Hacker News Reader

Comment by SilasX | Hacker News Reader

Whether that's good or bad depends entirely on the content of the tests. You have to ask, "is this stuff that a graduate of the system should be able to do?" If no, then it's fair to criticize them for having to spend time teaching this, and instead achieve a lower proficiency but teach a broader skill set.

But if yes, then any criticism of "teaching for the test" falls flat: this is stuff students need to be able to do, and to the extent that you're finding it hard to do, then you were failing all along, and removing the tests would just hide that. [1] (Plus, it's not like a student that can't meet this minimum is going to somehow do just fine in "real literature".)

However, to conclude a "no" answer to that question, you would need to cite specific questions from the tests, and go on record saying "nope, no reason a graduate of our system needs to know that, so why are we making sure they can answer it?"

So I'm confused as to why such testing critics never discuss this crucial piece of evidence, instead relying entirely on innuendo about suppose dangers of "teaching to the test".

[1] Which, of course, doesn't means the teachers specifically were the cause; in the extreme case, if students are literally starving, then you need to fix that. But regardless, any root-cause analysis must start from the detection of a failure, irrespective of where it ends.

View on HN

"Teaching to the test" generally doesn't mean covering the material that the test is intended to cover in theory, it means drilling the exact format of questions, studying previous years, knowing exactly what you can sacrifice coverage of, how to guess multiple choice questions when you don't know the answer etc. Basically over-optimizing to fit an imperfect model.

Now, I'm a good test taker generally, and it has always helped me in life, and I will ensure my children know the rules of the game. But from the perspective of the country or planet, that's not time and effort well spent, it's a zero-sum arms-race that could have been better spent.

There's more to this, e.g. the fact that the tests are really testing the teachers (again very imperfectly), that some people want to privatize education and so on, but "teaching to the test" is a well known anti-pattern for good reasons, even though the individual incentives push us in that direction.

>"Teaching to the test" generally doesn't mean covering the material that the test is intended to cover in theory, it means drilling the exact format of questions...

Sure, if you're an incompetent teacher. But then maybe, just maybe, you shouldn't be teaching at all.

Or you're a good teacher with students learning what they should, but the other classes got higher numbers despite not knowing the topic as well, so now you're under pressure to copy them.

> Sure, if you're an incompetent teacher. But then maybe, just maybe, you shouldn't be teaching at all.

But the teacher that does this will have students with higher scores, so by all metrics they are not the incompetent ones.

Like in software engineering, metrics lose meaning once they are used to justify rewards and punishments.

Says someone with I'm guessing no teaching experience, and no background in education.

Teach the test, get better scores... Better teacher? Not likely.

You're making a number of bad assumptions:

1. The test actually covers what's important

2. The teacher has the time, resources and support needed to fully convey the material to every student

3. The teacher and the school are receiving students who are realistically capable of reaching the expected level

4. The test results will be interpreted in good faith and used only to help students and teachers perform better

In the U.S. public education system, years of simplistic fixes have largely ensured that none of those are true. Instead there are vicious feedback loops: unprepared students will do worse on tests, which is held against the teachers and school no matter how hard they were trying, which leads the most motivated parents to take their kids elsewhere and the best teachers to leave teaching or find another school or district where their efforts are appreciated. After a few iterations, the district may close the “failing” school and make life even harder for kids who now have the same problems plus a more of their day commuting to a school where they'll probably bear the stigma of having come from a bad school/neighborhood.

I don't think that disagrees with me: yes, schools should teach a general understanding, rather than drilling a narrow toolbox that works on one specific test. But then:

- As I said above, you would need to cite which test question are game-able, and which encourage this narrow teaching, which critics never do.

- If the problem is that teachers try to satisfy this goal by trying to game the tests, then the problem is with this way of teaching, not the tests per se.

"From September until Christmas vacation, [Brookside] was like any school you would imagine. Then, once they got back from Christmas break, for the next nine weeks until testing began, it was a different animal. What they did was drop their curriculum, drop their texts, and instead study exclusively from a standardized-test prep book. Kids weren't getting a liberal arts education, but prepping to a very narrowly drawn standardized test in primarily language arts and math. Because they were interested in passing the test more than anything else, for that 22 percent of the school year, they taught primarily to the broad middle section of kids that were going to pass. Plus, the school went and reached out to those kids who they thought were on the cusp of possibly passing. So who gets left out? The kids at the bottom and the kids at the top." [0]

It's not the tests per se, but it's what is put on the line. Raises, funding, evaluations, keeping your job - these are all disincentives to well-rounded education. Please don't make me quote the plethora of studies that show how important arts, literature, and the sciences are to primary education. Completely stopping studying these things for half the school year is bad.

So it doesn't matter if the tests are filled with good-to-know knowledge - they're positioned to dis-incentivize and devalue anything that isn't math, language arts, and a narrow reading of how to structure an essay.

[0] http://www.usnews.com/opinion/articles/2013/04/11/why-excess...

Do you (A) oppose standardised testing in general, or (B) just object to (i) the way the test results are used as incentives/whatever, and (ii) think they test too narrow a set of subjects, or (C) something else?

You raise an objection to raises and funding being tied to test outcomes. Why would this be bad? Sure, if the tests are testing the wrong things, then we should fix the tests. But, it's not impossible to measure educational outcomes. Why should teachers continued employment, and pay, not reflect how well they are measured to be doing, at the thing they are paid to do?

The most profitable companies on earth got their by having a time horizon of longer than 8 months . there are critically important things that you can't measure on a multiple choice test

Here are some of the arguments I've seen:

-- testing itself takes a lot of time away from instruction, sometimes days at a time for each of multiple tests.

-- In addition to learning the material that's officially tested by an exam, students are forced to study the idiosyncracies of the exam: how questions are phrased, how graders expect to see written answers, etc. That takes more time away from studying actual curricular material and forces students to focus on something they, their parents and their teachers all find silly and boring, reducing respect for the education system.

-- The material that's on the test is often the lowest common denominator for what students should know, calculated over a US state or group of states. This means there will be material that's not on the test but that everyone thinks in a particular community thinks kids should learn (history, art, music, etc.) or even that most people in a state think should be taught but a vocal minority oppose (comparative religion, black history, evolution, etc.). That material will be left off the test, and a teacher won't have time to cover it because he or she has to spend all the class's time on stuff on the test. If a science test will never mention Neil Armstrong or Neil deGrasse Tyson, a teacher has no incentive to mention either of them, and may even be penalize for doing so at the expense of more practice with the density formula.

-- Teachers are evaluated based on test scores, often to the exclusion of other factors. This stresses teachers out at test time, which causes them to stress students out. Students come to dislike school and learn less.

-- The tests are sometimes flawed, but by the time people realize the results are wrong, their results have already factored into policy, personnel decisions and student placement.

So suppose you have a test which covers reading, writing and arithmetic only (3R). Assuming the teacher has already effectively taught 3R, and has time to spare, there is nothing to prevent them from teaching black history.

If the teacher hasn't effectively taught 3R with time to spare, I'd suggest that black history is a topic of far less import than 3R and the teacher should skip it.

This stresses teachers out at test time, which causes them to stress students out. Students come to dislike school and learn less.

tl;dr; Teachers are unprofessional and just generally horrible people who inflict their problems onto innocent third parties.

The problem is that the test doesn't just offer a pass-fail threshold, but is graded on a sliding scale, which means that so long as there is a chance of increasing the class average, kids will continue to be drilled on the test topics, over and over again.

My kids were sent home with worksheet after worksheet of basic arithmetic problems, long after they had completely mastered those skills.

> tl;dr; Teachers are unprofessional and just generally horrible people who inflict their problems onto innocent third parties.

… and you have the peer-reviewed studies to prove that an entire field is full of unqualified bad-actors? Or is this just the casual, unthinking racism implied by your decision to use “black history” as your example rather than, say, music or science and the corresponding assumption that it's some how distinct from and less important than “history” rather than being an essential component?

Scroll up - it was smelendez who made the claim that teachers take their stress out on students, not me. I just phrased it in a manner that gives teachers agency.

Black history was also an example taken from smelendez. History of any sort is far less important than literacy and numeracy, as is comparative religion, evolution, art and music (his other examples).

But I guess calling me racist is easier than actually addressing my arguments.

> Scroll up - it was smelendez who made the claim that teachers take their stress out on students, not me. I just phrased it in a manner that gives teachers agency.

No, you were making a blanket statement about an entire profession. Saying that people react poorly under prolonged stress is a simple statement of fact, with decades of concurring evidence from fields ranging from business and education to neuroscience, and it doesn't imply that those people chose to do anything wrong other than being an average human in a bad situation.

In contrast, your statement shifted all of the blame to one of the parties with the least agency and used loaded terms like “unprofessional” or “horrible” without any supporting justification.

> Black history was also an example taken from smelendez. History of any sort is far less important than literacy and numeracy, as is comparative religion, evolution, art and music (his other examples).

There were quite a few other things which he included which are not 3Rs and I find it interesting that you picked the only one which is the hobby-horse of right-wing discussion about schools.

> But I guess calling me racist is easier than actually addressing my arguments.

That's why I said “casual, unthinking racism” because there are so many tropes common to popular U.S. discussion which are rooted in racism but often propagated by people who haven't thought deeply about the origin or implications.

No, you were making a blanket statement about an entire profession.

I didn't claim that teachers take their stress out on students. I simply claimed that if they did, they are horrible and unprofessional. My claim is conditional on smelendez being right. Again, scroll up.

If you want to dispute that characterization, and argue that it's professional behavior to let your emotions get in the way of work have at it.

I don't know how you think teachers have the least agency. Their choice sets include a) doing their job, b) not doing their job and c) quitting and finding a job they don't suck at. (I did the last one, although emotional leakage was not what made me a bad teacher.) In contrast, the students usually don't have the choice of finding a teacher who does their job.

> I didn't claim that teachers take their stress out on students. I simply claimed that if they did, they are horrible and unprofessional.

That's the linkage I'm talking about: that ignores the possibility that the job has unreasonable expectations. One person, sure, maybe they have problems but when a high percentage of the field reports low job satisfaction and cites things like long hours and poor support as reasons for leaving, it's irresponsible not to ask whether the system is setup correctly.

Here in DC, hitting the right numbers gets a bonus which is close to 50% of your salary – or nothing if you're slightly low, and the school administrators both track things closely and are prone to saying the only reason for not hitting your numbers is that you don't care enough, weren't willing to put in the effort, don't believe disadvantaged kids deserve quality education, etc. That produces a cycle where you get very enthusiastic, motivated teachers fresh out of college who are basically in crunch mode for the entire school year before eventually realizing that random chance makes it very hard to hit the targets consistently and their efforts won't be appreciated otherwise.

> I don't know how you think teachers have the least agency. Their choice sets include a) doing their job, b) not doing their job and c) quitting and finding a job they don't suck at. (I did the last one, although emotional leakage was not what made me a bad teacher.) In contrast, the students usually don't have the choice of finding a teacher who does their job.

I said one of the parties with the least agency because they don't have control over the students coming in, the curriculum or the expectations (e.g. one school near here puts second-year ESL students in AP English based on age, even if the teacher knows they would learn more with more basic coverage first), and don't have the ability to get the school or parents to provide support. The students were the reason I said “one of” since they do have even less control.

I'm glad that you were able to take the option of going somewhere else but that's hard for many people to do unless they happen to have skills which are in demand in industry. Unlike many other jobs, there are only a few employers in most areas and they hire at set times of year. If you're the CS teacher and have picked up some PHP, that's probably manageable but if you're an English teacher you're probably looking at a career reset or either taking a much longer commute or moving.

If teachers cite long hours, they are lying.

http://www.bls.gov/opub/mlr/2008/03/art4full.pdf

Kind of makes you wonder how truthful their harder to verify claims are.

Here in DC, hitting the right numbers gets a bonus which is close to 50% of your salary – or nothing if you're slightly low...

You've found a bad bonus structure. Making the bonus linear in value-add would solve this problem. Again - not a problem with testing at all.

Or maybe it's not such a bad bonus structure - I'm told that cliffs are a great way to motivate salespeople. I guess salespeople are better at managing their emotions than teachers?

> I didn't claim that teachers take their stress out on students. I simply claimed that if they did, they are horrible and unprofessional.

Maybe there is misunderstanding around the phrase "take out on" (it doesn't imply intentionality to me), but how could stress not affect a teacher's performance in the class room? It doesn't mean they're horrible and unprofessional, it means they're human!

Standardized tests measure students' ability to take standardized tests. This loosely correlates with their knowledge and understanding of the subject matter, and correlates more tightly with knowledge of test-taking strategies specific to the test they are taking. So no, most of what students need to know to pass the tests is not useful real-world knowledge.

To put it another way, knowing the material is not the easiest way to pass the test, so even if the test nominally evaluates useful real-world knowledge, a high score won't guarantee that a student actually possesses that knowledge.

> You have to ask, "is this stuff that a graduate of the system should be able to do?"

Uhm, I don't feel like I do? Or at least insofar as I do, that set feels like it should be really small, because: Which graduate?

There are many things that we'd like a graduate to do, but we don't need for every graduate to be able to do. I would quite like my CS grads to understand big O notation - I would not attempt to teach it to everyone. I would quite like my history grads to be able to perform independent research - I don't really care if my receptionist can.

There are basic low level things that everyone should be able to do. Addition, multiplication, subtraction, division. But that set is quite small, and it beggars belief that one needs a hundred plus tests to figure out where someone is with respect to those things.

Structured within that context, the idea that it's a good model to teach the tests; to have a list of things that you'd like graduates to be able to do and if they don't do that they're failing and the school's failing (and so on); seems supremely wasteful. If the students do some maths in the mean time and discover a passion for some particular element of it, great, but it's not useful to attempt to make them meet some idealised standard that doesn't reflect reality, rather than focusing on teaching people where their inclinations and skills lie.

Here are some real standardized tests. Which students don't need to be able to answer "Roberto paid $43.08 for 3 CDs. All 3 CDs were the same price. How much did each CD cost?" Which students don't need to be able to compute 3 x (3/4)?

http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqmath7.pdf

http://www.nysedregents.org/Grade8/Mathematics/20100505book1...

http://www.nysedregents.org/Grade8/EnglishLanguageArts/04261...

Since you seem to think the test covers too many topics, perhaps you can read it tell us concretely which ones should be removed?

> Since you seem to think the test covers too many topics, perhaps you can read it tell us concretely which ones should be removed?

I think you've somewhat missed the point, though I'm happy enough to play that game.

My question would be which adults need to know those things? You ask me, "Which students don't need to be able to compute 3 x (3/4)?" And I would be inclined to answer anyone who doesn't want to go into some field that uses a lot of mathematics; accountancy, physics, computer science, biology, et cetera et cetera. Outside of the education system, for a lot of people, that knowledge has no value. And it's the same with the questions upon angles, the questions about area... people who aren't going to be working in particularly quantitative professions do not need to know these things.

Your secretary does not need to know (taken from the sheets you posted) what an angle given by a line bisecting two parallel lines is. They don't need to know what 833,000 is written in scientific notation. They don't need to know what 2 over 3 to the power of four is, or which of the following: the square root of 144, the square root of 16, the square root of four, the square root of three - is an irrational number. They don't need to know what a 20% discount on a price of $37.50 is, it will be marked on what they want to buy. They do not need to know what has the same value as 5 to the power of 6 multiplied by 5 to the power of -2. Or what (jk)^-5(jk)^3 is. They do not need to know what the value of 4 to the square root of X is when X is 100. Or which graph shows that Y is equal to minus X squared.

These things all have a use, but they don't have a use to everyone. They don't have a use to nearly everyone. Most people do not work in a profession where that sort of maths is useful.

Your taxidriver does not need to be able to understand algebra, your secretary does not need to be able to understand geometry, your customer service representative does not need to be able to do calculus. And it is a waste of time, effort, money, and passion to try to teach them to do so if they are not interested.

I would suggest, in the place of general standardised tests, a system more similar to the badges given out for scouting: pass fail assessment of a particular skill, voluntary participation, fine-grained certification. You have kids in a school, and if they want to go for their level 1 geometry badge, or whatever, then you help them do so. You retain the absolute basics that everyone has to have in order to get by in society, like addition, multiplication, division. And everything else you take out into a much finer-grained system that vouches for specific skills.

That would allow both a better analysis of the sort of skills that are being promoted in particular areas by particular schools and it will allow children to pursue their aspirations rather than being shoehorned into a process that is not suitable for everybody and manages to say very little with respect to specific careers. People shouldn't end up shit-listed for life because they ended up studying a bunch of stuff they had no interest or passion for but which unfortunately, because of the way the system was set up, is the only way that their employer had to assess anything about their education.

For the people who don't need to realize that a 20% discount on $37.50 is $30, why bother sending them to school past 6th grade at all?

Now that I see your argument more fully, it seems less like an argument against testing and more like an argument against wasting resources on unneeded education. Do you believe the people who don't need the specific topics you mention actually do need education beyond grade 6? If so, why?

What is this hypothetical 12-year-old going to do for the next six years until they are old enough to get the kind of minimum-wage job that accepts people without a diploma? Child-labor laws are still a thing...

We're running into the other problem with public schooling: it's not so much about education as warehousing children while their parents work during the day, until like a tree, they grow the requisite number of rings that magically grants them status as an (more-or-less - see alcohol, car rentals, etc.) independent being. You can see this with the expansion of organized after-school sports and activities - school usually runs from 7:30-8:00AM to 2:30-3:00PM, except parents are still working until 5:00PM, so you've either got to trust your kids to get off the school bus and not burn the house down in two hours, send them to grandma, pay for ruinously expensive child-care, or hope little Johnny or Sally is into soccer/football/baseball/band/art, etc.

On the first point, I would argue that understanding how money works is a pretty fundamental mathematical competency - percentages like that come up all the time with sales taxes, meal taxes, etc, and they are usually not built into the prices on the sticker/menu.

> For the people who don't need to realize that a 20% discount on $37.50 is $30, why bother sending them to school past 6th grade at all? Now that I see your argument more fully, it seems less like an argument against testing and more like an argument against wasting resources on unneeded education. Do you believe the people who don't need the specific topics you mention actually do need education beyond grade 6? If so, why?

It's an argument against a specific form of testing. Frequent standardised tests; testing the same things across all the schools and all the students; using that as your measuring stick, shapes the fact that you're going to get a lot of unneeded, even harmful, education. And the more frequently you run those tests, the better your 'data' is (data which is not politically neutral, as some might think) the more pronounced the effect. Test scores are the incentive.

There's two answers I can give to your question. One is the practical answer, as things stand at the moment. The other is the idealistic answer, as things could stand.

For the practical answer, the most that I can say about someone who matches that pattern persisting in education, in the current system, after grade 6 is that they may be getting something else out of some of the other subjects that they study there. If you were a parent, and you couldn't afford to educate your child yourself, then it would probably still make sense to send your child to school beyond grade 6. If you don't do so, they won't have the qualifications to get by particularly well in life, and they may learn something useful in the process (though I wouldn't bet too much on it.)

Besides, you still need some where to stick your children while you're at work. If nothing else, education is free child-care for poor people.

That's not a good argument, nor is it an argument for the current system over the potential alternatives, mind. It's just saying that sometimes crap's the best thing on the menu.

For the idealistic answer: What I'm advocating for is a different model of testing, in which the statement that someone would need an education 'beyond' grade 6 is not as meaningful. There are different skills, different areas of expertise that they could go into, but it would be very difficult to rank those skills: Is someone who we've certified can refit a central heating system more or less skilled than someone who we've certified can rewire a house? Someone with both is more skilled than someone who only has one, but at the same time are they a better electrician than someone who only has one? Is someone who understands the mathematics underlying musical theory more or less skilled than someone who understands the mathematics underlying computational complexity? If you can apply Bayes Theorem, are you more or less skilled than a frequentist statistician? It's a lot harder to rank people when you throw out the idea of 'this year,' or grades, and just have specific skills and people who can or can't do the job.

Ideally I'd be able to answer your question by saying that children are given the chance to immerse themselves in a wide range of different subjects and projects - to follow those that appeal to them as far as they can go so that when they leave they have a wealth of ability that carries them through their lives. That if you're interested in mechanics, for example, you should be able to study mechanics all the time you're at school. Wouldn't we have some fantastic mechanics if they'd been learning on cars and lorries and boats and so on every week day for five or ten years under coaching appropriate to their skill level? Wouldn't we have some fantastic builders if they'd been learning building under that setup? Fantastic artists, fantastic musicians. Especially when we could focus on those who were interested. And who knows, they might - as they get further in that area - discover that maths is useful, and then they could go and get some maths badges when they've got a passion and a reason to drive their learning, (rather than it being something forced down their throats with no real promise of a relationship to their actual interests materialising.)

But I can't - and so the former answer is what we're saddled with. Do you need it? Sure. Unless you've got reasonably well-off parents, you've got to go through the paces. Should you need it, in that form? No.

I'm sure the shop-owners will be champing at the bit to have customers that can't check discounts in their heads, or employees that can't manage a till...

> Frequent standardised tests; testing the same things across all the schools and all the students; using that as your measuring stick, shapes the fact that you're going to get a lot of unneeded, even harmful, education.

Harmful? Really? Please tell what harmful education is coming out of standardized tests. Even the standard test taking strategy itself is useful in a general sense. You don't know the solution so narrow down to ones that seem reasonable, pick one and move on.

> Harmful? Really?

In my charity work I regularly interact with people whose education has been harmful to them. They failed, and from that failure gained the impression that they were stupid, and/or unable to learn specific subjects. Even putting aside the harm of taking up someone's time to no profit for themselves, you learn more than the information in the curriculum. You learn an attitude towards education, an assessment of how you relate to it. What many people learn is that it's not for them.

That's the fault of a poor education process and not that of education or even testing for that matter. This was posted on HN the other day and it is certainly something I had to overcome as I transitioned from being told I was smart to almost failing out of college.

http://akaptur.com/blog/2015/10/10/effective-learning-strate...

I think we need more methods for teaching (I wish I had Kahn Academy when growing up!). Everyone gets to where they understand basic math and reading comprehension in their own way, and that's fine. But if we are not checking up on students progress and making sure they have some basic level of general education, we are failing the students.

If you were a parent, and you couldn't afford to educate your child yourself, then it would probably still make sense to send your child to school beyond grade 6. If you don't do so, they won't have the qualifications to get by particularly well in life...

My rebuttal: Your secretary does not need to know (taken from the sheets you posted) what an angle given by a line bisecting two parallel lines is...These things all have a use, but they don't have a use to everyone...

Your idealistic answer seems to argue for changing the relevant topics. That's fine. That's an argument against the curriculum, not testing. All testing does is measure whether the curriculum is actually being taught.

All testing does is measure whether a very narrow curriculum taught in a very specific way with a very specific text and test prep guide as guidance is being taught. Since so much is put on not only passing these tests but improving every year (a near mathematical impossibility) schools define their curriculum by what is being tested, not what constitutes a well-rounded education (backed by scientific studies into the importance of topics and areas of study not tested).

You know what generally gets better test scores out of kids? More time spent studying how to answer questions and rote memorization of test topics. All done studying that stuff? If you study it more maybe one kid does better and we get more funding.

> Your idealistic answer seems to argue for changing the relevant topics. That's fine. That's an argument against the curriculum, not testing. All testing does is measure whether the curriculum is actually being taught.

A relevant curriculum is going to be different depending on what someone's interested in and what jobs are available - and what you measure and incentivise is what you get. Testing is not politically neutral.

There isn't anything wrong with testing, in principle, at some point you have to see whether someone can do the job. But the decision as to what to test, when, how... that influences what you're going to end up with. Just standardising the tests and running them often is a bad approach. That's what I'm saying.

Yes, testing does enforce the curriculum. If you don't like the curriculum, that might be bad.

I'm curious though: why do you think that, absent testing, teachers would be ignoring the prescribed curriculum and secretly implementing your preferred curriculum instead? If they are not secretly doing this, then without testing teachers wouldn't be doing what you want them to do anyway.

So you are arguing that we as a society need to lower our general education standards? Is this not the exact opposite of what we need to be doing? Math in particular is so important whether dealing with personal finances or simply thinking abstractly. What happens when the hypothetical taxi driver job goes away? If society didn't care enough to try and teach that person some general education when we had the chance, are we now going to do it in retraining?

> So you are arguing that we as a society need to lower our general education standards? Is this not the exact opposite of what we need to be doing? Math in particular is so important whether dealing with personal finances or simply thinking abstractly. What happens when the hypothetical taxi driver job goes away? If society didn't care enough to try and teach that person some general education when we had the chance, are we now going to do it in retraining?

I am arguing that as a society we need a different approach to assessing skills. That the incentive structure that the current model of teaching and assessment provides is not useful for providing the skills that our young and the labour market that they will hopefully become part of require in order to advance and profit. I am not necessarily saying that mathematics is not a valuable skill, but if it is valuable then it should show up in the course of teaching things that children are actually interested in - and if it is widely applicable then most of them should pick up a few mathematics badges here or there in the process of pursuing those interests. I do not believe that children will acquire and retain any great facility with a subject that they detest, or that bores them.

Is the taxi driver, with his five years experience of taxi driving and limited knowledge of mathematics, physics, law, medicine, et cetera; in other words the jobs that would be harder to automate entirely in the short and mid-term future (by which I mean the next 20 years or so); really going to compete with people who have been doing those jobs the last five years on the strength of half remembered mathematics, which he probably hated when he did them anyway? Especially since we don't have a system of retraining, at least not in any serious sense. There is no option to go to the local benefits centre, state that you are done with working in retail and want to retrain to be a programmer, and have funding and an education available to do so. I don't know of anyone, anywhere, that makes that sort of investment in people. If you want to retrain, you'd best have a bit of money.

The taxi-driver is probably better off not having taken a mathematics course (under the current curriculum) at school, if that subject did not appeal to him, and not thinking of learning the subject as an act of suffering, or operating under the impression that he cannot learn it based on failing a number of tests on the subject some time ago. I regularly work with people with a background in in low income industries, as part of my charity work, and a great many of them have the assumption that they are simply incapable of learning and trace the roots of this assumption back to their failures in the education system. They don't have a faith that they can learn, or an understanding that anything good for them will come from investing in subjects that they have previously hated. It won't have made him competitive with people who were actually interested in the subject in any case - and there's no clear route of retraining that would let him become so.

As for the importance of mathematics to "thinking abstractly", I will observe that it is an old chestnut trotted out whenever one wants to justify a subject, and that as such I've ceased to take it seriously. That you claim it to be a particular virtue of mathematics, and others will claim it to be a virtue of English literature, philosophy, history, and so on and so forth. Indeed, it is hard to think of any subject that has not claimed it is a virtue of its own. At some point we simply have to stop taking the excuse seriously or accept that it is a general enough skill that you can pick it up in a wide range of subjects, and that as such it is not a great argument for retaining any specific subject.

If it is important to "think abstractly", and if we eventually come up with a way of understanding quite what people mean when they say that, then we may well profit by separating that skill out from the particular application of it and teaching the skill specifically. I understand that there are people trying to make a study of how one learns rationality, and that if one wish to teach the skill one might perhaps consult them and see what their methods were.

I'm not sure I can relate at all to your argument when you are arguing against basic math education. Standardize testing is not testing physics or law or medicine. It is testing bog standard basics. If we cannot get our youth up to that standard then something is very wrong, and blaming it on a test is a huge mistake.

>The taxi-driver is probably better off not having taken a mathematics course (under the current curriculum) at school, if that subject did not appeal to him, and not thinking of learning the subject as an act of suffering, or operating under the impression that he cannot learn it based on failing a number of tests on the subject some time ago.

This is not maths fault or the curriculum. It is the fault of a very poor teacher who can probably never be fired. Even then, doing things that you don't want to do, but they are good for you is part of growing up and becoming an adult. Is your opinion really that we should keep churning out young adults who have no concept of the basics. I have a few more title/payday loan shops I need to go open up.

The bog standard basics presumably relate to more advanced areas, for the purposes of your argument. Otherwise the taxi driver would be unemployed, and out of luck, regardless.

Nonetheless, I've yet to be convinced of the necessity of meeting that standard, basic or not. If one is to look at the UK education system, which doesn't seem to produce measurably worse employment or lives for its participants than the US, then one will note that the maths being taught in the papers given by the person I was responding to in the US is not dissimilar to the lower stream maths GCSE - taken at around 16 - in which a C is a quite acceptable grade for most purposes. Even then, there are things there that would not show up in a GCSE paper - a kid wouldn't need to know scientific notation to pass that test with a C.

As for payday loans etc. The obvious answer is 'don't accept deals you don't understand' it's possible to sting people on a great number of things, based on your advantage in some area that they do not understand. If it's not maths it will be penalty fees hidden in the legalize. By the time you're up to needing scientific notation and square roots to understand your loan, it's a deal that someone ought not to have taken in the first place.

It does not seem unfair to me to ask: You describe it as basic, and threaten all these consequences if it's not taught... there are places where that level of performance is not expected, and these consequences do not seem any more in evidence. So, why should I buy into the idea that this knowledge is needed?

Don't you think there's a qualitative difference involved in teaching for the purpose of instilling enough knowledge to pass an exam, versus teaching to instill a passion for the material? Making dioramas, drawing political cartoons, and wearing togas while reciting Mark Antony's speech from Julius Caesar were the kinds of things that kept me motivated to read and understand material in which I held no innate interest, and all of that seems superfluous to a test-driven approach.

It's far more important that students can add than that they got to goof around in togas. Ideal world? They can do both. But if they can't do the math, then the togas just have to wait.

Sounds like you have a lot of experience teaching.

Reply on news.ycombinator.com