Why Is Mental Math Important?

Date: 03/25/2004 at 23:05:35
From: John
Subject: Importance of mental math

How can I convince a 14 year old girl who is in 8th grade the 
importance of mental math?  I tried to point out some real life 
situations but her teacher told her it is not really important since 
there are calculators and computers.  I also pointed out that if she
does not learn such things it could make her unsuccesful further down
the road in life.

I think that things like adding 2 digit numbers together using
techniques such as adding the tens place first and then adding the
ones place and then adding the results are critical skills.  Similar
skills include doing subtraction mentally when using 2 digit numbers
and being able to mentally estimate multiplying 2 digit large numbers.  

Date: 03/25/2004 at 23:45:45
From: Doctor Link
Subject: Re: Importance of mental math

Hey John, thanks for writing in.  This is a great question!  I happen
to love mental math, and used to pass time in class by working on my
skills!

There are many reasons why mental math is extremely important.  I will
start with what I believe to be the most important of these reasons.

Mental math, irrelavent of its applications, is an excellent way to
stimulate one's mind.  Not only does it generally stimulate your mind,
but it also helps one get a better "number sense."  In other words,
one becomes more familiar with how numbers interact--this is very
important, because as you know, math is something that builds on
itself.  If you don't have a good grasp on how numbers interact, then
more complicated math will seem like more of a challenge.

I wasn't going to mention it, but since you brought it up I will.  If
you can't add and subtract without the help of a calculator, it can
certainly reflect poorly on you.  Even if you really are a very
intelligent person otherwise, this inability may give people a
different idea.  For better or for worse, our society puts a lot of
stock into appearances.  If one doesn't appear to be educated or
"smart" at first glance, society will often just label that person as
such.

Also, the fact is that calculators are most useful in a setting that
requires either a) things that are essentially impossible for humans
to compute at any reasonable speed (like evaluating the cosine of a
number) or b) for calculations with rather large numbers.  For two
digit addition, not using a calculator should actually be faster,
given that you have learned the techniques well.

There are a myriad of other reasons, from being able to dazzle one's
friends and future coworkers to giving one confidence about their
abilities.  Ultimately though, I am very surprised to hear that your
daughter's teacher fueled this.  When I was growing up (which wasn't
too long ago), students constantly questioned the usefulness of mental
math.  My teachers always maintained that it was very important to be
able to do these calculations ourselves.  After all, thinking is what
makes us human--not dependance on machines to do our thinking for us!

My brother also reminded me of one other important thing.  What if you
are getting your change, and the cashier has either accidentally or
purposely given you less change then they should have.  Without the
ability to do mental math, you may overlook this--so there's your
real life scenario for you.

I hope this helps a little--good luck with convincing your daughter!

If you would like more advice, write back and I will see what more I
can come up with.

- Doctor Link, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 03/26/2004 at 09:33:32
From: Doctor Peterson
Subject: Re: Importance of mental math

Hi, John.

I'd like to add something that Dr. Link did not explicitly mention, 
though you touched on it, which is estimation.

In the modern world of computers and calculators, mental estimation 
skills are MORE important, rather than less!  That's because, although 
calculators and cash registers make it unnecessary to do exact 
calculations in many instances, it can be easy to trust them too much.  
People can make mistakes in using them, entering the wrong amount or 
doing the wrong thing with it, and if we just blindly accept the 
answer it gives without checking, we'll lose out a lot.  One major 
kind of error is putting the decimal in the wrong place (or failing to 
enter it at all), another is to miss a key so that what should have 
been 1234 is taken as 124, off by a factor of ten!  Or how about 
hitting "percent" instead of "divide"!  These kinds of mistakes are 
easily caught by estimating the correct answer.  Estimation won't 
catch errors of pennies, but it will catch dollars, which are more 
important anyway.  You can probably find other examples where this 
will be important in her life, but money is a good motivator!

It's worth noting that estimation uses the same skills as exact 
mental arithmetic, and more.  It also builds number sense by making 
you aware of what matters most.  A teacher who says arithmetic skills 
are unimportant is depriving students of an essential life skill.


- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 03/26/2004 at 14:19:19
From: John
Subject: Thank you (Importance of mental math)

Thank you very much.  Being 14 years old--appearances are paramount. 
I think your point about appearances might strike a chord.  Perhaps I
will even have her teacher read your response.