“When are we ever going to use this?” What a great question! This is a teachable moment. Too bad most teachers blow it. Instead of seizing the opportunity, they reprimand the student for asking. At least that was my experience.
Why would someone not explain how their subject is used? Often because they don’t know. Or they don’t know how to articulate what they do know. But teachers are supposed to know things and be good at articulating them. That’s their job.
Sometimes the student asking how a subject is going to be used is just a lazy whiner. He’s not asking a sincere question, and he will not find a sincere answer satisfying. But maybe the student is genuinely curious. Or maybe there’s at least a drop of curiosity in the whiner. Or maybe someone else sincerely has the question that the whiner insincerely asked.
I am not saying that content needs to be more practical. Attempts at being more “practical” have often been shortsighted. Many subjects that have been discarded as impractical are actually quite practical. We’ve just grown impatient, unwilling to wait for long-term benefits. I’m saying that more teachers should know and articulate the value of what they’re teaching.
It’s more difficult to convey the value of things that are not immediately useful, but it’s also more important.
Good post.
I am very hands on, and while I like theory, I ALWAYS wanted an application.
And, in fact, I’ve found applications for the vast majority of what I learned in a great undergrad CS program.
…it just took 10 to 20 years in some cases.
My dad suffered from this. Teacher couldn’t explain the point of it, so he didn’t see the point of it. Then had to go to night school when he finally worked out the point of it!
TJIC: I’ve had a similar experience, that nearly everything was useful, but it might take 10 or 20 years. I had a consulting gig a few weeks ago where I used some esoteric math that I never thought I’d make money from.
My ideas of what I would and would not find useful were largely wrong, often backward. And I imagine the same is true for most people, unless it’s a self-fulfilling prophesy: of course you’ll never find a use what you don’t know.
There is a huge difference in the possible contexts of the question. “When is math used?” is much different from “When is long division used?” – or the like. There are many good answers to the first question and very few to the second. Further, even if the latter – in its specificity – admits an answer attractive to some students it may be of no interest to others. The bottom line, I do not believe you can just blame the teachers for having no good answer to that inquiry. The problem is with the educational (or even societal) system wherein education is seen as serving utilitarian goals instead as a transmitter of the accumulated human culture. It does not help of course with having the lamp posts of achievement (like NCLB) promoted by the government and the NCTM.
I agree that having education serve utilitarian goals is short-sighted. I was cautious in writing this post because I don’t want to give the impression that I agree with the folks who want to make everything “practical,” i.e. those who think everything should have an direct materialistic application.
However, I think it’s a tragedy when a teacher says something like “I have no idea how this is used” or “You shouldn’t ask such questions” or even worse “I don’t think anyone would ever use this, but it’s on the test, so shut up and learn it.”
Unfortunately, there may be teachers around who would bumble nonsense trying to answer this question. You are right about that. But teachers are concerned with the problem and try to overcome it, see, for example, my post
When am I ever going to use this? Why do we need to learn this?
Alexander: Thanks for the link. I liked the line “Students who question the utility of the present math class are unlikely to be convinced by the utility of a future class.”
By the way, I hate the name “pre-calculus.” To me, this course title says “The material in this course has no intrinsic worth. If you don’t go on to take calculus, this course will be a complete waste.” A big part of “pre-calculus” is trig, something that is very useful and interesting in its own and not just a warm-up for something else.
John, I agree with you about the “pre-calculus” name. To top it all, those students who usually take a pre-calculus course either take no more math courses after that or take just one more – which may or may not be calculus.
I would suggest that, by and large, teachers have no use cases because the only time they have had to use this is to teach people.
I used to love word problems (and wonder why everyone else disliked them) because they were examples of when and how you were going to use this.
I agree with most that’s written here, but I wanted to expand on the point about teachers not knowing uses becasue they have only used the knowledge when teaching it.
I think this is true, and may reflect a lack of imagination or experience on the part of teachers, but it can also be that while they use or benefit from the knowledge they are not aware of it. Some explanations for cultural traditions boil down to this, although I would immediately point out that (as Freud pointed out) human behavior is generally overdetermined. For example, studying medical antrhopology I ran across a lot of cases where traditional practices (making hominy using lye, mixing grains and legumes in a meal, ordeals in rites of passage, even a superstition about mice) do in fact have measurable objective benefits, even though the people who follow those practices were unaware of those benefits. Closer to home, practices which inculcate grit or determination or mental toughness can benefit a child in later efforts, although the practice itself may on the face have no practical point or seeming value on its own. Even studying the writings of classical philospohers in a Greek or Latin class provides exposure to great minds, even if the language itself isn’t practical, although knowing Greek and Latin is a huge help for English users due to the language’s eclectic roots. Exposure to such ideas can have a profound effect, although it is probably hard to notice in oneself.
The rest of the story is the way we (and I mean specifically Americans, although I’d bet it is much more applicable) approach education. In most cases, and especially in children’s education, professionals in a subject do not teach that subject. Instead, the teacher is a professional in teaching. This isn’t necessarily bad, but without professional experience in the subject matter, professional teachers would have little experience in seeing the application of knowledge in a specific field. To take John’s example of making money off of exotic math, even he did nbot expect the knowledge would prove lucrative, and if his consulting gig involved an application, I’d bet he had not thought of that application before. And he’s a professional in the field!
Now imagine you are an elementary school teacher (in the USA). You may know a lot about how to teach children, but chances are you have not had professional experience in writing, math, history, social studies, and so on. If you do, it is probably not in more than one of those subjects. Suppose for the sake of argument you had professional experience in writing, and can bring that experience to bear in the classroom. Then you get assigned to teach math. When the kids ask you what practical use you can make of math, even arithmetic, you are probably limited to thinking of things like balancing your checkbook, comparison shopping, units conversion — hardly compelling stuff, and these days easily performed without any knowledge of arithmetic at all. If the class covers something a little more exotic, such as real numbers versus rational numbers versus integers, or ratio versus interval versus ordinal versus nominal data, how could you realistically be expected to make a compelling case for learning the differences and similarities? Even among professionals I’d bet it would take them some time to think of why a kid would care, except that those things are fundamentals necessary to further progress in the area of study, which is hardly different from arguing that it is in the book and on the test. At least with the fundamentals of writing (spelling, grammar, puntuation) you can argue that without that knowledge they could seem ignorant and be embarrassed, although as with innumeracy, illiteracy and even ignorance are losing social stigma.
For myself, I think the natural answer to the question, “When are we ever going to need this,” is the question, “When are you ever not going to need this.”
I agree that some students ask it out of pure laziness, while others out of true curiosity. But problems in motivation of learning math (which answering these questions should contribute to) seems a lot like people who abandon music lessons or learning a foreign language. I’ve never met anyone who told me that they only took a year of piano and now that they are older, they are glad that they cut their losses.
We are human, and when learning all of these things, we are young. Reasons I see now for learning any of these things would not have registered with me when it was critical. I learned math because I was the type of person who liked it. I suppose I could have been demotivated, but I can’t think of what someone would have told me that would have motivated me to learn it if I didn’t already like it. Same with music. Not the same with language — I was bad at German, and got out as early as possible. Now I wish I had the skill.
It isn’t trivial to figure out the answer to the question. As Alexander Bogomolny pointed out above, all of the things that people think of as answers, when they think hard, often fall short of being a satisfying answer. The STEM (Science, Technology, Engineering, and Math) initiative is trying to answer that by integrating math in with science and engineering at the school curriculum level.
One view of STEM could be that it is being dulled by trying to shoehorn it in with application, and we lose sight of the pure mathematical beauty. True for some, maybe not for all. Other people take the approach of this not because it is necessarily practical, but because of the belief that by some version of “ontogeny recapitulates phylogeny,” that rediscovering what motivated some mathematical usage (and discovery) will help students see why math was and is important. But it is far from definitively answered.
Point being, what motivates me now did not motivate me at 14. If I could go back in time, I would try to change my course to satisfy me now, but I’m not confident even I could succeed.
I have had this question come up at least twice this week. Of course there is the obvious, “You need it for the test next week,” but that is just my normal smart-alecky response. I will be honest and say that most of them will never need to solve 4x^4 + 12x^3 – x^2 – 3x = 0. But knowing how to solve it and process the information is vital for doing much more complicated concepts. I give them the tools to form the foundation for higher level math. I don’t expect everyone to go on to major in mathematics or other math-heavy majors, especially since I teach Transitional (aka Developmental) Mathematics. That doesn’t mean that I can’t change their perspective or elevate their academic goals. I encourage them to see math on a deeper level and not just a bunch of numbers on the board. I hold them to a high level of precision, not only in their answers, but also in their notation. I have them consider the thought process. What is the next step? Why? How did you get that answer? Can you back it up? Their understanding of the more basic concepts goes beyond our class and into almost everything else they take.
This post reminded me to thank you for posting a link to Dan Meyer’s work some time ago (in the “Too much time on their hands?” post) — I started reading and got totally hooked. He has a knack for presenting math lessons in a way that connects to “the real world” from the start, so I imagine the question of “when would you use this” rarely comes up for his students. For example, annuli:
http://blog.mrmeyer.com/?p=7126
And contrariwise, he discusses the dangers of “pseudocontext.” When you shoehorn the math into a “practical” problem where the context is blatantly false and/or the math really has nothing to do with the context, it’s worse than admitting you’re not sure when they’ll use it — you’re telling them math is only to be used in artificial situations with no link to common sense reality.
http://blog.mrmeyer.com/?p=8002
So yes, teachers should not just know how to *do* what they’re teaching, but also how to convey its real value!
In my undergraduate “computational methods for engineering” course, a student asked the question, “When are we ever going to use this?”
The instructor’s response? “You won’t unless you go into research.”
That’s not true, and it’s much worse than saying, “I don’t know.” What a disappointing thing to tell a group of college sophomores who really have no idea whether they would want to go into research, or what that even means. That was all the impetus most of the class needed to dismiss everything from there on with that instructor.
I’m probably the only programmer that I know who can do math in duodecimal with any real efficiency — it is the chromatic scale, and I am a trained music theorist.
I’ve read many math teachers who claim to answer along the lines of, “You’ll probably never use this directly, but by learning this, you are learning how to learn.” Which is perhaps a little more honest than some of the standard answers. But still disingenuous. The best ways of “learning how to learn” don’t involve a curriculum, as Papert showed.
The most honest answer I’ve seen is in Lockhart’s lament, where he simply admits that mathematics is an art form, pursued for its intrinsic beauty, and in many cases, students are being taught a subject because it’s an important part of the culture. Like Shakespeare and Bach.
A preemptory rebuttal from the paper:
SIMPLICIO: Are you really trying to claim that mathematics offers no useful or practical applications to society?
SALVIATI: Of course not. I’m merely suggesting that just because something happens to have practical consequences, doesn’t mean that’s what it is about. Music can lead armies into battle, but that’s not why people write symphonies. Michelangelo decorated a ceiling, but I’m sure he had loftier things on his mind.
In some sense the question should be turned around. Teachers are not applying mathematics; it’s up to the students, who are the future, to find something to do with this stuff. “I don’t know, what are you going to do with it?”
(But I do agree that a sincere teacher’s time would be well spent looking up applications. What if one started every lesson with an application, added more applications, and concluded “Mathematics ties these examples together” ?)
Ben: People enrol in school for different reasons, right? Your example illustrates several conflicts of interest within higher ed.
The teacher wanted to be a scholar (and maybe didn’t want to teach all that much, but had to?) and the students [or their parents] wanted [them] to be taught useful skills.
John,
some of the problem teachers, and others, see in the question “When are we ever going to use this?’ is a feeling that they are expected to know the answer.
Why?
What theory of teaching tells us that teachers are supposed to know the answers?
A young man in one of my teacher education classes opined that he couldn’t be a teacher of mathematics because he wasn’t as smart as the 10 year old girl in a video we showed. He resolved this dilemma by the end of the course.
Pre-service elementary teachers have often told me that my job is to tell them the answers.
It’s a widespread, naive and unreflective view, that a teacher’s job is to tell students answers.
How about a response like: “You know, I have no idea how quadratic functions and quadratic equations are used. Why don’t we find out?”
Doesn’t that feel liberating. Wouldn’t kids respect a teacher who asked that? I know I would.
Just knowing that a tool or method exists allow you to think about how it might be applied. The old saying applies: To the man whose only tool is a hammer, every problem resembles a nail.
My favorite reply to the “When are we going to use this?” question was the following:
“It depends. If you turn out to be a genius, maybe you will use this in an unexpected way to reveal a hitherto unknown truth. If you continue in this profession, you’ll use it now and then to do useful work. If you’re just scraping by, you’ll use it to pass the text next Wednesday. Maybe.”
Probably related:
http://worrydream.com/SomeThoughtsOnTeaching/
I remember having this problem with Computational Geometry. It was one of the Mathematics subjects we had during our Computer Science major.
Well, it was computational and we had to write programs to execute those matrix algorithms, but no one ever told us where we’ll practically use it.
I was quite surprised when I had to use it within two years of starting my job. I always wondered if I’d have been able to solve the real world problem (converting a JFC Swing layout to a web based table layout without floodfill) I was facing if I hadn’t know that Computational Geometry existed.
Frankly, practical application is over emphasized in schools and by students and teachers alike.
The question “when are we ever going to use this” is an absurd question. And it has no place. The desire to learn a subject is independent of its usability in any practical way. I, for one, study in order to gain insight and broaden my understanding of reality. I self-educate for the sake of education, and for no other purpose.
Students who dont want to learn a subject shouldnt be enrolling in the courses in the first place.
Students who seek practical application are really seeking immediate profitability. There is a concept from infantile psychology that comes to mind here: the need for amusement. The greedy, capitalist need for immediate usefulness and immediate profitability, or else it simply isnt worth doing. That is the notion in our society.
Instead of focusing on practical application and mindlessly going through homework and practice problems, reiterating procedures thoughtlessly, regurgitating rote memorization… what we need to be teaching instead is concept and proof, and focusing on the appreciation for the subject in its purest of forms – only then will people learn and learn well.
Cogitoergocogitosum, that’s a fine perspective if your money issues are already taken care of. I don’t think there’s anything wrong with wanting to learn how to support yourself, or with querying those who say T is the topic that you need to study, and B(T) are the books you need to read about it.
I’m ripping this paraphrase off of an economist whose name escapes me: “The following are useful, valid, and appropriate questions for a student to ask.
• ‘Oh yeah?’
• ‘Says who?’
• ‘Why should I care?’
Those are very similar to the questions academics ask in research.”