“Why do I have to learn this if I’m not going to use it?”
“I have never once in my life have had to use Calculus, it was good that I didn’t waste my time learning it.”
“Most people just need to know how to add, subtract, divide, multiply, and work with percents. They don’t need to know more math than that.”

Almost every instructor, not just of Mathematics, has heard statements similar to these throughout their career.

The basic problem with these statements is that they are simultaneously a denial and admission of one’s ignorance. On the one hand, there is open acknowledgement that the individual does not know something. On the other hand, there is an open defiance that the very topic that the individual does not know is also not worth knowing. How can someone know that he doesn’t need to know something if he never knew it in the first place? Herein is the contradiction and it is a fascinating one.

Let’s imagine a person who only knows addition, subtraction, division, multiply and how to work with percents (whatever that means). Now suppose, this person wants to purchase a home. How is he going to determine

1. if it is affordable;
2. which loan terms are favorable and which are just a bad deal;
3. what types of risks are inherent in the loan structure (e.g., ARMs, prepayment penalties, etc.);
4. what the tax implications are early in the loan and later in the loan;
5. how much of a down payment to make?

One may argue that the loan provider (bank, e.g.) will provide answers to all those questions. This may be true. But how much faith is one going to have in an entity who has an immediate conflict of interest? And if we want to assume high integrity, then how much faith is one willing to have that a) no mistakes were made in entering information, b) the borrower’s side is correctly understood, and c) both sides are working off of the same assumptions? Mathematics touches all our lives in so many ways that it is always helpful to continue to learn more.

Reliance on others and on technology is not bad. In fact, one can accomplish quite a lot if one leverages correctly. However, blind faith in others and on technology is a recipe for disaster.

As we are finite beings, we simply will not be able to learn everything about everything and as a consequence, we end up having to put our trust implicitly in people and on things of which we have no understanding. The crime, though, is perpetuating the notion that “one does not need to know something because one has never used it” when the person never knew it in the first place!

Any instructor who hears something like this spoken within earshot should make a real effort to dissuade that mentality and promote a mentality of learning. Imagine how wonderful this blog would look if I had any talent in graphic design. Never will I claim though that I don’t need to know graphic design because I have never used it. How could I have ever used it, if I never knew it?