Sometimes it feels like our goal of improving math education has been one of failure
and futility especially when I think if one particular aspect of math
education; the use of the word "borrow" when completing the subtraction
algorithm.

For around 75 years in the US we have been using the word in a context which makes absolutely no sense at all. We have corrupted the use of the word "borrow" to become a synonym of steal since when we borrow in the subtraction algorithm we never pack back. At least 75% of the students I work with use the term "borrow" when completing subtraction algorithms.

This wasn't always true of course. Up until around the early 1940s we used a subtraction algorithm that was significantly different from the standard one taught in elementary schools today. It was called the equal addition method of subtraction and involved adding ten ones to the top number and one ten to the bottom number when the bottom number in, say, the ones or tens place, was larger than the top number.

In the example above the 3 is larger than the 2 in the top number in the tens place so you "borrow" ten tens (you actually just pluck them out of the air) and then you pay them back as one hundred in the bottom number (again, just literally plucked out of the air). So, this is done to the words "borrow one and pay it back"; all very ethical. This method is still used in many places around the world such as Bosnia.

Around the early 1940s we changed the method of subtraction in the US to the decomposition method where you decompose the number by regrouping the ones and tens and so on. In this example, you cannot

take 3 from 2 in the tens place so you regroup 600 and 500 and ten tens, adding the ten tens to the 2 tens so that you now have 12 tens from which you can take 3 tens resulting in the 9 tens or 90 in the answer.

This method was far more logical and much easier to teach especially if you used the concept derived term "regroup".

Unfortunately, for some strange, bizarre, odd, curious, quirky, irrational and totally mystifying breach of logic, the word "borrow" survived as a metaphor.

This is almost as illogical as ma and Pa Kettle's explanation of 25 divided by 5 equaling 14.

For around 75 years in the US we have been using the word in a context which makes absolutely no sense at all. We have corrupted the use of the word "borrow" to become a synonym of steal since when we borrow in the subtraction algorithm we never pack back. At least 75% of the students I work with use the term "borrow" when completing subtraction algorithms.

This wasn't always true of course. Up until around the early 1940s we used a subtraction algorithm that was significantly different from the standard one taught in elementary schools today. It was called the equal addition method of subtraction and involved adding ten ones to the top number and one ten to the bottom number when the bottom number in, say, the ones or tens place, was larger than the top number.

In the example above the 3 is larger than the 2 in the top number in the tens place so you "borrow" ten tens (you actually just pluck them out of the air) and then you pay them back as one hundred in the bottom number (again, just literally plucked out of the air). So, this is done to the words "borrow one and pay it back"; all very ethical. This method is still used in many places around the world such as Bosnia.

Around the early 1940s we changed the method of subtraction in the US to the decomposition method where you decompose the number by regrouping the ones and tens and so on. In this example, you cannot

take 3 from 2 in the tens place so you regroup 600 and 500 and ten tens, adding the ten tens to the 2 tens so that you now have 12 tens from which you can take 3 tens resulting in the 9 tens or 90 in the answer.

This method was far more logical and much easier to teach especially if you used the concept derived term "regroup".

Unfortunately, for some strange, bizarre, odd, curious, quirky, irrational and totally mystifying breach of logic, the word "borrow" survived as a metaphor.

This is almost as illogical as ma and Pa Kettle's explanation of 25 divided by 5 equaling 14.