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Wednesday, 22 July 2015

The Language of Math

   You could say that each discipline or area of academic study has its own language and terminology. This is true also for mathematics.  The symbols and numbers enable us to think about our world in terms of size, shape and quantity.  One of the interesting things about math is that, until you get to word problems, foreign students are able to continue to excel in this subject even if their language skills are lacking.
   However, I recently came to realize how one's language of instruction does have an impact upon mathematical knowledge and understanding, thanks to Malcolm Gladwell's book Outliers: The Story of Success.  He points out that the words for numbers in some languages either help or hinder mathematical understanding.  I learned English and Dutch virtually simultaneously before the age of six, so I did not spend much time analyzing the differences between them at that time.  I do remember noticing at one point, no doubt influenced by the fact that I was learning math at school in English, that in Dutch the numbers above 20 seemed backwards to me.  In English, we say "twenty-five", but in Dutch it's literally "five-and-twenty."  (Apparently at some point in history English used that same format of placing the ones before the tens, as preserved in the nursery rhyme "Sing a Song of Sixpence" where "four-and-twenty blackbirds" were baked in a pie.)
   What dawned on me this week is that English has it more backwards than Dutch.  In the numbers between 13 and 19, we place the ones before the ten (or "teen") as we say these numbers.  However, after twenty, English reverses them and places the ones last.
From The Chinese Quest website
   Gladwell did not speak about Dutch in his book; instead he spoke about Chinese.  The words for the numbers 1-9 in Mandarin & Cantonese are much shorter and quicker to say than in English and most other languages.  In addition, after ten they follow a consistent pattern divided into tens and ones.  So, for example, literally 34 is stated as "three-tens-four" and 19 is "one-ten-nine."  These simple differences alone mean that an average Chinese child can count to 40 at the age of 4, while Canadian/American children are expected to reach only 15 by age 4.
   A second mathematical advantage in Chinese has to do with its words for fractions.  We say 3/4 or three-quarters.  For the child learning this, it is not particularly visual.  Yet in Chinese, it is more like "out of four parts, take three" (Gladwell, p. 230).
    Even though math is considered to be a language one can use without words, it would seem from this simple analysis that one's language does influence whether math is seen as a simple, logical discipline or a difficult, frustrating one.

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