Oh, and also for trigonometry, which you cannot do without a calculator.

Yes you can, this is why the good lord gave us log tables.

When I was doing GCSE Maths about two years ago, it was very focussed on passing exams, not setting you up for how to use it in life. Same for most of high school to be honest. How I came out with an A* is beyond me.

This was starting to be the case when I did GCSE Maths, they don't seem to actually teach you how to do anything any more.

It depends what kind of maths is being failed. Not everyone needs to be able to solve equations and use trigonometry in their daily lives. If someone can't even do simple arithmetic, then that's more of a problem.

If one does not learn the logic of how to minipulate variables in equations, a lot of further consepts, not only in Mathematics, Science and Engineering, but a lot of aspects that apply in daily life will start to puzzle the population. Such as some of the very basic consepts of collation of groups, if one doesn't know this, some things will be very challenging.

That said, we now have machines to do a lot of number crunching for us, so being able to do mental arithmetic quickly is somewhat redundant. Times tables also suffer from the same problem; they were very helpful when we had pounds-shillings-pence, but now everything is in multiples of 10.

If you don't know how the machine crunches the numbers, or at least what the result should look like, then when someone's finger slips inputting the number, the mistake will not be noticed and it will cost money. Quick arythmatic is never going to be redundant, if you can't add, subtract, multiply and divide, god help us.

Don't start me on how one can think 'times tables are not useful' it has sod all to do with £/s-d and yd/ft/in since this is more a base of units problem rather than a times tables problem. And not everything is in multiples of 10, far from it. "How much do these seven drinks cost if one costs this?" is that a multiple of 10, no...

Then it comes to the point of those who are going into higher levels of mathematics, engineering etc. I have known students not be able to spot a very simple inverse laplace transform from tables because the're unable to solve arytmetic calculations without a calculator, and thus have a great deal of difficulty in spotting patterns. Also a problem that is putting off employers these days who are increasingly using phycometric testing, such as FastTrak that does not require any complex mathematics, but the arethmetic and analysis skills one gains by completing arythetic problems without the use of any calculators.

If someone doesn't know what 25 + 36 is without a calculator then we're going to see problems, let alone if I started speaking in terms of different units and outside of base 10. (it's 61 by the way...)

If I asked someone in this forum to add up 143 inches, 3 yards and a chain, I wonder how many people could tell me how many feet that is in total... (This ISN'T hard!) but if you don't have arythmetic skills that are very simple to know, it will be very hard. If these are no longer being taught in schools, when will they learn this?