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.

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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.

>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.

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?

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?

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.

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.

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.

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.

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.

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.

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.

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.

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.