I have a maths degree, but completely screwed up some basic arithmetic recently. Arithmetic is, as you said, a branch of mathematics, but it not the sum total (pun intended) or even a necessary part. Rather than equating it with not knowing the letters of the alphabet, I'd liken it to being unable to spell:
Good spelling, while useful in every day life isn't nearly as important as being able to write well and understand complex texts; a computer can help you with spelling. Similarly in maths, good arithmetic can be useful in life in speeding things up a bit, but with calculators on every phone and computer it isn't crucial. Whereas the important bits of maths (analytical thinking, the rigours of proof, reasoning, deduction etc.) are much harder to get a computer to help with, and are much harder to spot in oneself if not present.
It doesn't really matter if people can't remember how to do long division or multiplication by hand; what matters is that they find out/work out how to do so when needed. Given that, the OP's point does have some validity, and is not merely pedantic. That said, the title mentions "numeracy", not mathematics.
Of course, the real problem seems to be not that people cannot do maths (which, anecdotally, ime, they usually can when given encouragement and a few pointers), but that they're being taught to answer maths test questions, rather than understand the principles behind the problems; as such, it's easy to forget the specific methods, and hard to work them out later when needed. Sadly this seems to be a problem across much of the UK education system.
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/buKrtOsdZEo/is-poor-numeracy-ruining-lives
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