Numeracy and Mathematics

I have asked for a little space on the new blog created by my wife, as I had recently come across something I felt worth sharing with the interweb, and felt I might come across similar things as time goes on.

The specific thing was a quote on the nature of Mathematics and how it may relate to this ill-defined thing, Numeracy. 
I guess I need to give some background to this before progressing to the quote and some thoughts on it. A few years ago I completed a Level 5 qualification in teaching Adult Numeracy, to go with another qualification that I got a few years before in teaching Adult Literacy. These qualifications are undertaken by those who teach, or are interested in teaching, individuals over 19 years old ‘basic’ Maths and English. They are specified as a requirement to teach the subject full time with government funding (though this often gets overlooked as the qualification is far from universal).
As part of the course we had to write a short piece on the history of Mathematics and also another piece on the difference between Mathematics and Numeracy. Both ideas caught my attention somewhat and they are subjects that I have returned to in my thoughts from time to time. 
When I studied, I was lucky enough to have access to a reasonably well-stocked set of libraries (by no means exhaustive, but I know other colleagues have not had such opportunities). Not only that, as I continue to read and think about these things I come across things that make me say, “I wish I knew about that when I was reading for the first time.” These blog posts are my effort to share things that I have found interesting, and save those who come after me a little bit of effort in hunting these things down.
Last week I bought the the Loeb Classic’s Greek Mathematical Works – Thales to Euclid, compiled and translated by Ivor Thomas,  initially in 1939. See here. It has both the Greek and an English text and looks as thought it will keep me challenged for a while. The very first quote in the book is from Anatolius, who Ivor Thomas tells us was Bishop of Laodicea about AD 280. He said;
“[Some teachers] say that … poetry and the whole of popular music can be understood without course of instruction but no one can acquire knowledge of the subjects called mathematics unless he has first gone through a course of instruction in them;”
p3, Greek Mathematical Works, vol 1 Thales to Euclid (Loeb Classical Library No 335)  Ivor Thomas, Harvard University Press, Cambridge Mas, First printed 1939 Reprinted with Additions 1980
What I find interesting here is the idea that Mathematics is something that is defined by the fact it has to be taught. Almost by implication you may wish to define Numeracy then as something that does not need to be taught. I think that does a disservice to Numeracy, and to those who struggle to pick it up. Perhaps what we are reaching for in 21st Century education, though, is a truth that was stated all those years ago in the 3rd Century AD: that Mathematics requires formal study to be understood, whilst Numeracy can be learned through more informal learning. Mathematics then is the stuff of the academy, a world of rigour, technical language and thought. Numeracy though, consists of the everyday informal conceptions of quantity and amount. I would say defining Mathematics by its need for formal tuition is almost a back to front definition, defining first not what it is, but what it needs. It is like finding a burglar by the impression of their boot by the broken window. It is an interesting clue to the nature of Mathematics that it needs to be defined in such an unusual way.
Frank