Can a Simple Brain Hack Cut China's Lead over the USA in Mathematics Rankings? How the West can unleash 'wordfare' to fight Asian supremacy!

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CURRENT SITUATION (OECD School Math Scores 2012,) 
1 Shanghai, China 613
2 Singapore 573
3 Hong Kong, China 561
4 Taiwan 560
5 South Korea 554
6 Macau, China 538
7 Japan 536
... 19 Australia 504
... 26 UK 494
... 36 United States 481

Somewhere, sometime, a six year old girl might learn how to count to seven billion because of this article, and think it's easy!  Meanwhile, North American four years olds count to 15, while Chinese four year olds count to 40. [1] 

Forget amazeballs, twerking and selfie... read on to discover why  onety
should be Word of the Decade!

In case you missed it, 'emoji' is Oxford Dictionary's 'Word of the Year' for 2015.  Meanwhile, over at Collins Dictionary, 'binge-watch' got the prize.

Whether or not you are financially successful in life, may, in fact, be determined by one simple thing.  This article is about that simple thing and how to supercharge that simple thing, and in so doing, increase not only GDP per capita, but reduce human misery. As you may have figured out, this is about the foundations of figuring; counting. Notably, distinguished Professor of education, Dr Greg Duncan, said 

“Early math skills are by far the number one predictor of later achievement, ahead of reading and attention skills.” [2]

Yet it's not just about counting. If the West is to ever come close to catching up with Asia in Science, Technology Engineering and Medicine, its basic math words will need a 'light bulb moment'.

It's as simple as flicking a switch, 
from complexity to simplexity!

The most essential pre-school mathematical insight isn't just about counting. It's about India's base ten place value system. Yet the counting words little children are taught in English destroy the most important foundation of mathematics!

If you watched the YouTube video above, you may recall I suggested a child may know that ten plus ten is twenty. Yet simpler math words are much more powerful! Ask any little girl that can add one plus one what one ty plus one ty is and she will answer "two ty" without any drama whatsoever!

According to the Oxford English Dictionary, the suffive -ty is an abbreviation for ten [3]. This is why we use such words as ninety, eighty, seventy, sixty and forty. Each number word embedded describes a count of tens. Simple!

Now mathematics has been described as a 'science of patterns' [4] it makes sense to let our children both 'see' and 'hear' the patterns in their number words. that's what the Chinese and Japanese do, yet it's NOT what the West does.

Germanic origin words such as eleven and twelve cannot be split into tens and units [5]. When was the last time you used the word 'twen' on its own in conversation? You haven't? That's because it became the word 'two', yet we keep saying twenty instead of twoty, while not thinking twice about saying sixty. At least we moved on from twentig which came before twenty! [6] Also, when was the last time you sat on a thir legged stool? You haven't? What about a three legged stool? When was the last time you counted to tyne? You can't remember? That's because tyne morphed into ten.

To make matters worse, the teen words such as seventeen (seven ten) for 17 are read backwards! We let new words such as 'dadbod' enter our vocabulary, yet fail to weed our mathword garden, let alone plant new flowers!

Here's another short video that makes the point about the West's problematic number words.  

Yet it's not just kids getting confused by our number words. This is crazy!

Long ago, India had a fascination with numbers large and small. Infinity and zero were being embraced many centuries before churches in the West said such concepts were the work of the devil. Notably, India had a name for every place, each ten times the value of the place to its right, or one tenth the value of the place to the left. Recycling the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 with place value is the heart of all mathematics, and all modern science. (Apart from the Babylonians base 60, which we still use for time and angles.)

So while Western children count to every higher numbers, Asian children only ever count to nine before they recycle their number words and apply base ten to reduce their mental RAM overload. A Western child is more likely to think of 12 blocks without any simplification as twelve blocks, while an Asian child is more likely to think of 12 blocks as one ten group and two blocks. Why?

It's in the simpler number words Asian use that reveal, rather than hide, the mathematical pattern of place value. North America's Common Core State Standard for Grade 4 (Ref: CCSS.MATH.CONTENT.4.NBT.A.1) has the objective: "Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right."

How much easier (and earlier and cheaper) would this standard be achieved with kindergarten level words that revealed place value? Currently there are the reverso teen words and the 'unsplittable' Germanic words like twelve that hide math patterns.

From the book Outliers, by Malcolm Gladwell, we read: 

"Four year old Chinese children can count, on average, up to forty. American children, at that age, can only count to fifteen, and don’t reach forty until they’re five: by the age of five, in other words, American children are already a year behind their Asian counterparts in the most fundamental of math skills.

The regularity of their number systems also means that Asian children can perform basic functions—like addition—far more easily. Ask an English 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 nine and 30 and 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.

“The Asian system is transparent,” says Karen Fuson, a Northwestern University psychologist, who has done much of the research on Asian-Western differences. “I think that it makes the whole attitude toward math different. Instead of being a rote learning thing, there’s a pattern I can figure out. There is an expectation that I can do this. There is an expectation that it’s sensible. For fractions, we say three fifths. The Chinese is literally, ‘out of five parts, take three.’ That’s telling you conceptually what a fraction is. It’s differentiating the denominator and the numerator.”

The much-storied disenchantment with mathematics among western children starts in the third and fourth grade, and Fuson argues that perhaps a part of that disenchantment is due to the fact that math doesn’t seem to make sense; its linguistic structure is clumsy; its basic rules seem arbitrary and complicated.

Asian children, by contrast, don’t face nearly that same sense of bafflement. They can hold more numbers in their head, and do calculations faster, and the way fractions are expressed in their language corresponds exactly to the way a fraction actually is—and maybe that makes them a little more likely to enjoy math, and maybe because they enjoy math a little more they try a little harder and take more math classes and are more willing to do their homework, and on and on, in a kind of virtuous circle.

When it comes to math, in other words, Asians have built-in advantage. . ."

OK, so the ammunition for the West's word war follows.

  1 one
  2 two
  3 three
  4 four
  5 five
  6 six
  7 seven
  8 eight
  9 nine
10 onety
11 onety one
12 onety two
13 onety three
14 onety four
15 onety five
16 onety six
17 onety seven
18 onety eight
19 onety nine
20 twoty 
21 twoty one
22 twoty two
...
30 threety
31 threety one
...
40 fourty/forty
...
50 fivety
...
60 sixty
...
70 seventy
...
80 eighty
...
90 ninety
...
99 ninety nine

At this point we can see our mental RAM requirements are much less. We no longer have the backwards/dyslexic teen words and we no longer have the oddball sounds such as twen and thir and we no longer have twelve and eleven hiding the existence of base ten/ty.

When I was a child in the sixties, my mother Judith never said she was born in the twoties and my father Peter never said he was born in the threeties. And now, we still have no name for our current decade! Is this madness? OK, so children born this decade must know they were born in the oneties.

Another relic that hangs around western mathematics is our grouping on digits in clusters of three, as in six hundred and twelve thousand, seven hundred and thirty five, written 612,735. In the words we say both six hundred and seven hundred. Why? Well, we can blame Pythagoras' arcs written over groups of three letter/numbers for that. We say one hundred thousand, while India says one lakh. Yet India's advantage falls over as they don't have the word million, and say instead, ten lakh. Yet in the year 499 CE,  the Indian, Aryabhata, gave different Sanskrit names to each of the first ten places, saying "... from place to place each ten times the preceding." [7]

So how can a little girl count to seven billion more easily than counting to one hundred? Simple. Each place has a name and you skip count from 1 to 9 along each place name.

1 one
10 onety/ten
100 one hundred
1000 one grand/thousand
10 000 one ayuta
100 000 one lak(h)
1 000 000 one million (mill)
10 000 000 one crore
100 000 000 one nyarbuda (ny)
1 000 000 000 one billion

If we use grand as a synonym for thousand, we now have unique initial letter place value names. Units Ties/Tens, Hundreds, Grand, Ayuta, Lak, Million, Crore, Nyarbuda, and Billion.  

The unique place value names create new options for mathematics education. The number 927 843 can now be thought of as 9L, 2A, 7G, 8H, 4T and 3U where L is Lak, A is Ayuta, G is Grand, H is hundred, T is ty/ten and U is unit.

LAG HTU is much simpler than: HT, TT, T, H, T, and U. 

All change is resisted. Math education bureaucrats may dismiss such ideas. Yet as long ago as 1852, many little children in London, were taught to understand onety, twoty, threety alongside the 'adult' words such as twenty and thirty.

"...you should teach your pupil how to add up tens, explaining that twenty means twoty, or two tens; thirty means threety, or three tens; forty means four tens, and so on." [8]

 The ideas in this article ARE common sense, even if more than 150 years old. So is the problem with the West an enduring arrogance? Why should the West adopt simpler number words at kindergarten and elementary school level just because the Asian have simpler number word structures?

In Australia, rich Asians are snapping up houses. The 'Asians' are eating the West for lunch at the moment, and they deserve to. Without the Chinese economy the world would have experience another great depression. I've heard the Chinese produce ten times more scientists and engineers than lawyers, while in the USA this is the other way around.

This article is a cry for help. PLEASE can we do something about math education that: a) makes mathematical sense and b) costs almost nothing!

Given preschool and early school numeracy is the most important predictor of adult 'success', making this small change is likely the best return on investment parents and kindergarten teachers could make.

Thank you for reading!

Jonathan Crabtree
Mathematics Researcher:
The Evolution of Elementary Mathematics
Melbourne Australia
www.jonathancrabtree.com/mathematics

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ABOUT THE AUTHOR
Jonathan Crabtree reviews the evolution of arithmetic via the original writings of the people who invented arithmetic; spanning thousands of years, 16 languages and counting!

PISA OECD MATHEMATICS RANKINGS  2012 Source: https://en.wikipedia.org/wiki/PISA_2012#Results 

==============
REFERENCES

[1] Outliers, The Story of Success, Malcolm Gladwell, Chapter 8, Rice Paddies and Math Tests. "The number system in English is highly irregular. Not so in China, Japan and Korea. They have a logical counting system. Eleven is ten one. Twelve is ten two. Twenty-four is two ten four, and so on. That difference means that Asian children learn to count much faster." 

[2] https://news.uci.edu/feature/kids-skilled-early-in-math-do-better-in-school/ and https://edsource.org/2013/early-math-matters-top-researcher-discusses-his-work/50061

[3]  From the Oxford English Dictionary
-TY, SUFFIX Denoting ‘ten’, forming the second element of the decade numerals from 20 to 90 (in Old English to 120), as twenty, thirty (Old English twentig, trítig), etc. The Old English -tig (gen. sing. -tiges, gen. pl. -tiga, -tigra, dat. pl. -tigum) corresponds to Old Frisian -tich, -tech (pl. -tiga, -tega), Middle Dutch -tigh (Dutch -tig), Old Saxon -tig (-thig), -teg, -tich, -tech (Middle Low German and Low German -tig), Old High German -zug, -zuc, -zoch (Middle High German -zec, -zic, German -zig), and is the same as ON. tigr, tegr, t?gr, tugr (pl. tigir, etc.) and Gothic tigus (pl. tigjus), which are not suffixed but remain independent words, as ON. tveir tigir, Gothic twai tigjus, twenty. For examples of the Old English forms and syntactical usage, see the various numerals.

[4] The American mathematician, Lynn Arthur Steen, wrote: "Mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination." (a) The British mathematician, G. H. Hardy, wrote: "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." (b) Sources: a) Science, 1988, Vol.240, p.611-16
b) A mathematician's Apology, Cambridge University Press, 1940. Books about mathematical patterns include: Mathematics as a science of patterns, by Michael D Resnik; Mathematics, the science of patterns, by Keith Devlin and Mathematics as the Science of Patterns, by Michael N. Fried.

[5] From the Oxford English Dictionary
 ELEVEN Etymology: Common Germanic: Old English ?ndleofon corresponds to Old Frisian andlova , elleva , Old Saxon elleban (Middle Dutch elleven , Dutch elf ), Old High German einlif (Middle High German eilf , German elf ), Old Norse ellifu (Swedish ellifva , elfva , Danish elleve ), Gothic ainlif < Old Germanic *ainlif- < *ain- (shortened < *aino- ) one adj., n., and pron. + -lif- of uncertain origin. Outside Germanic the only analogous form is the Lithuanian v?nó-lika, where -lika (answering in function to English -teen) is the terminal element of all the numerals from 11 to 19.
The Old English, Old Frisian, Old Saxon, and Old Norse forms represent a type *ainlifun , apparently assimilated to *tehun ten adj., n., and adv. The theory that the ending is a variant of Old Germanic *tehun , Aryan *dekm ten adj., n., and adv., is now abandoned; some would derive it from the Aryan root *leiq or < *leip (both meaning to leave, to remain) so that eleven would mean ‘one left’ (after counting ten.)

TWELVE Etymology: Common Germanic: Old English twelf , (also tuelf , and in Lindisf. gl. tuoelf ), = Old Frisian twelef , twilif , twelf (Old West Frisian tolef , West Frisian toalf ); Middle Dutch twalef , twaelf , twelef , twelf (Dutch twaalf ); Old Saxon twelif , twilif , twulif (Middle Low German twelf , twolf , twalf , Low German tw?lf ); Old High German zwelif , Middle High German zwelif , zwelf , German zw?lf , Old Norse tólf , (Swedish tolf , Norwegian, Danish tolv ), Gothic twalif < Old Germanic *twali?i- , < twa two + li?- or lif- , of uncertain origin, but generally considered to belong to the same root as Old Germanic *li?an to leave n.1 (q.v.), and thus to denote ‘two left or remaining over (ten)’; compare eleven adj. and n. Analogous formations to eleven and twelve are the Lithuania vên?′lika 11, dvylika 12, in which the second element, Lithuania -lika, has also the meaning of ‘left over’. All other Indo-European languages have or had forms composed of ‘two’ + ‘ten’, like the numbers 13 to 19; compare Latin duōdecim, Greek δ?δεκα, Sanskrit dwāda?an.

THIRTY Etymology: Old English trítig , < trí, three adj. and n. + -tig (= Gothic *tigus decade: see -ty suffix1); = Old Frisian thritich; Old Saxon thrītig (Low German d?rtig, Dutch dertig); Old High German dr?zzug (Middle High German dr?zec, German dreissig); Old Norse trírteger (-tigir), later trjátigi, trjátíu (Swedish trettio, Danish tredive); Gothic treis tigjus ‘three tens’. The metathetic form thirty appears in literature in 15th cent. and has prevailed since 16th cent.
In the oldest English, erítig was a neuter noun singular construed with a genitive plural, e.g. he genam tritig tegna he took (a) thirty (of) thanes (Beowulf 123), he w?s eritiges geara eald he was of (a) thirty (of) years old ( Past. C. xlix). Later it was construed as an adjective plural, with dative trittigum, genitive trittig(r)a, e.g. tara trittigra manna of those thirty men. Few traces of these inflectional forms remained in early Middle English.

 [6] Cardinal Numerals: Old English from a Cross-Linguistic Perspective, P. 85, Ferdinand von Mengden, Walter de Gruyter, New York/Berlin, 2010.

[7] The Aryabhatiya of Aryabhata. An ancient Indian Work on Mathematics and Astronomy, Walter Clark, Professor of Sanskrit, Harvard University. Page.21 Published by The University of Chicago Press, 1930. 

[8] Hints on arithmetic : addressed to a young governess, Frances Verney, Groombridge and Sons, London, 1852.