Some Responses...But Do You Agree?
A young math teacher writes: "One question that comes up again and again from students is "why do we have to learn this? Or when will I ever use this?"
Readers sent varied responses (partially edited so that all could be included)...
"I had many students in algebra 1 and algebra 2 who were very involved in the arts programs at the high school where I taught. I would get the same question. My response was usually, 'you may never need to know the sine of 45 degrees, the logarithm rules, or how to solve a quadratic equation when you are 35. However, you will need to know how to think and have some understanding of the difference between linear growth and exponential growth.' I told them I didn't care if they didn't remember sines, cosines, logs, etc., but I did want them to be able to think, and math is one very good way to help develop thinking and reasoning. And then I assured them that they still had to do the work!" [A.C., WA]
"...the passage you quoted from Philip Davis is a good start.
I tell my students that in 'real life' they will never have to do the problem that prompted the question, 'when will we ever use this?' However, the process that they followed to set up the problem, solve it, check the answer, extend to other problems, is vital. To be able to generalize a situation, define variables and equations to represent the situation is invaluable. Also, I tell them that mathematics is a wonderful human creation, a work of art. Although much of mathematics is applied and concrete, much is also a world of the mind. We often think of and work with things that are infinitely small or infinitely large or infinitely numerous. Strange objects like Gabrielís horn, the Mandelbrot set or Kochís snowflake can be approximated on paper but truly only exist in the mind. Objects like the Klein bottle are even more bizarre. Why limit yourself to three dimensions? We deal with seemingly paradoxical situations. How can there be just as many even integers as there are integers? How can (0, 1) contain exactly as many members as all of the real numbers?
On a different, more practical level, I also tell my students that if they avoid mathematics, over half of the University is closed to them; all physical sciences, engineering, economics, business, psychology, etc. Why limit your opportunities so severely?" [D.H., OR]
"I tell my students that in most cases, you will not directly use the formulas and ideas learned in the class. There is only a small percentage of you that will. In some cases, I canít think of a time you ever will use the concepts being taught. However, I think the true learning that is happening is when we analyze situations and become critical thinkers. If we can be really good at problem solving, I think that applicable to any situation you encounter (work, home, etc.).[M.S., OR]
"I always think of the star trek episode where there is a race of people that are all dying because they don't understand the life support computers that their ancestors built.
Without algebra you'd have to stay out of careers in science and technology, you might have trouble getting promoted if you are stumped by problems most people can solve, you could be mislead by the media or in financial matters, and you might be restricting what you can create or your ability to be innovative in any field. Don't limit yourself so early!" [T.D., WA]
"...I taught college algebra to Coast Guard personnel (coasties) for a few years. They asked the same questions: Why do we have to learn this stuff? [and various naughty words in place of stuff] When will I ever use this stuff?
One (unsatisfactory) answer: You need it to get the Associate of Science degree that you want to obtain.
...I also created many 'algebra-in-context' exercises and test questions involving: Coast Guard motor lifeboats, cutters, rescue helicopters, and fixed-wing aircraft; longitude and latitude; distance to the horizon; maps, charts, navigation; maximum speed of a displacement hull boat; et cetera, et cetera.
As long as we teach algebra to the current standards with the current type of textbooks, for sure students will ask: Why to I have to learn this stuff? When will I ever use this stuff? How does stuff help me in my life?
And multitudes will say, 'I hate algebra.'
Later in their lives, most will say, 'I was never good at math.' or 'I hated math.' or 'Math was totally irrelevant to my life.' or . . . [B.A. & G., OR]
"For the first many years of my career, I felt the same frustration. As you or any math teacher knows, that question is common. Very common. It is also a good question that is pretty complicated and what I am about to write is not intended to be THE ANSWER.
I bought the poster [with] title, something like " WHEN WILL I EVER NEED THIS?" It has all sorts of math areas and they are all cross-hatched with job types. For this job, you will need this, this, and that. It seemed to me, that the only students truly interested in the poster were the ones who were math oriented types anyway.
I would make up wild stories like, 'Okay, you're walking along a street in Bellingham and a guy comes up and grabs you. He pulls you into an alley, sticks a knife to your throat and says,' All right, Bucko, what are the prime factors of x squared plus three x plus two?'.' Even though the kids enjoyed the humor, it obviously was worthless in terms of actually answering the question. And the question kept coming.
I often mentioned the idea that it helps people to think logically, and I firmly believe that to be true. However, I don't think that that fact does much for most teenage kids. It doesn't impress them.
Over the years, I decided to try a new tactic. Honesty. Sort of. I told them that I didn't have a clue. The only way I can even attempt an answer to that question would be to know just what he or she has chosen for a career. Some will tell you honestly about their hopes for the future. Then you can be quite specific in giving advice.
Some will say they don't know. You can respond that it is going to be difficult to tell how much math is necessary. There is a big difference between a job working in a grocery store and working for a television station. The math requirements for those jobs are not the same. You get the idea.
There are billions of ways for kids to take my argument and try their best to twist it, bend it, shape shift it, whatever they can. One thing is to tell you that what their stated goal is does not include the math we are learning in this class, so what's the point? Good question, but I think I should ask them if they have any idea how shocked people who knew me in high school were when they found out I became a math teacher. Now, just between you and me that's not true, but it is a way to point out that they might very well change their minds.
It also helps to turn the question around. Ask them what math concepts are necessary? Is knowledge of addition, subtraction, multiplication, and division enough for some jobs? How do you know?
I would, from time to time, allow a discussion of this sort in the classroom. I know that there are districts that would frown on that because we must spend our time on the material in the book. I disagree, but that's just me. [J.S., WA]
Do you agree with these responses....or what would you like to add? Again, I will pass on all viable responses.