Oh, they need it alright. They just don't have it. Which is why there are so many on this thread screaming "burn the witch!"
I did not once say burn the witch....Explain to me how someone who is numerically illiterate but can write proofs like made is useful own daily life????
The truth is day to day tasks require one to be numerically literate (i.e. the ability to add subtract multiple and divide) That requires memorization. It is rather like telling me someone understands everything about sentence and paragraph structure but is unable to read.
First things first, We are talking about elementary school NOT high school and college.
Just out of curiosity what is the highest level math class you have taken?
The "old" method is based on a notational system that represents arbitrary integers by grouping numerical symbols in sequence by powers of ten. As long as you understand how to add the numbers from 0 to 9 and a simple rule involving borrowing (or carrying) you can add and subtract arbitrarily long sequences of symbols. It has no practical limitations whatsoever, and extends easily from the integers to the reals.
Period.
Introducing a "new" system retains the same representation of integers (so, no "improvement" there.) But which now also involves adding numbers to a subtrahend to obtain multiples of five, followed by multiples of ten until you reach the minuend. This is needlessly complicated, and still requires you to know how to add all of the numbers from 0 through 9. It has no conceptual extension to addition in the real number system.
In fine and in sum, there is no conceptual advantage to the "new" method, and in fact it introduces needless complication which is both conceptually and pedagogically disadvantageous.