matter) has than the education of its children. When we stop rewarding extraction and start measuring contribution teachers will quickly take their place at the head of line.
Until then be consoled by the fact that stupidity is self limiting.
As a Bay Area public school parent this doesn't jive with my experience of my own kids or our friends and neighbors. I'm sure all the individual stories are mostly true. For example, San Franscisco did stop teaching algebra in middle school, but they still taught it in 9th grade and the other Bay Area districts did not follow suit. But clearly there's exaggeration even in this particular headline item, and something is being missed in weaving this into a narrative of widespread failure. Our kids are fine. They're 1-2 grades ahead in math and they're actually learning the material. Our friends and neighbors kids are fine.
Its worth pointing this out because there is a repeated cycle if dysfunction in these discussions. The worst atrocities of misguided education reformers are inflicted on poor kids in underfunded districts, whose parents are too busy working 4 jobs each to put food on the table to participate in discussions about education reform. We agree, I imagine, that the best thing you can do for those kids is provide a public education that will teach them the material and show that they've learned it. Pretending to teach them so they can pretend to pass tests and pretend to go to college ultimately will do no good. Its presumably these kids and not my neighbors kids who go to UCSD unable to add 66 and 44.
But its overwhelmingly going to be my neighbors who read these articles and push for more acceleration for their kids. While this particular wave of education "reform" is clearly misguided, there was some logic to the impulse behind it. Beyond some point further streaming and acceleration is just selecting for wealth and socio-economic status. The willingness and ability to put your kid in after school math so they can do calculus in 9th grade is a test for leisure time and wealth as well as ability. That's fine, but that kid shouldn't take a spot in AP calculus from a senior whose parents couldn't pay for that additional schooling. You want the majority of public education spending to go on kids who can succeed with help, not on kids who are already guaranteed to succeed.
The risk, what has happened before and still happens in some parts of the country, is that demands for acceleration benefit kids who are already going to do well due to the SES of their parents, and not the kids who have the ability but whose parents don't have the spare time and cash to actively push their education.
The primary issues for academic acceleration are intelligence and conscientiousness. If the schools screened widely for capability it would be straightforward to provide efficient selection into accelerated tracks. Since the schools have actively chose NOT to widely screen for capability, highly educated parents will supplement either directly or via commercial channels - an opportunity that the schools have actively chosen NOT to provide to poorer students. We supplemented via our own efforts except for two courses where our daughter needed placement, so I did correspondence classes and served as a guide when needed.
The lack of support for capable students is an active choice of the school system.
And by the way, Alex's photo of the grading rubric is greatly at variance with the situation that prevailed 60 years ago. As I remember it, it was:
90 -> 100 A
80 -> 90 B
70 -> 80 C
60 -> 70 D
<60 F
missing work was a 0, and (slightly) late work was minus half or a full grade, depending upon the circumstances. Special situations could be considered - hospital, ...
You are underestimating the difficulty of providing acceleration in a fair way. I’ve seen a school system based on giving everyone an IQ test at 11, and it’s not great. People can train to do IQ tests. Upper middle class parents and the schools they sent their kids to trained them to do IQ tests. So again you are over-selecting for kids who already have advantages and don’t need help. As for testing for conscientiousness, that’s even worse - how do you tell the difference between a kid who can’t be bothered to do their homework and a kid who didn’t do their homework because they had to work to support their family?
Public schools have limited resources and should focus them where they make the biggest difference. That’s on low socio-economic status kids with potential, not upper middle class kids whose parents train them to test well. Tracking is fine. De-tracking is generally a bad idea. But we should not be providing calculus courses to 9th graders if the cost of that is not providing calculus courses to seniors, because the latter has much higher leverage in terms of improving people’s lives. A kid who does calculus in 9th grade can do it in 12th grade and it won’t make that much difference. A kid who misses the opportunity to do calculus in 12th grade is at a disadvantage going into college, may not even get into college.
Yes, you can train against IQ tests or SAT/ACT tests. In general, you gain less than half a standard deviation in doing so, with very few test takers gaining as one standard deviation. But it is better than anything else we have available - the alternatives are all more gameable.
I grew up going to school with the children of the Holocaust survivors. They were NOT upper middle class at the time - but on the average they were bright and hard working students.
Where college-in-high-school / Running Start is offered, students can attend college starting in 11th grade. If they are going to go the STEM route, they need to be ready for STEM calculus by 11th grade, and frankly, it would be better to take calculus in 10th grade and then take the harder STEM calculus when they start college study in 11th grade.
As long as the schools have teachers who can teach the classes, it does not cost more to teach Calculus than it does to teach Algebra. Frankly, in schools with insufficient students for advanced classes, I expect that virtual classrooms or eventually AI based instruction will be a better alternative than idling.
I raised all types of grief when my youngest daughter went to high school. She did take calculus - for college credit - in 10th grade. Then she dropped out and did early admissions to the university where she did her engineering degree. She did not belong in high school any longer. She just finished up faster. We had planned on my daughter doing the Running Start program.
Her younger brother did the Running Start path - but he was ready for calculus when he started Running Start. He ended up doing Business - MIS. But Running Start essentially reduced his time in college - and his college expenses in half.
Unfortunately, it appears that most Running Start students are not so diligent.
Half a standard deviation of IQ is an enormous gain. If you're close to the mean, that's more than a decile. And that's on a real IQ test properly administered. If you were trying to track by IQ you'd end up with a much simpler test that would be much easier to train for. This is how the old UK system worked, which was only abolished in Northern Ireland in the 1980s. Kids spent weeks learning how to figure out what day of the week a particular date was because that was a well known test question. It does require a certain amount of native ability, but its mostly just measuring which kids went to the right primary school. The SAT is basically similar - training can produce a 200 point gain, presumably again only close to the median, but that's massive.
If you're going to track, and as I said I think we should track up to a point, it needs to be done based on an objective test of the academic prerequisites for the accelerated material. Any attempt to measure "raw ability" is far too easily gamed by spending money on preparation and on the flip side disadvantages people who can't do that.
> The SAT is basically similar - training can produce a 200 point gain
"Can" is doing a lot of work here.
The people who most want to believe the SAT is trainable is Princeton Review. They say they have research that shows it works, they are the ones who claim "200 points."
They refuse to publish it. If it was good it would be the best possible advertising in the world.
> Once scholars control for all these factors as best they can, they find that coaching has a positive but small effect: Perhaps 10 or 20 points in total on the SAT, mostly on the math section, according to careful work by Derek Briggs of the University of Colorado Boulder and Ben Domingue of Stanford University.
You will see some students get a little more, if they really work at it. And, yes, a true, pure, delivered-by-God test wouldn't be trainable for, at all. But if the way it's broken is "extreme mental effort can be put in to raise the score modestly" then that's the way we would want the error to go.
When the ultra-rich people want to buy good results for their kid, they don't just put them in 30 hours of training. They hire someone to pretend to be them.
I should add something in defense of the schools - it appears that they don't come close to having enough teachers who can teach the more advanced math topics - typically pre-calculus and calculus. While one of my high school math teachers was a coach, he had studied math and loved coaching - so he taught high school math and coached basketball - a rarity I believe. But the schools are short on math and I presume physics teachers (anybody who can survive university physics can teach elementary calculus).
I have a question for Zvi here. Let us assume that students get through calculus in 8th or 9th grade. What then? Completing calculus in 10th grade makes sense for students who are heading to Running Start / early admissions because they are leaving the high school. Completing calculus earlier results in the question - do the schools need to offer multi-dimensional and vector calculus, differential equations, and linear algebra? The schools already don't have enough staff who can teach pre-calculus and calculus and it may be hard to get a classful of students for such material. If the students can use computers for virtual classes / AI tutoring - then by all means, they should be encouraged to do so.
Late to this but california math teachers with full credentials have to pass a calculus test.So they do know how to teach calculus. Physics teachers have to pass a physics test. And i'm sorry, but if you're teaching eighth and ninth grade of calculus, then you're teaching them by rote, and there is a real problem with kids learning math early and then by sophomore year not recalling or not understanding the math I have no problem with teaching calculus to advance students at junior or senior levels.But there's no reason to talk about getting a few fringe kids to take in calculus at the age of thirteen.
I'm very sure I didn't take anyone's spot in AP Calculus – why would spots be limited?
Maybe you've got some kind of weird districting, but ultimately acceleration is cheaper for schools! Let the kids that can graduate whenever, unless there really is some tragic tradeoff that must be made to not allow any more kids to learn more sooner or faster or both.
It's possible your exact school system is fine!
But many many others are badly extruding almost everyone at the same slow pace, and NOT teaching very many very well, and also slowing down any students succeeding in spite of it all. Take one for the team please.
This is probably not the case everywhere, but we have one high school locally where freshman parents get very upset and try to pull all kinds of stuff when there aren't enough spaces for their kids to take calculus in 9th grade. No high school will actually let a freshman displace a senior from a calculus class, but there are definitely people who want this.
I don't have any problem with acceleration. My own kids are on accelerated tracks, so I'd be a massive hypocrite if I did. My problem is with the view that's very evident in these comments, and somewhat in your last paragraph, that says that the US education system as a whole is failing, and failing smart kids in particular, and that the solution is to accelerate those smart kids and forget everyone else.
This view is not grounded in reality. The US education system is mostly fine, ahead of peer competitors in fact, and in particular its not failing smart kids. The only real problem is that it fails poor kids in poor districts. And yet when we talk about reform inevitably we end up talking about kids doing accelerated math, which is fine, but its a distraction from (and possibly a detriment to) solutions to the actual problem.
As Simon Kinahan sort of implies, this looks like policy, class warfare based on zero-sum relative status thinking, a limited number of college places and/or "good jobs" after college.
Yes. I think the class warfare is kind of accidental. But what I see is upper middle class parents demanding ever more absurd levels of acceleration for their kids, because they're terrified that Johnny will lose status opportunities if he doesn't "keep up". In the process of trying to cater to them the kids who aren't able to do accelerated math because they're looking after siblings or working aren't even getting decent opportunities because the paths to showing ordinary academic ability through the regular system are being shut down by well meaning but confused reformers.
What you want - and honestly in spite of various claims I think this is actually where most school districts are - is a system where all kids have the opportunity to finish AP calculus by the end of 12th grade if they can. Not in 8th grade. But also not never, or only with great effort, because again needing to arguing with administrators about schedules is something only upper middle class parents can guarantee to be able to do.
There are two facts that I just can’t wrap my head around. First, when a kid complains that 99 percentile SATs don’t get him into an Ivy, someone’s always right there to point out that there just aren’t enough places. Second, we are told that a significant number of Ivy students struggle with the basics of math and can no longer read a book. What’s going on?
The Ivy League, and elite US universities in general, are too small. Especially given the large number of international students, by global standards they are tiny. That's one problem. There's no test yet devised that can select 17,000 students from 3.7m. Its just not doable in any rational way.
I'm going to wait a couple of years until the kids who were in high school during COVID flush through the system and we get a bit more perspective before passing any judgement. It sounds really bad. But it doesn't match my experience of my kids slightly younger cohort. They don't read for pleasure much, but they're perfectly capable of doing it, and their math is fine.
The nonsense of "Solve this simple calculation in a bonkers way" absolutely matches my experience with my kids' schools. Across two different districts for my kids, and one for my older nephew, the kids had teachers who didn't teach adding/subtracting numbers by columns but instead using all manner of odd graphical or other methods. They were awful, slow and prone to error; when I taught my oldest "Look, just line them up over each other like this, then start from right and go left" she was amazed and asked why they didn't teach that in school. Numerous times I got calls from my sister asking if I could figure out what the hell her son's teacher even wanted him to do to solve a simple division problem, and half the time I had no idea no matter how much I read the instructions.
Most instructional technique has gone the way of click bait, with every researcher trying to come up with some crazy new tech that blows old methods out of the water with this one simple trick! In reality they are simply inferior ways of performing the calculation. They might show neat aspects of math interesting to the very advanced student, but they are terrible for the basics of how to find the answer.
The slow-walking the teaching aspect is real, too. Our middle school tried to talk my oldest out of pre-algebra in 6th grade because she only had a low A in 5th grade math; now at the end of the year she has a 98%. The downside if she had failed? Taking pre-algebra again, so... zero. Mean while, my 4th grader is teaching my 1st grader how to work with fractions; she can now pass the tests for the 4th grade "advanced math" class. Now sure, my kids are obviously brilliant, and having 10 year olds provide 1 on 1 tutoring to every student doesn't scale, but damn, it seems like the ceiling for in school performance is pretty low. Especially considering how much we pay to be in a top 10 district in this state.
Zvi thinks we have godlike Superintelligence that will either smite us or render our cognition irrelevant coming in the next like 3 years. I don’t really see how 8th graders do at calculus as really relevant in either of those scenarios.
Genuinely curious about this because I’m in college right now and find the godlike Superintelligence very demotivating
Generally speaking, the weirder the timeline, the less control over your fate you're able to exercise (it's not a given that your actions do not matter, but in a sufficiently weird system, it's virtually a given that you cannot meaningfully predict their impact). Thus, unless you're already in a very unusual space, for the purpose of control you should operate mostly on the assumption of reasonable non-weirdness.
I have two kids in public school in a rich Boston suburb and I’m pretty happy with their math education but I do have both kids using Math Academy to work ahead of their grade level and I can’t recommend it enough.
I’m very glad my kids went to good Montessori schools through elementary. And, also, there are still public schools where the expectation is that if you take AP classes you take and pass the AP exam. Our public high school’s principal is proud of the share of students who pass AP exams. Now maybe those too have suffered from grade inflation?
I agree with a lot of the critiques in this argument in this article, but I don't agree with the concerns raised with teaching them alternative techniques. I tutor math - the box technique is a great way for kids to learn to do this type of problem mentally. It's similar to how I do this type of math in my head. And yes, you do need to make sure the kids understand the technique if they're going to evaluate it for their own use.
That's not the concern raised though, the issue (borne out by many reports) is that you MUST use that technique. Even if it makes no sense to you, even if you've learned another technique that works great, even if you're just doing the problems in your head. You must show your correct working of the technique.
Ok, you want to do it on a few worksheets? Fine, no complaint from me. You want to include a few "must be done via X method showing the steps" questions on a test? Ehhh ok. But what seems to happen in practice is the teacher finds it easier (or for some other incentive is applying) to teach only one technique.
So it's not you have do a block A (quiz on A), block of B (quiz on B) and then block of C (quiz on C) followed by a test with a large # of problems (any method) +2 A, 2 B, 2 C problems.
It's you only learn A and LORD HELP YOUR BUTT if that method doesn't work for you. Better luck next year!
Wife and I are knocking on 40, she works in a heavily math/excel/data field and is good at it. Yet one of her traumatic education experiences was a teacher accusing of her "just guessing" b/c, for some reason, Gaussian summation didn't stick in her brain in that class so she was manually reproducing the summation to do test problems like "add up all the numbers from 50 to 75" in a quick chart.
Repeatedly the teacher accused her of "just guessing" and gave her 0 credit. Obviously (I say obviously, but if only if it really was so) a student that can do a chart and add them all up quickly is a gnat's fart away from understanding the full method.
No other techniques were allowed, no further work on this done, just 0 credit and a few notes about how she needed to "stop guessing". Also, and just to be clear, calling that "guessing" was... not faith in school inspiring.
This is the concern, and based on talking to friends and reading links from here/other places, it is fairly well demonstrated. Whatever the standards/curriculum provides, in practice you get one algorithm for each problem and then the class has moved on.
That is not how these "weird" techniques for basic arithmetic are taught. Its exactly as you suggest it should be - they teach one one week, one the next week. The kids are supposed to understand each one, but once they're past that point no-one cares which one they use.
I don't disagree that's the theory, and I'm sure it happens a goodly portion of the time. However, based on an overwhelming number of reports as well as the personal experience of friends and family (and soon, potentially, my own kids) you also have a goodly portion of the time only one method gets covered.
Maybe they intend to cover them all. Maybe they're all crammed into a Friday afternoon, I don't know. But somewhere between intent and actual practice there's a gap and into that gap falls kids taught one weird/abstract/visual (what have you) method instead of a bunch of them.
I spent some time subbing in a special ed assistantance room and had to make my own damn worksheets on how to do basic math for kids because all they had was the other stuff, and not enough of it. Don't know what to say, the system was perfectly happy to let them struggle (apparently indefinitely) vs just teaching them some brute force algorithms. If the reports from online/friends/fam weren't enough this experience also drove home the msg that something is deeply borked with how we teach math now.
I am very skeptical of some of these reports. There’s a whole genre of education horror slop that’s older than the internet. Older than I am. Parents see one thing that’s different from what they learned out of context, probably because their kid asks for help, and then rather than trying to understand they just adopt is evidence that the kids aren’t learning right. Zvi clearly isn’t being very careful with the reports he repeats above and I suspect you’ll find that when you hear these reports the people reporting them are not being very careful either.
I completely agree with you that schools and teachers sometimes fail to adopt the right approaches to special ed kids. My older son is dyslexic and we had some interesting experimences with the regular ed staff. Fortunately the special ed folks were great. But I think this is different and unrelated to the multiple approaches thing they do with math now.
That was not our experience. Properly run and funded integrated special ed doesn’t take extra class time because there are special ed teachers in the classroom
Not the point, I know, but I'm so confused as to how substantially more students got #17 on that test than got 14, 15, or 16. How can you know how to add fractions with different denominators and not know how to add fractions with the same denominator, or divide a fraction by 2?
Math was always one of my dump skills; I had a Real Non-Fake Calculus Class in highschool, got an A with significant effort, and then squeaked past the AP Calc BC Exam with a 3 (so a 4 on the AB Exam, I think?). Haven't touched Real Math for like 15 years since then. But it's kind of reassuring to be able to still do up till Grade 7 in my head, and then 7-8 are easy with <s>unmonitored CoT</s> paper scratchpad. One can mostly get by in life with jagged math capabilities like this, especially blue-collar. God forbid I don't sweat the technique too...136 -> close to 120 -> 120 is three 40s -> rest is 16 -> 16 is four 4s -> 34. Staring at that array gives me a headache. It's also confusing because that's...not long division, just regular? I mean you can use long for non-remainder stuff too, but why would you?
Wait, when did letter grades stop referring to deciles? That's wild and explains so much. 90+, 80-89, 70-79, 60-69, 59-, same scale across all classes K-12 and 3 different colleges...I guess things really have changed a lot since 2013 or so. Because addition is commutative, see..."64? How did 64 get into it?", I hear you cry. Well, 64 is just a B. Ask a silly question, get a silly grade! Hooray for New Math, it's so simple that only a Zoomer can do it...
(The real math anxiety is remembering that you *used to* be able to do xyz math, but no longer know how. Like I can see the shape of the argument for rederiving the daily compound interest formula, but actually one-shotting it myself in a reasonable timeframe? No thanks, I'll just look up a calculator...Many Such Cases. Stupid Socrates and his Doubling Cube, that one nerdsniped me for awhile too.)
My middle school had ten-point ranges, but I think my high school had either 93+ or 94+ as an A, 85+ as a B, 76+ as a C, and maybe 67+ as a D? It definitely seemed like an unreasonably narrow range at the time, so spreading those out a bit seems like a good move.
Pasadena public schools has a math academy https://www.mathacademy.us/ that teaches kids up through AP calculus before high school. When thinking about relocating to the bay area I was shocked to see that math acceleration is actively discouraged and even the main math curriculum seems to be decelerated from the standard
The bay area has hundreds of school districts with different math acceleration programs. There's no single standard or even an average approach as far as I can tell. San Francisco was very unusual in refusing to do any acceleration before high school at all.
I can see how to push Calculus down to 8th grade, but you have to drive the elementary school coverage a bit for that. I get my youngest daughter to take calculus - for college credit, in 10th grade. It was taught by one of the math faculty members from a local college. But there was a big problem with the school system - the high school was required to teach students 3 years of math - clock time. She skipped 8th grade so to get her ready for calculus in 10th grade I had her do Geometry by correspondence over the summer before 9th grade, and pre-calculus by correspondence over the summer after 9th grade. She got placement - but no credit for those.
My daughter could not meet the state education requirements, which were time based, not mastery based and the principal was not happy about it. My daughter solved the high school education requirements by dropping out after 10th grade and doing early admissions to the University, where she did her engineering degree.
Some of the methods taught were ridiculous - so I taught my kids the standard approaches - "you have to know it the teacher's way, AND my way". It turned our that the standard way of multiplication and division works just fine with complex numbers, polynomials, and other mathematical objects.
I work 25 hours a week at a Mathnasium in Oregon (franchise drop-in teaching - parents pay to be able to drop their kids off for an hour a day ten times a month) and I'm proud of what I do. I go home every day having helped about forty kids get about an hour better at math.
Our teaching is effective (we're mastery based; kids repeat topics as often as they need to), but it doesn't scale. We maintain ratios of one instructor per four students and I don't think the job can be properly done with much less. So it's a "solution" that only can work for kids with affluent parents.
I don't know what the solution is for public school. I have a couple teacher friends in my book clubs (not math, but the issues generalize) and hear enough horror stories to be glad I'm not there.
Sometimes public schools have a math interventionist, and sometimes they're good, but it's something like one interventionist to 600 children, so they can't help, for instance, students who are at grade level but far behind their potential.
My partner has both tutored and substitute taught k-12 math in Sonoma / Marin counties for the past 4 years. The level of malpractice and bad methodologies should be considered negligent at best and possibly criminal.
Most classes do not have books. Teachers give (sometimes ok, often very bad) notes on how to do a specific operation or problem, and then give out questions on homework. If your notes were bad or you didn't understand it exactly, you are often screwed. No book to go look into, so the kids are often left not learning a thing.
Past this, things are often taught in online "discovery" modules. And these should just be considered awful. They are math problems on subjects that the teachers haven't even taught, as a way to have the kids "teach themselves" how to solve these problems with no outside references.... UHHHH WHAT?
Then, most of the class is just taught on a Chromebook, with access to the internet? Meaning that these kids have the choice of either doing hard math, or messing around on the internet. Almost all the kids are going to choose to mess around on the internet as opposed to doing hard things.
Then, somehow the teachers tend towards awful? There is definitely some selection bias here, but almost all the kids who get tutored by my partner wish she was their math teacher for the full classes, because she actually sits down and takes the time to explain how the math works and work with them. This is bias towards one on one teaching, which is obviously superior but not scaleable, but the amount of teachers just phoning it in and not caring about the individual kids learning math is way too high.
And again, this is despite teaching and tutoring at some of the best districts in the Bay Area (and to be fair, some of the less good ones too).
Baffles me how some districts can be so bad. Who the hell decides not to have a text book at all? Or to allow internet access from chrome books during class?
But again I am stuck with my "does not jive with my experience" problem. We're in San Mateo county, but not an especially special district. My kids have textbooks. Their school network only has very limited internet access. How is it that these accute problems exist in multiple districts in Marin and Sonoma and not in San Mateo?
California has a weird thing where every few thousand kids is a completely separate school district. So while you say "not a problem in San Mateo", you might mean "not a problem in the 2 or 3 districts my kids go to", as San Mateo County has 23 different school districts. This means 23 different standards of using math textbooks versus not using textbooks, etc. Marin county has 15 or so districts. Sonoma County has 30 school districts. This means massive bloat in the administration and paperwork and taxes and teaching standards, since everything is different in each and every separate school district. And each district only has about 2000 students on average.
It's very confusing overall to me, as I grew up in the Denver metro area, where there is 1 district for every ~75,000 - 100,000 kids, meaning general alignment in an area. Having these tiny school districts in the bay creates an incredibly vast amount of duplicate work in administration, contracts, etc (and certainly bloats the costs of actually running the schools).
That was kind of what I was thinking. It’s hard to generalize because every district is different and they’re so small, especially elementary districts. Even within our elementary district we have had big differences for instance in ‘phone use policy. But people make these big sweeping generalizations about California or the Bay Area that can’t apply with so much generality
I do kind of agree that the small districts are expensive. My wife is a trustee so I see some of the cost more closely than most people do.
But I’m also pretty happy not to be part of SFUSD or LAUSD, which both seem pretty bad in different ways.
There is a reason why the bay area suburbs don't have all the problems that San Francisco Oakland and San Jose have. That's because each one of them is their own little city.And they don't have to find consensus. That is why the bay area does not have the problem that Los Angeles does.
Now it is true that declining enrollment is gonna hit them hard.But on the other hand that's something los angeles isn't escaping, either.
There’s already a noticeable trend where there are cities people move to to have kids because they have good elementary schools, and cities people move to when their kids leave home, because they’re cheaper, and then you have noticeable clusters of young families. Then the other districts need to close schools, and the administration has accelerated this by yanking federal subsidies. Very likely this just gets more and more exaggerated, but that’s not great because there are lots of families that can’t afford to live in Cupertino.
California doesn't have a weird thing. California simply has school districts based on cities rather than on counties. San Mateo county has twenty three school districts because it has twenty cities. California always defines its school district by cities not by county. And it also has something that's fairly rare, which is high school only districts and these do cross city boundaries.
The peninsula and south bay are very different from San Francisco and Marin. Both the latter have a huge number of private schools, therefore, their public schools tend to be overwhelmingly centered on the extremely low-income students who are also low achievers. Outside of the cities, the rest of the bay area has exceptionally good schools.
It's extremely weird for anybody to talk about California county like it has any meaning whatsoever. About the only time I can think of in the past 40 years that county distinctions have mattered is during COVID when San Mateo County was considerably less hawkish than Santa Clara and Alameda county.
In any event, it 's bizarre that you would think that counties have any meaning in California schools particularly in the Bay Area. And given the Bay Area public schools outside of the cities are extraordinarily good they wouldn't want to be like Denver.
There is no greater obligation a nation (or species for that matter) has than the education of its children. When we stop rewarding extraction and start measuring contribution teachers will quickly take their place at the head of line.
Until then be consoled by the fact that stupidity is self limiting.
As a Bay Area public school parent this doesn't jive with my experience of my own kids or our friends and neighbors. I'm sure all the individual stories are mostly true. For example, San Franscisco did stop teaching algebra in middle school, but they still taught it in 9th grade and the other Bay Area districts did not follow suit. But clearly there's exaggeration even in this particular headline item, and something is being missed in weaving this into a narrative of widespread failure. Our kids are fine. They're 1-2 grades ahead in math and they're actually learning the material. Our friends and neighbors kids are fine.
Its worth pointing this out because there is a repeated cycle if dysfunction in these discussions. The worst atrocities of misguided education reformers are inflicted on poor kids in underfunded districts, whose parents are too busy working 4 jobs each to put food on the table to participate in discussions about education reform. We agree, I imagine, that the best thing you can do for those kids is provide a public education that will teach them the material and show that they've learned it. Pretending to teach them so they can pretend to pass tests and pretend to go to college ultimately will do no good. Its presumably these kids and not my neighbors kids who go to UCSD unable to add 66 and 44.
But its overwhelmingly going to be my neighbors who read these articles and push for more acceleration for their kids. While this particular wave of education "reform" is clearly misguided, there was some logic to the impulse behind it. Beyond some point further streaming and acceleration is just selecting for wealth and socio-economic status. The willingness and ability to put your kid in after school math so they can do calculus in 9th grade is a test for leisure time and wealth as well as ability. That's fine, but that kid shouldn't take a spot in AP calculus from a senior whose parents couldn't pay for that additional schooling. You want the majority of public education spending to go on kids who can succeed with help, not on kids who are already guaranteed to succeed.
The risk, what has happened before and still happens in some parts of the country, is that demands for acceleration benefit kids who are already going to do well due to the SES of their parents, and not the kids who have the ability but whose parents don't have the spare time and cash to actively push their education.
The primary issues for academic acceleration are intelligence and conscientiousness. If the schools screened widely for capability it would be straightforward to provide efficient selection into accelerated tracks. Since the schools have actively chose NOT to widely screen for capability, highly educated parents will supplement either directly or via commercial channels - an opportunity that the schools have actively chosen NOT to provide to poorer students. We supplemented via our own efforts except for two courses where our daughter needed placement, so I did correspondence classes and served as a guide when needed.
The lack of support for capable students is an active choice of the school system.
And by the way, Alex's photo of the grading rubric is greatly at variance with the situation that prevailed 60 years ago. As I remember it, it was:
90 -> 100 A
80 -> 90 B
70 -> 80 C
60 -> 70 D
<60 F
missing work was a 0, and (slightly) late work was minus half or a full grade, depending upon the circumstances. Special situations could be considered - hospital, ...
You are underestimating the difficulty of providing acceleration in a fair way. I’ve seen a school system based on giving everyone an IQ test at 11, and it’s not great. People can train to do IQ tests. Upper middle class parents and the schools they sent their kids to trained them to do IQ tests. So again you are over-selecting for kids who already have advantages and don’t need help. As for testing for conscientiousness, that’s even worse - how do you tell the difference between a kid who can’t be bothered to do their homework and a kid who didn’t do their homework because they had to work to support their family?
Public schools have limited resources and should focus them where they make the biggest difference. That’s on low socio-economic status kids with potential, not upper middle class kids whose parents train them to test well. Tracking is fine. De-tracking is generally a bad idea. But we should not be providing calculus courses to 9th graders if the cost of that is not providing calculus courses to seniors, because the latter has much higher leverage in terms of improving people’s lives. A kid who does calculus in 9th grade can do it in 12th grade and it won’t make that much difference. A kid who misses the opportunity to do calculus in 12th grade is at a disadvantage going into college, may not even get into college.
Yes, you can train against IQ tests or SAT/ACT tests. In general, you gain less than half a standard deviation in doing so, with very few test takers gaining as one standard deviation. But it is better than anything else we have available - the alternatives are all more gameable.
I grew up going to school with the children of the Holocaust survivors. They were NOT upper middle class at the time - but on the average they were bright and hard working students.
Where college-in-high-school / Running Start is offered, students can attend college starting in 11th grade. If they are going to go the STEM route, they need to be ready for STEM calculus by 11th grade, and frankly, it would be better to take calculus in 10th grade and then take the harder STEM calculus when they start college study in 11th grade.
As long as the schools have teachers who can teach the classes, it does not cost more to teach Calculus than it does to teach Algebra. Frankly, in schools with insufficient students for advanced classes, I expect that virtual classrooms or eventually AI based instruction will be a better alternative than idling.
I raised all types of grief when my youngest daughter went to high school. She did take calculus - for college credit - in 10th grade. Then she dropped out and did early admissions to the university where she did her engineering degree. She did not belong in high school any longer. She just finished up faster. We had planned on my daughter doing the Running Start program.
Her younger brother did the Running Start path - but he was ready for calculus when he started Running Start. He ended up doing Business - MIS. But Running Start essentially reduced his time in college - and his college expenses in half.
Unfortunately, it appears that most Running Start students are not so diligent.
Notice how some people can be convinced to abandon a working system because someone tells them it isn't "fair."
Where is this working system of which you speak and in what sense does it work?
Tracking works fine.
Half a standard deviation of IQ is an enormous gain. If you're close to the mean, that's more than a decile. And that's on a real IQ test properly administered. If you were trying to track by IQ you'd end up with a much simpler test that would be much easier to train for. This is how the old UK system worked, which was only abolished in Northern Ireland in the 1980s. Kids spent weeks learning how to figure out what day of the week a particular date was because that was a well known test question. It does require a certain amount of native ability, but its mostly just measuring which kids went to the right primary school. The SAT is basically similar - training can produce a 200 point gain, presumably again only close to the median, but that's massive.
If you're going to track, and as I said I think we should track up to a point, it needs to be done based on an objective test of the academic prerequisites for the accelerated material. Any attempt to measure "raw ability" is far too easily gamed by spending money on preparation and on the flip side disadvantages people who can't do that.
> The SAT is basically similar - training can produce a 200 point gain
"Can" is doing a lot of work here.
The people who most want to believe the SAT is trainable is Princeton Review. They say they have research that shows it works, they are the ones who claim "200 points."
They refuse to publish it. If it was good it would be the best possible advertising in the world.
What we see in reality is maybe 10-20 points, which is more-or-less the standard measurement error: https://slate.com/technology/2019/04/sat-prep-courses-do-they-work-bias.html
> Once scholars control for all these factors as best they can, they find that coaching has a positive but small effect: Perhaps 10 or 20 points in total on the SAT, mostly on the math section, according to careful work by Derek Briggs of the University of Colorado Boulder and Ben Domingue of Stanford University.
You will see some students get a little more, if they really work at it. And, yes, a true, pure, delivered-by-God test wouldn't be trainable for, at all. But if the way it's broken is "extreme mental effort can be put in to raise the score modestly" then that's the way we would want the error to go.
When the ultra-rich people want to buy good results for their kid, they don't just put them in 30 hours of training. They hire someone to pretend to be them.
I should add something in defense of the schools - it appears that they don't come close to having enough teachers who can teach the more advanced math topics - typically pre-calculus and calculus. While one of my high school math teachers was a coach, he had studied math and loved coaching - so he taught high school math and coached basketball - a rarity I believe. But the schools are short on math and I presume physics teachers (anybody who can survive university physics can teach elementary calculus).
I have a question for Zvi here. Let us assume that students get through calculus in 8th or 9th grade. What then? Completing calculus in 10th grade makes sense for students who are heading to Running Start / early admissions because they are leaving the high school. Completing calculus earlier results in the question - do the schools need to offer multi-dimensional and vector calculus, differential equations, and linear algebra? The schools already don't have enough staff who can teach pre-calculus and calculus and it may be hard to get a classful of students for such material. If the students can use computers for virtual classes / AI tutoring - then by all means, they should be encouraged to do so.
Well, yes. Only ~5% of the adult population can actually do basic calculus.
Late to this but california math teachers with full credentials have to pass a calculus test.So they do know how to teach calculus. Physics teachers have to pass a physics test. And i'm sorry, but if you're teaching eighth and ninth grade of calculus, then you're teaching them by rote, and there is a real problem with kids learning math early and then by sophomore year not recalling or not understanding the math I have no problem with teaching calculus to advance students at junior or senior levels.But there's no reason to talk about getting a few fringe kids to take in calculus at the age of thirteen.
I'm very sure I didn't take anyone's spot in AP Calculus – why would spots be limited?
Maybe you've got some kind of weird districting, but ultimately acceleration is cheaper for schools! Let the kids that can graduate whenever, unless there really is some tragic tradeoff that must be made to not allow any more kids to learn more sooner or faster or both.
It's possible your exact school system is fine!
But many many others are badly extruding almost everyone at the same slow pace, and NOT teaching very many very well, and also slowing down any students succeeding in spite of it all. Take one for the team please.
This is probably not the case everywhere, but we have one high school locally where freshman parents get very upset and try to pull all kinds of stuff when there aren't enough spaces for their kids to take calculus in 9th grade. No high school will actually let a freshman displace a senior from a calculus class, but there are definitely people who want this.
I don't have any problem with acceleration. My own kids are on accelerated tracks, so I'd be a massive hypocrite if I did. My problem is with the view that's very evident in these comments, and somewhat in your last paragraph, that says that the US education system as a whole is failing, and failing smart kids in particular, and that the solution is to accelerate those smart kids and forget everyone else.
This view is not grounded in reality. The US education system is mostly fine, ahead of peer competitors in fact, and in particular its not failing smart kids. The only real problem is that it fails poor kids in poor districts. And yet when we talk about reform inevitably we end up talking about kids doing accelerated math, which is fine, but its a distraction from (and possibly a detriment to) solutions to the actual problem.
As Simon Kinahan sort of implies, this looks like policy, class warfare based on zero-sum relative status thinking, a limited number of college places and/or "good jobs" after college.
Yes. I think the class warfare is kind of accidental. But what I see is upper middle class parents demanding ever more absurd levels of acceleration for their kids, because they're terrified that Johnny will lose status opportunities if he doesn't "keep up". In the process of trying to cater to them the kids who aren't able to do accelerated math because they're looking after siblings or working aren't even getting decent opportunities because the paths to showing ordinary academic ability through the regular system are being shut down by well meaning but confused reformers.
What you want - and honestly in spite of various claims I think this is actually where most school districts are - is a system where all kids have the opportunity to finish AP calculus by the end of 12th grade if they can. Not in 8th grade. But also not never, or only with great effort, because again needing to arguing with administrators about schedules is something only upper middle class parents can guarantee to be able to do.
There are two facts that I just can’t wrap my head around. First, when a kid complains that 99 percentile SATs don’t get him into an Ivy, someone’s always right there to point out that there just aren’t enough places. Second, we are told that a significant number of Ivy students struggle with the basics of math and can no longer read a book. What’s going on?
Short version: scores on SATs are not the metric Ivy's are selecting for.
The Ivy League, and elite US universities in general, are too small. Especially given the large number of international students, by global standards they are tiny. That's one problem. There's no test yet devised that can select 17,000 students from 3.7m. Its just not doable in any rational way.
I'm going to wait a couple of years until the kids who were in high school during COVID flush through the system and we get a bit more perspective before passing any judgement. It sounds really bad. But it doesn't match my experience of my kids slightly younger cohort. They don't read for pleasure much, but they're perfectly capable of doing it, and their math is fine.
The nonsense of "Solve this simple calculation in a bonkers way" absolutely matches my experience with my kids' schools. Across two different districts for my kids, and one for my older nephew, the kids had teachers who didn't teach adding/subtracting numbers by columns but instead using all manner of odd graphical or other methods. They were awful, slow and prone to error; when I taught my oldest "Look, just line them up over each other like this, then start from right and go left" she was amazed and asked why they didn't teach that in school. Numerous times I got calls from my sister asking if I could figure out what the hell her son's teacher even wanted him to do to solve a simple division problem, and half the time I had no idea no matter how much I read the instructions.
Most instructional technique has gone the way of click bait, with every researcher trying to come up with some crazy new tech that blows old methods out of the water with this one simple trick! In reality they are simply inferior ways of performing the calculation. They might show neat aspects of math interesting to the very advanced student, but they are terrible for the basics of how to find the answer.
The slow-walking the teaching aspect is real, too. Our middle school tried to talk my oldest out of pre-algebra in 6th grade because she only had a low A in 5th grade math; now at the end of the year she has a 98%. The downside if she had failed? Taking pre-algebra again, so... zero. Mean while, my 4th grader is teaching my 1st grader how to work with fractions; she can now pass the tests for the 4th grade "advanced math" class. Now sure, my kids are obviously brilliant, and having 10 year olds provide 1 on 1 tutoring to every student doesn't scale, but damn, it seems like the ceiling for in school performance is pretty low. Especially considering how much we pay to be in a top 10 district in this state.
Zvi thinks we have godlike Superintelligence that will either smite us or render our cognition irrelevant coming in the next like 3 years. I don’t really see how 8th graders do at calculus as really relevant in either of those scenarios.
Genuinely curious about this because I’m in college right now and find the godlike Superintelligence very demotivating
Generally speaking, the weirder the timeline, the less control over your fate you're able to exercise (it's not a given that your actions do not matter, but in a sufficiently weird system, it's virtually a given that you cannot meaningfully predict their impact). Thus, unless you're already in a very unusual space, for the purpose of control you should operate mostly on the assumption of reasonable non-weirdness.
I have two kids in public school in a rich Boston suburb and I’m pretty happy with their math education but I do have both kids using Math Academy to work ahead of their grade level and I can’t recommend it enough.
Has anyone published the full UCSD math exam? I want to give it to my kid.
I’m very glad my kids went to good Montessori schools through elementary. And, also, there are still public schools where the expectation is that if you take AP classes you take and pass the AP exam. Our public high school’s principal is proud of the share of students who pass AP exams. Now maybe those too have suffered from grade inflation?
I agree with a lot of the critiques in this argument in this article, but I don't agree with the concerns raised with teaching them alternative techniques. I tutor math - the box technique is a great way for kids to learn to do this type of problem mentally. It's similar to how I do this type of math in my head. And yes, you do need to make sure the kids understand the technique if they're going to evaluate it for their own use.
That's not the concern raised though, the issue (borne out by many reports) is that you MUST use that technique. Even if it makes no sense to you, even if you've learned another technique that works great, even if you're just doing the problems in your head. You must show your correct working of the technique.
Ok, you want to do it on a few worksheets? Fine, no complaint from me. You want to include a few "must be done via X method showing the steps" questions on a test? Ehhh ok. But what seems to happen in practice is the teacher finds it easier (or for some other incentive is applying) to teach only one technique.
So it's not you have do a block A (quiz on A), block of B (quiz on B) and then block of C (quiz on C) followed by a test with a large # of problems (any method) +2 A, 2 B, 2 C problems.
It's you only learn A and LORD HELP YOUR BUTT if that method doesn't work for you. Better luck next year!
Wife and I are knocking on 40, she works in a heavily math/excel/data field and is good at it. Yet one of her traumatic education experiences was a teacher accusing of her "just guessing" b/c, for some reason, Gaussian summation didn't stick in her brain in that class so she was manually reproducing the summation to do test problems like "add up all the numbers from 50 to 75" in a quick chart.
Repeatedly the teacher accused her of "just guessing" and gave her 0 credit. Obviously (I say obviously, but if only if it really was so) a student that can do a chart and add them all up quickly is a gnat's fart away from understanding the full method.
No other techniques were allowed, no further work on this done, just 0 credit and a few notes about how she needed to "stop guessing". Also, and just to be clear, calling that "guessing" was... not faith in school inspiring.
This is the concern, and based on talking to friends and reading links from here/other places, it is fairly well demonstrated. Whatever the standards/curriculum provides, in practice you get one algorithm for each problem and then the class has moved on.
That is not how these "weird" techniques for basic arithmetic are taught. Its exactly as you suggest it should be - they teach one one week, one the next week. The kids are supposed to understand each one, but once they're past that point no-one cares which one they use.
I don't disagree that's the theory, and I'm sure it happens a goodly portion of the time. However, based on an overwhelming number of reports as well as the personal experience of friends and family (and soon, potentially, my own kids) you also have a goodly portion of the time only one method gets covered.
Maybe they intend to cover them all. Maybe they're all crammed into a Friday afternoon, I don't know. But somewhere between intent and actual practice there's a gap and into that gap falls kids taught one weird/abstract/visual (what have you) method instead of a bunch of them.
I spent some time subbing in a special ed assistantance room and had to make my own damn worksheets on how to do basic math for kids because all they had was the other stuff, and not enough of it. Don't know what to say, the system was perfectly happy to let them struggle (apparently indefinitely) vs just teaching them some brute force algorithms. If the reports from online/friends/fam weren't enough this experience also drove home the msg that something is deeply borked with how we teach math now.
I am very skeptical of some of these reports. There’s a whole genre of education horror slop that’s older than the internet. Older than I am. Parents see one thing that’s different from what they learned out of context, probably because their kid asks for help, and then rather than trying to understand they just adopt is evidence that the kids aren’t learning right. Zvi clearly isn’t being very careful with the reports he repeats above and I suspect you’ll find that when you hear these reports the people reporting them are not being very careful either.
I completely agree with you that schools and teachers sometimes fail to adopt the right approaches to special ed kids. My older son is dyslexic and we had some interesting experimences with the regular ed staff. Fortunately the special ed folks were great. But I think this is different and unrelated to the multiple approaches thing they do with math now.
Accommodation for special ed kids is one of the great time wasters
That was not our experience. Properly run and funded integrated special ed doesn’t take extra class time because there are special ed teachers in the classroom
Not the point, I know, but I'm so confused as to how substantially more students got #17 on that test than got 14, 15, or 16. How can you know how to add fractions with different denominators and not know how to add fractions with the same denominator, or divide a fraction by 2?
17 is mechanical and has no tricks.
Yes, they don't show why the kids got it wrong.Almost certainly the students didn't answer it in the correct form.But did the calculations correctly.
Math was always one of my dump skills; I had a Real Non-Fake Calculus Class in highschool, got an A with significant effort, and then squeaked past the AP Calc BC Exam with a 3 (so a 4 on the AB Exam, I think?). Haven't touched Real Math for like 15 years since then. But it's kind of reassuring to be able to still do up till Grade 7 in my head, and then 7-8 are easy with <s>unmonitored CoT</s> paper scratchpad. One can mostly get by in life with jagged math capabilities like this, especially blue-collar. God forbid I don't sweat the technique too...136 -> close to 120 -> 120 is three 40s -> rest is 16 -> 16 is four 4s -> 34. Staring at that array gives me a headache. It's also confusing because that's...not long division, just regular? I mean you can use long for non-remainder stuff too, but why would you?
Wait, when did letter grades stop referring to deciles? That's wild and explains so much. 90+, 80-89, 70-79, 60-69, 59-, same scale across all classes K-12 and 3 different colleges...I guess things really have changed a lot since 2013 or so. Because addition is commutative, see..."64? How did 64 get into it?", I hear you cry. Well, 64 is just a B. Ask a silly question, get a silly grade! Hooray for New Math, it's so simple that only a Zoomer can do it...
(The real math anxiety is remembering that you *used to* be able to do xyz math, but no longer know how. Like I can see the shape of the argument for rederiving the daily compound interest formula, but actually one-shotting it myself in a reasonable timeframe? No thanks, I'll just look up a calculator...Many Such Cases. Stupid Socrates and his Doubling Cube, that one nerdsniped me for awhile too.)
My middle school had ten-point ranges, but I think my high school had either 93+ or 94+ as an A, 85+ as a B, 76+ as a C, and maybe 67+ as a D? It definitely seemed like an unreasonably narrow range at the time, so spreading those out a bit seems like a good move.