Computers are useless. They can only give you answers.
Pablo Picasso

## “Why don't they let us use calculators here?!”

The above question is asked by nearly every single freshman at Johns Hopkins. I'm going to attempt to explain to you why calculators are forbidden on exams and generally discouraged for use in most math classes here and at other institutions of higher education.

“What's with Hopkins?”
Almost anybody involved in higher education beyond the community college level anywhere in the world would agree that learning mathematics should have nothing to do with using calculators. At one community college where I taught, I and my colleagues were forced by administrators to integrate calculator use into our lesson plans despite our objections.

The feeling that calculators hinder students is in no way unique to JHU. Prof. Wilson has compiled an ad hoc list of math professors around the world who agree.

“So you don't think calculators are good for anything?”
Calculators certainly have their place. When I'm adding the scores on your final exam, I'm going to be typing them into my trusty TI. I don't trust myself to add long lists of numbers by hand accurately. When I'm finished with a long and difficult problem, I often check the answer on my calculator or computer to see if I've messed anything up.
“What's wrong with calculators anyway?”
1. They lie.

The calculator is a machine. It doesn't know anything about mathematics. A smart engineer has programmed it to give some pretty good answers to some math questions, but these are usually approximations, and, in the strictest sense, very often incorrect.

For example, once you've become acquainted with elementary manipulation of exponents in algebra, you, a human, can tell that 20x×30x=600x so 20x×30x – 600x=0.

Look at what calculators think the graph of 0 looks like when you write it as above:

 TI-92: \$60 Maple: \$995 Michelle - age 13: Priceless

This problem is called “overflow error” and it's one of the many ways calculators lie to you if you don't carefully guess real answers based on their approximations. One instance of this error may have cost over \$370,000,000.

2. They can't understand or explain anything subtle.

Humans can understand that the functions

 f(x)= x2x
and
g(x)=x
are slightly different: g can take any number as an argument, but f is not defined at 0.

Calculators understand this:

but have no way to tell you when you're studying the entire function by looking at its graph:
 TI-92 Maple Esther - age 15
3. They can only give answers to a few types of questions and only if you ask just right.
 TI-92 Maple Catherine - age 14
4. Asking for something to be done for you is not the same as doing it yourself.

Depending on a machine to do your intellectual work is not just degrading, it also limits your understanding. If you want to do any kind of science from Engineering to Biology to being a practicing physician, you're going to have to understand mathematics. Understanding comes from doing.

5. You need to be able to recognize when they err and possibly supply an alternative answer yourself!

Your graphing calculator is a precision instrument that will probably not have a real bug for years to come. But, if you only learn how to do math with a calculator, you're going to have to depend on whatever machine happens to be around when you're doing your job. That machine might not be as dependable:

“Why do they want me to be good at calculating stuff by hand? It's so tedious.”
Math teachers don't want you to be fast accurate human replacements for calculators. Most teachers consider it their responsibility to craft test questions and exercises in such a way that the arithmetic involved doesn't invite too many errors. Limiting calculator usage in class is to help you learn mathematics, not learn fast arithmetic.
“But I don't know a bunch of elementary arithmetic!”