English as a dialect of mathematics

The West writes and reads text from the left to the right while Hindu-Arabic numbers are from the right to the left. Thus 14 is “fourteen”. English switches order from 21, to “twenty·one”, while Dutch still has “een en twintig” and so on till 100.

There exists an alternative number system that satisfies didactic clarity so that pupils could learn arithmetic rather quickly. This uses the language of mathematics. The translation to English would be a mere matter of learning another dialect, which cannot be a burden in any way also given the small set of words and concepts. For example 59 can be “five·ten·nine” where English as a dialect has “fifty·nine”.

Perhaps the English and American reluctance to learn other languages and accept dialects is a larger bottleneck than possible doubts about the didactic advantages. The key notion thus is to regard English as a dialect indeed, and extend lessons on arithmetic with clarification of the dialect.

The issue came to my attention by Gladwell (2008:228):

“Ask an English-speaking seven-year-old to add thirty·seven plus twenty·two in her head, and she has to convert the words to numbers (37 + 22). Only then can she do the math: 2 plus 7 is 9 and 30 plus 20 is 50, which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It’s five-tens-nine.”

There is not only the notation of 59 and the pronunciation, but also the notation of the pronunciation. Instead of “five-tens-nine” a better notation is “five·ten·nine”, thus no “tens” and thus the use of a high dot. The hyphen is unattractive since it is too similar to subtraction. The dot is not pronounced, like the hyphen or comma.

The choice derives from mental working space. Gladwell (2008:228): “(…) we store digits in a memory loop that runs for about two seconds.” English numbers are cumbersome to store. He quotes Stanislas Dehaene: “(…) the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits.” The quick fix is to use Cantonese internationally, yet this will meet with some bottlenecks.

This paper contains the longer discussion. The Appendix contains a stylized presentation for six-year olds. This is not intended for actual use in class but contains the framework for starting to think about that. It was written at the occasion of my son M.’s sixth birthday.

PM. Dehaene has also this useful quote here: “A lot of conceptual difficulties could be clarified if mathematicians and theoretical physicists paid more attention to the basic distinction between model and reality, a concept familiar to biologists. ” Mutatis mutandis for economics.

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