Since this blog seems to be read in over 30 different countries from time to time I thought I would see if anyone would like to share how they complete simple arithmetic activities.

For example, the image on the left shows two different ways of doing a simple subtraction activity. The one to the left is labeled the equal addition method while the one on the right, the one currently used as a "standard algorithm" in US schools, is labeled the decomposition method. (The use of the term "borrow" in this one is an error as we will see) If you are familiar with the one on the right and still use the term "borrow" you might have wondered why the "borrowed one" was never paid back.

The "borrow" language actually originated with the method on the left which was used in the US prior to the 1950s. This method is still used in Bosnia and many other countries. The way it works is like this; 9 from 5 you can't so borrow 1(1 ten) to make the 5 into 15. Since you "borrowed" 1 from the tens you have to "pay it back" by putting a 1 next to the 3 (or changing the 3 into a 4 in this example). You now take 9 from 15 to get 6 and 4 from 6 to get 2 (actually 40 from 60 to get 20). It was called the equal addition method because you added ten ones to the top number (5 +10 = 15) and one ten to the bottom number (3 tens + 1 ten = 4 tens). The word "borrow" just stuck even though it didn't really make any sense.

In the method used in the US today, the one on the right, we decompose (or regroup) 65 into 50 plus 15. This is still frequently and erroneously referred to as "borrowing 1". In the decomposition method there is no "payback" so it really should be "steal 1".

To use the word "borrow" today is to use it as a metaphor. The correct conceptually-based language is "regroup 65 into 50 and 15". I learned the equal addition method of subtraction growing up in England and still use it today, but only for my personal math calculations, and only when no-one is around. Let me knowif you do something different.

For example, the image on the left shows two different ways of doing a simple subtraction activity. The one to the left is labeled the equal addition method while the one on the right, the one currently used as a "standard algorithm" in US schools, is labeled the decomposition method. (The use of the term "borrow" in this one is an error as we will see) If you are familiar with the one on the right and still use the term "borrow" you might have wondered why the "borrowed one" was never paid back.

The "borrow" language actually originated with the method on the left which was used in the US prior to the 1950s. This method is still used in Bosnia and many other countries. The way it works is like this; 9 from 5 you can't so borrow 1(1 ten) to make the 5 into 15. Since you "borrowed" 1 from the tens you have to "pay it back" by putting a 1 next to the 3 (or changing the 3 into a 4 in this example). You now take 9 from 15 to get 6 and 4 from 6 to get 2 (actually 40 from 60 to get 20). It was called the equal addition method because you added ten ones to the top number (5 +10 = 15) and one ten to the bottom number (3 tens + 1 ten = 4 tens). The word "borrow" just stuck even though it didn't really make any sense.

In the method used in the US today, the one on the right, we decompose (or regroup) 65 into 50 plus 15. This is still frequently and erroneously referred to as "borrowing 1". In the decomposition method there is no "payback" so it really should be "steal 1".

To use the word "borrow" today is to use it as a metaphor. The correct conceptually-based language is "regroup 65 into 50 and 15". I learned the equal addition method of subtraction growing up in England and still use it today, but only for my personal math calculations, and only when no-one is around. Let me knowif you do something different.

Neither a borrower or a lender be..... now who said that? It wasn't for math.

ReplyDeleteI was a borrower and pay back guy and it's still my way today (but I am not a math teacher).

If you read back your example:

You now take 8 from 15 to get 6 and 4 from 6 to get 2 (actually 40 from 60 to get 20).

I think you've put 8 instead of 9.

My daughter is going to do some middle school math tutoring to make ends meet -- I have sent her Math on Call, linked to your math page and now to this blog.

Cheers,

A Forest Fan