E
I read with great interest a statement by an elementary teacher, “Developmentally, children will write numbers backwards until they are 8 years old “
No! These children write numbers, as they should be! The rest of us write numbers backwards! For example, the number 6154 should be written 4516. (In the Scandinavian countries, it is common usage to speak of numbers under 100 in the reverse order. They say the number “24” is four and twenty. “56” is spoken of as six and fifty, but they still write numbers backwards like the rest of us.) Justification for my claim requires the consideration of the way we developed written words and numbers.
The languages of the Western world were derived from Latin, which is read and written from left to right. There is no particular advantage in doing it this way. We could just as well read from right to left, top to bottom, or from bottom to top, but whatever we do, it is vital that we be consistent. When one finishes reading a line of text, the beginning of the next line must be easily located. To facilitate this, almost all written text is left justified. Our typewriters and computers do this for us automatically.
The Latin languages work very well for words, but are an abomination when it comes to numbers. Try adding the numbers, MCX XIII and MCCXI. the correct answer is MMCCCXXIV. There is a very good reason we limit Roman numerals to clocks and Super Bowl games. While our written words come from the Hellenic civilization, our written numbers come from the Arabic civilization, and as you might guess, the Arabic-based languages are written and read from right to left, and are right justified.
Try adding up the numbers, 8045, 24, 906, 5, and 83. I think that everyone would agree that the job would be made easier by arranging these numbers in a column.
8045
24
906
5
83
No! These children write numbers, as they should be! The rest of us write numbers backwards! For example, the number 6154 should be written 4516. (In the Scandinavian countries, it is common usage to speak of numbers under 100 in the reverse order. They say the number “24” is four and twenty. “56” is spoken of as six and fifty, but they still write numbers backwards like the rest of us.) Justification for my claim requires the consideration of the way we developed written words and numbers.
The languages of the Western world were derived from Latin, which is read and written from left to right. There is no particular advantage in doing it this way. We could just as well read from right to left, top to bottom, or from bottom to top, but whatever we do, it is vital that we be consistent. When one finishes reading a line of text, the beginning of the next line must be easily located. To facilitate this, almost all written text is left justified. Our typewriters and computers do this for us automatically.
The Latin languages work very well for words, but are an abomination when it comes to numbers. Try adding the numbers, MCX XIII and MCCXI. the correct answer is MMCCCXXIV. There is a very good reason we limit Roman numerals to clocks and Super Bowl games. While our written words come from the Hellenic civilization, our written numbers come from the Arabic civilization, and as you might guess, the Arabic-based languages are written and read from right to left, and are right justified.
Try adding up the numbers, 8045, 24, 906, 5, and 83. I think that everyone would agree that the job would be made easier by arranging these numbers in a column.
8045
24
906
5
83
____
?????
This is still not the best way. Try:
8045
24
906
5
83
_____
9063
9063
Much easier!
Now try writing the numbers backwards and adding left to right (the same direction we teach our children to read and write):
--2 1 1
5408
42
609
5
38
____
--2 1 1
5408
42
609
5
38
____
3609
5+4+6+5+3 = 32 (23); put down the 3 and carry the 2
2+4+2+0+8 = 61 (16); put down the 6 and carry the 1
1+0+9 = 01 (10); put down the 0 and carry the 1
1+8 = 9; put down the 9. The answer is 3609 (9063).
5+4+6+5+3 = 32 (23); put down the 3 and carry the 2
2+4+2+0+8 = 61 (16); put down the 6 and carry the 1
1+0+9 = 01 (10); put down the 0 and carry the 1
1+8 = 9; put down the 9. The answer is 3609 (9063).
I first became aware of the problem, when using an old key punch machine. These were the machines that one used to punch little holes in IBM cards, which were read by computers. The cards contained words of written instructions as well as numbers. The machines automatically left justified everything, which worked quite well for entering words. However, there was a real problem when entering numbers. Each number was placed in a field of fixed length, and needed to be right justified. The operator had to stop, and count the number of digits in the number and subtracted it from the length of the field, in order to know the precise place to start typing the number so that would be right justified.
The handheld calculator illustrates the modern version of this problem. Calculators automatically right justify all numbers even though we enter them from left to right. Observe that when entering a digit all of the previous entered digits march magically to the left. One can observe this phenomenon by setting your word processor to right justify, and start typing.
You
you get
you get something
you get something just
you get something just like
You get something just like this!
Bizarre!
I certainly do not plan a crusade to have everyone write numbers in the correct direction, but I hope that you will better understand a young student’s dilemma.
DICK
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