In
the article, "No. 1631 - Borrowing a One" by John H. Lienhart, he
states that the word "borrowing" may be getting grade school students
in trouble. Trouble in the sense of getting the answer to a subtraction
problem but not truly understanding how they got the answer. I remember
clearly my second grade teacher, Mrs. Miller, using the words borrowing and
carrying when learning how to subtract.
She even used the example of "borrowing a cup of sugar" from
your neighbor when subtracting. But is that really what we are
doing? Borrowing a one? No, it really isn’t a one, it’s a group of ten, so it
can definitely be somewhat misleading. Today in many classrooms the word “regrouping”
is used most often. It’s a better word
to use in order for student to see exactly what is being done to the numbers
because we are actually taking a group of tens and regrouping them into the one’s
column in order for us to subtract. Leinhart also mentions the use of
manipulatives, like the abacus, and I have found it a great help when using
blocks of tens and ones to show how numbers like 62 and 49 can be subtracted
and so have my students.
This comment has been removed by the author.
ReplyDeleteThis is an interesting point you bring up Verisha. Borrowing is a term that I also used while I was in elementary school. I catch myself now having to say REGROUP when dealing with subtraction. Many of my students this year pointed out your exact thoughts... I try to show my students multiple methods for solving problems if I know that they are having trouble. One simple word like borrowing can throw off any student who is trying to understand the idea of "regrouping".
ReplyDeleteVery nicely put. =)
Yes, regrouping does make more sense and I use it instead of borrowing pretty consistently these days. I too had to train myself to say it. I love using base ten blocks to exemplify regrouping. For a while I had to "borrow" the blocks from other teachers, but now I have my own set. ;) I also love how my mind works since I went back to college for my undergrad degree and teaching credential. I now add and subtract easily using mental math whereas in my youth, I didn't use strategies to solve things mentally. Making ten is a wonderful way to add and subtract mentally. I spend a lot of time with manipulatives, ten frames, and part-part-whole mats in my room with the hopes that eventually the student will start to start to see the movement of the parts or numbers in their heads. It works! They need to work out with their hands what they will eventually do in their minds.
ReplyDeleteYou bring up a very valid point Verisha. Teaching our students concepts and terminology such as "borrowing," can often be misleading. I share a similar experience learning math by "borrowing/borrowing a cup of sugar," when in fact its much more then that. I am sure we have to make a conscious effort to teach our students whats correct instead of using our learning norm when we where in school.
ReplyDelete