Here
is a picture that I saw the other day. Many of you may have seen this already
as it appears to be circulating on various social media websites.
At
first glance, I was thinking this is ridiculous. What in the world is this? Are
we supposed to teach math like this? What do all these numbers really mean? It appears
to be a method of doing subtraction that takes multiple steps of addition that
seem to make no sense at all. I read this article on the topic and it made much
more sense to me.
The
upper portion is how many of us learned to do subtraction questions. Often times,
these numbers that we determine are based on what the calculator tells you,
what you calculate with your fingers, or what you have memorized over the
years.
The
bottom portion is something many of us actually do in our heads. When I look at
the question 32 - 12, yes I know the answer is 20 (from memorization) but if I needed
to calculate it in my head, I would think 12 to 22 is 10, 22 to 32 is also 10. So
now, 10 and 10 make 20. This is also how many of us calculate how much change
we should get back when we pay for an item or service. We calculate how many
cents to get to the next dollar, and then just add up how many more dollars we
need.
Example:
You
owe $4.90, and you hand the cashier a $20.
$20
– $4.90
To
perform the mental math, I would think $0.10 to get to $5, and then $15 to get
to $20. Thus, I would get $15.10 in change back.
Essentially, that is what the bottom half of the original picture is depicting. The article also had a second image, which contains an easier description of how this method works.
I think this is a great way to teach subtraction, but I do not think it should be the only method that is used. Students need to be given the option of which method suits their understanding the most and be allowed to use it accordingly.
It's funny - I had the exact same reaction to the alternative method that was described in the article. It certainly looks much more complicated than the traditional way of doing things. However, I also see what they are getting at. It makes sense to echo on paper the same process that we utilize to answer these simple math questions in our heads.
ReplyDeleteI also agree with your point about how this should be pushed as an alternative for students that wish to do it this way, and not as the ONLY way to do it. This reminds me of an old episode of the Cosby Show, where Vanessa demonstrates a "new" way of doing math to her father, Cliff, who insists that the more traditional approach is far superior. I found a link to the episode on youtube in case anybody is interested : https://www.youtube.com/watch?v=LM5u6sZK_tI
I just watched the video you posted. It was hilarious. Even more so because I see that in parents all the time. They already learned how to solve problems once, now they have to learn new methods to keep up with the times for their children!
ReplyDeleteGreat analysis Sumeet. I tried to figure out the logistics before reading your post for comparisons sake. I couldn't help but come away thinking to myself, "this kid is only ever going to learn and is never going to learn how to subtract." But as you pointed out, and especially when it comes to decimals, we often use addition.
ReplyDeleteI agree that I wouldn't want to have kids do this all the time, or at least writing out all the time (it would just be time consuming). My hope would be to expose a student to it, and hope that in time they would learn to do it in their head, kind of like how you explained someone might do at the cash.