An earlier weblog discussed that English is a dialect of mathematics. Compare:
Number Math English
14 ten⋅four fourteen
21 two⋅ten⋅one twenty-one
Professor Fred Schuh of TU Delft wrote about the different mathematical pronunciation in books in 1943 and 1949, and addressed the Dutch minister of education in 1952 (see here). Many others observed this issue too. There is a gap though between understanding the idea given by these few examples and seeing it developed fully. Thus I decided to write out the alternative.
The issue is discussed in A child wants nice and no mean numbers. For some particular languages, the suggestions are in Marcus learns to count with ten. Select your language (text in English, numbers in the particular language):
Update Sept 3: There now is also this proposal on developing an international standard for the mathematical pronunciation of the natural numbers.
The devil hides in the details
When you look at details then subtle problems show up. First of all, it appears better to use the middle dot instead of the hyphen, to prevent confusion with the negative sign.
Secondly, when mathematical pronunciation in German would use zehn for 10, then 90 in math would be neun⋅zehn, which would conflict with the current use of neunzehn for 19. You cannot seriously propose such a change because it would create confusion. Germans would have to ask each other continuously: “Are you speaking math or dialect ?”
There is already a regularity in German for the numbers of ten 20, 30, 40, …, 90: zwanzig, …, neunzig. Hence, German has at least these options: (a) adopt English ten for 10, (b) use zig for 10. The latter would give least change.
Number Math in English English Math in German ? German Math in German !
19 ten⋅nine nineteen zehn⋅neun neunzehn zig⋅neun
90 nine⋅ten ninety neun⋅zehn neunzig neun⋅zig
A compromise would be to accept 10 = zehn = zig, and to use zehn up to 20 and zig from 20 onwards. When you are accepting change then rather do it properly though. My suggestion is to use zig. Dutch has the same problem, and here my suggestion is to use tig.
Danish might use their current word ti for 10. However, I have listened in Google Translate for the Danish pronunciation of ti⋅ti for 100, and though it sounds like tea-tea, I find it less convincing. My proposal for Danish is to use ten, which they already use for the numbers 13-19.
English actually has the same issue. The numbers of ten 20-90 use ty (e.g. forty, fifty), so that we might consider using ty instead of ten. This would give least change as in German. Then 90 would be nine⋅ty instead of nine⋅ten. However, English ty⋅ty for 100 is less convincing again. Thus ten for English is best.
German, Dutch and Danish might all adopt English ten. They already adopt Google or computer, and it would be curious when they are prim on 10, while change would benefit the learning of arithmetic by their young children enormously.
French can use dix for 10 without problem. French has some curious twists and turns. It suddenly relies on addition (soixante-dix = 60 + 10 for sept⋅dix = 7 × 10) and then swiches to multiplication with 20 (80 = quatre-vingts for huit⋅dix = 8 × 10). When 20 changes from vingt to deux⋅dix, then it becomes advisable to change the whole system.
Overall, we again see that mathematicians are trained for abstract thought and have insufficient awareness of the empirical realities of education. Mathematicians should explain to both teachers and language managers about the difference between mathematical pronunciation and national dialects. The problem doesn’t necessarily lie in education but rather in mathematical neglect.
Professor Fred Schuh explained much of this already in 1943-1952, and thus one can argue that mathematics did explain it to education, so that it is the responsibility of education that they did not make the change. This is too simple a view.
This simple view does not square with devoted teachers who explain to their beloved pupils that soixante-quinze + seize = quatre-vingt et onze (check the confusing hyphen), in the belief that they are doing perfect arithmetic. These teachers should have had proper mathematics education, so that they know that they are short-changing their pupils.
Mathematics education should accept its reponsibility and free itself from the stranglehold by the abstract thinking mathematicians who have no idea about the empirics of education. (See my earlier letter to IMU / ICMI.)