A recent article in my local newspaper, the Stillwater Gazette, provided enlightenment on our school district’s new way of adding numbers – from left to right, rather than right to left. I might have to try this – maybe it will help me improve my accuracy when tallying checks on deposit slips. (I always hand-calculate these as a way to maintain my math muscles.)
Supposedly this left-to-right approach makes it easier for children to learn, because it goes in the same direction for processing numbers as for reading words. Here’s how it works. Let’s say that you and your spouse both collect up pennies and the first jar nets 237 cents versus 159 for the second. How much in total can be taken to the bank? The way I learned to add one first adds 7 and 9, recording 6 as the right-most digit (the ones column), and then carrying a 1 to the second column (the tens). This carrying part is where I sometimes get off, mainly due to my poor handwriting, which even I cannot always read. The new left-to-right approach eliminates a lot of carrying, but not all, I figure, as shown in the following case. Start by adding the left-most (hundreds in this case) column of numbers:
247
+159
=300
Do not forget to put in the zeroes to hold the place of what you just added. Now go to the next column to the right and add it:
= 90 (4 + 5)
And so forth until there’s no more columns:
= 16 (7 + 9)
Finally, tally up all the numbers you calculated:
300
+90
+16
406
I have a feeling that the old saying about not trying to teach an old dog new tricks might be operative for me in regard to this new math. I think I will just keep adding the old way, or admit that using a calculator or, better yet, a computerized spreadsheet for doing my deposits would be smarter. Am I shortchanging myself (pun intended)?
PS. This innovation in learning math struck a chord with my son Hank, who programs for Stat-Ease. He made me aware that “endianness” is a major issue in coding. Evidently programmers continually feud over the order in which bytes in multi-byte numbers should be stored – most-significant first (Big-Endian) or least-significant first (Little-Endian).* The “endian” terms come from Jonathan Swift who mocked the pettiness of social customs, such as which end one ought to first attack when shelling an egg.
“…the primitive way of breaking Eggs, before we eat them, was upon the larger End: But his present Majesty’s Grand-father, while he was a Boy, going to eat an Egg, and breaking it according to the ancient Practice, happened to cut one of his Fingers. Whereupon the Emperor his Father published an Edict, commanding all his Subjects, upon great Penaltys, to break the smaller End of their Eggs.”
— Jonathan Swift, Gulliver’s Travels, A Voyage to Lilliput, Chapter IV.
*For more details, see Basic concepts on Endianness.