Math Mutation 70: Number Nonsense
Recently I was at a local fast food restaurant, and I saw a burger
that looked good for $1.98. I ordered two of the burgers, plus a soda
which was 99 cents, and the cashier told me the total was 6.93. I
looked at her, confused, and tried to reason with her. "You see that
burger I ordered is about 2 dollars? And I got two of them, plus a
one dollar soda. Shouldn't the total be around 5 dollars?" She was a
bit annoyed. "So, you're not going to pay the amount displayed on the
register?" I valiantly tried one more time to reason with her.
"Look, 2 + 2 + 1 equals 5. So the total should be close to 5
dollars. Something is wrong here." She gave up and went back to get
the manager. I could overhear her speaking to him, though she didn't
realize it. "An irate customer up front is refusing to pay for his
meal." Needless to say, after the manager finally sorted things out,
it turned out she had rung me up for an extra burger.
But I was still flabbergasted that a high-school-age American
would lack the basic skills to estimate that 2+2+1 = 5, and therefore
something had gone wrong. My confusion was cleared up when I did a
bit of internet research, and found that many school systems are using
calculators from as early as the first grade level. Don't get me
wrong, I think in some places, such as advanced science classes or
application of formulas, it might make sense to use a calculator in
school. But thinking back to my elementary days, I think I gained a
lot of my inherent "number sense" from working out lots of simple
calculations on paper. Sure, technically it's the same if you
remember 2+3=5 from repeating a lot of hand calculations, or if you
type 2 and 3 into a magical black box and get 5-- but the thought
process is a lot different. When you do it by hand, you can't help
but notice patterns and gain an inherent 'feel' for the numbers. If
all you do is mechanically type them in and always get a guaranteed
answer, you may lose even your basic impulses of curiosity about
what's happening.
On the net, there seems to be a clear backlash these days against
the trend of using calculators in schools. I've put pointers to a few
articles in the show notes, but I'm sure you can find many more. Like
me, many educated adults are horrified to see that if they ask for
simple calculations like 300 divided by 3, a sizable portion of
calculator-educated teenagers will reach for a calculator rather than
thinking about the problem and giving a quick answer. No matter how
sophisticated our technology gets, there will always be human fingers,
or brain waves, supplying inputs to our computing devices-- and thus
always room for human error at some point. Having a basic number
sense, and being able to understand whether simple, round arithmetic
results are in the right ballpark, will always be a critical component
needed to sanity-check calculations and avoid disasters. In a few
years will we hear about a bridge collapsing because some entry in a
computer was off by a factor of 10, and nobody noticed?
And this has been your math mutation for today.
References:
An
article on calculators in math classes
Another
article
One
more article