Why is Math important?

I’m loving my prereq class for teacher certification right now. Lots of interesting debate, discussion, and sharing about how to teach well. On thing we touched on today was that in order to hook a student and open them up to learning about a subject, three things had to be present: personality of the teacher, content or subject matter, and context or relevance.

Of all the subjects I’ve encountered as a student, Math was the hardest one to hook me into, and I suspect that I am not alone. Most people I know have an aversion to math that’s almost as strong as their aversion to dentists and pelvic exams. Just teaching math relevant to life skills (enough addition and subtraction to balance a checkbook, fractions, percentages, and basic Algebra, and so on), it becomes an enormous challenge to interest the student. Go on to more advanced subjects - Geometry, PreCalc, Trigonometry - and the number of students interested and willing to do the work drops precipitously.

I also remember that from eight grade on, I could never get a satisfying answer from any of my math teachers as to why math was important. Why did I need it?

Now I’m at the age where I appreciate intellectual pursuits for their own ends. I find myself wanting to recover the subjects I so strongly fought against learning in high school, and I want to be able to convince future students that math has relevance to them.

So, here I am, arithmophiles. Witness to me! Convince me! Tell me why I need math beyond the basic skills sets!

The most satisfying answer I got from a math teacher about why I needed it was in eighth grade. He said, “Mathematical skills teach you how to think rationally and logically.” I couldn’t argue with that, and I’d sure as hell say it’s a damn important (though more abstract) skill.

Why is math important? First, an editorial comment: this is the question that a nincompoop would ask. Unfortunately I’ve been surrounded by them all my life: journalists who don’t know if earnings were up by 5% or 50%; marketing people who don’t know if they got an acceptable ROI on the last ad campaign; pilots who don’t understand why they have headwinds 75% of the time.

So, why is math important?

  1. So you can tell whether an investment is a legitimate return or a scam.
  2. So you can judge the performance of your city government in its budgetary activities.
  3. So you can debunk urban legends, like “there was a rash of babies born 9 months after the NYC blackout.”
  4. So you can tell which direction you’re going in an airplane.
  5. So you can tell whether your job performance is actually better – or worse – this year than last year.
  6. So you can program a video game.
  7. So you have one chance in a thousand of beating the house in Las Vegas.
  8. So you can look at a chart of finances/baseball scores/ performance and have a chance of predicting the future.
  9. So you’ll be able to figure out what to order the next time you go to the hardware store.
  10. So you won’t be chumped by politicians. “Ninety percent of all marijuana smokers drink beer first.” Yeah, but 100% of all marijuana smokers drink milk first. . .
  11. So that you can judge the statistical risks of having sex. Or maybe the statistical risks to the rest of us from having you reproduce.
  12. So that you’ll properly assess the risks of being injured in a modern society.

If math isn’t important to your employment, be prepared for a minimum-wage existence.

Many of the usual, but eminently sensible, reasons are found in the following thread: Why do they teach algebra?

I would add that an appreciation of mathematics leads to (or perhaps is essential for) an appreciation for the beauty of the Universe.

Well, I may be among the worst people in the world to answer this question, since I always kind of liked math - but let me suggest a couple additional answers.

  1. It is practical. There really are a number of jobs where various kinds of math skills do make a difference - and not all of them are the ones we think of as mathematical. You might see if you can find some folks who do theatrical sound and lighting work, financial advising, marketing, construction, etc. Have one or more of them come in and talk to your students about what their work is like and how math is important in their work. This obviously works even better if the guests are engaging speakers, and works best if you can find some who can tell stories about how much more important math is to them then they ever thought it would be.

  2. It can be a fun challenge. I think that I always kind of liked things that did have “correct” answers and you could know that you were right. Getting to the answer gave a genuine feeling of accomplishment.

  3. It is important. We leave in an age where lots of different kind of information is thrown at us, and to be good citizens, and to operate in our own interest as consumers, we may need to understand a wide range of mathematical concepts. The story of the kids from Minnesota who discovered unusually high numbers of deformed frogs (and who had to be able to show that the numbers were “unusual”) could fit well here.

  4. It is associated with entertainment and hobbies. There are legions of stories about kids who hated math, until they discovered how a batting average is computed - and suddenly started practicing long division every morning as they looked over the box scores from last night’s baseball game. Other ways of linking math to fun are undoubtedly out there.

None of these should take away from friedo’s answer - I think that one is important too. But these might help a bit.

An expansion of the “math helps with critical thinking skills” idea: when engaging in debates, I am amazed at what passes for a “proof”. In mathematics, there’s a term that’s used a lot: “hand waving”. It refers to when you’re sure that something is true, and you think that it should be obvious to everyone else, and so you don’t bother to prove it. Any time mathematicians do any hand-waving, they are careful to acknowledge that they are doing it, and they don’t consider the proof done until they replace the hand waving with real reasoning. You won’t get anywhere in advanced mathematics if you aren’t able to tell the difference between real reasoning and hand waving. Yet it is amazing what passes for “logic” among the general populace. Non-sequitors like “entrophy is constantly increasing, so it must have been zero at some time” are disturbingly common. Mathematics teaches intellectual discipline: not matter how sure you are that something is true, no matter how much you want to say “it’s obvious true” and go on to the next problem, you have to actually think about why it seems obvious, and how to prove that it is actually true. When it comes to this sort of discipline, the average person seems to have an amount appropriate to a two-year old.

The following is from http://php.indiana.edu/~jbmorris/LYRICS/lehrer.misc :


“That’s Mathematics”
This song was originally written back in the 80s as a theme song and title for a PBS children’s show on math now known as “Square One TV”. The song was to the tune of “That’s Entertainment”. It was rejected as the theme song, partly due to not being able to get permission to use the music of “That’s Entertainment”.

On July 28, 1993, the Mathematical Sciences Research Institute (MSRI) presented a Fermat Fest in San Francisco to celebrate the fact that Andrew Wiles had proven the famous Fermat’s Last Theorem, which had gone unproven for centuries. Tom was not at the fest and this song was not
performed there, but he did record it on November 2, 1993, for use over the closing credits of a videotape they released of the event. At this time, Tom changed the tune a bit to avoid copyright infringement, and added the verse about Andrew Wiles.

About Fermat’s Last Theorem:
Fermat had written in the margin of a notebook that he had come up with a neat little proof of the theorem, but did not have space to write it there. Since then, people many times have claimed to have proven the theorem, but have been proven wrong. It has been speculated that Fermat did not actually have a proof. (The theorem states that for all integers n > 2, there exist no integers a, b, & c satisfying a^n + b^n = c^n, where ^ denotes exponentiation. Note that for n = 2 there ARE such integers, as this is the Pythagorean Theorem of right
triangles. The rest of you can look it up when you get home.)

The sheet music for this song has since been published in the April, 1997 issue of Math Horizons, which is put out by the Mathematical Association of America.

Counting sheep
When you’re trying to sleep,
Being fair
When there’s something to share,
Being neat
When you’re folding a sheet,
That’s mathematics!

When a ball
Bounces off of a wall,
When you cook
From a recipe book,
When you know
How much money you owe,
That’s mathematics!

How much gold can you hold in an elephant’s ear?
When it’s noon on the moon, then what time is it here?
If you could count for a year, would you get to infinity,
Or somewhere in that vicinity?

When you choose
How much postage to use,
When you know
What’s the chance it will snow,
When you bet
And you end up in debt,
Oh try as you may,
You just can’t get away
From mathematics!

Andrew Wiles gently smiles,
Does his thing, and voila!
Q.E.D., we agree,
And we all shout hurrah!
As he confirms what Fermat
Jotted down in that margin,
Which could’ve used some enlargin’.

Tap your feet,
Keepin’ time to a beat,
Of a song
While you’re singing along,
Harmonize
With the rest of the guys,
Yes, try as you may,
You just can’t get away
From mathematics!

I’ve always held that the average person wouldn’t need the highest levels of mathematics in their daily lives. Indeed, if taught calculus or trigonometry, they’d probably forget it really quickly (I know I have).

BUT (and you know there’s always a but)… by having learned these higher math skills, however briefly they stayed with me, I’ve found that mid-level mathematics (algebra, etc.) have become much easier for me to compute.

I think that the teaching system provides more knowledge than an average person would need on the expectation that some of the knowledge would be forgotten, while the knowledge that remains would be made easier as a result.

These are kids, right? That’s who usually starts the “Why do I have to take __________?” arguments. So point out to them the crowning glory of the field of Mathematics. It is never a matter of opinion, or interpretation. If you answer is right, your answer is right. If the teacher or the book is wrong, you can prove it, every time. And no one gets to say “Well, the reason we don’t do that any more is . . .”

Precision is about math.

Proof is about math.

You never have to worry about whether you know it or not. If you know, you get your answer, and you can use the answer to prove itself right or wrong. Sometimes the answer is very hard to get, but you don’t have to worry about opinion, popularity, politics, or personality. Correct is correct, wrong is wrong.

Tris

I would comment that in the last 30 years there has been a shift from concentrating on the subject matter to concentrating on teaching methodology etc. In the meanwhile, the subject matter has suffered. We are teaching bad stuff very well taught. Part of it is the feeling that learning should not be work, it should be fun.

My impression is that Americans have become lazier in the last few decades as life has gotten easier. I have already said in other threads that math is useful in everyday life but, even if it wasn’t, it is extremely useful for developing your mind for other things.

Your brain is like your muscles: you need to exercise it to keep it in good working shape. If you do not exercise your brain it becomes dull and less able to resolve everyday situations and the quality of your life will diminish. If you do not exercise your body, you will become overweight and the quality of your life will diminish. Laziness is not good whether it is mental or physical.

If I might add my own 2 cents…

I read an article in the now sadly defunct Science Fiction Eye on the big surge in popularity of paleontology among adults, a few years back. The author’s idea was that you have some guy who is working at, say, an investment firm, and he’s got his pretty trophy bride, and the money’s rolling in, and he’s got an important sounding title and a fancy sports car, but somehow life has no zest for him. And at the class reunion he meets the guy who he picked on in high school. The reason he picked on this guy is because the nerd was always reading a lot of books on useless crap, like science and math, when he could have been studying for an MBA. And as he watches the nerd, he realizes that the nerd is actually quite happy with his life. So the next day, the investment banker goes out and finds a book on the most useless, nerdy thing he can think of: dinosaurs.

I had a friend in college who had to show some of his in-laws around NYC. I suggested maybe they could go to a museum, but they don’t like museums. Maybe a Broadway play? They’d sleep through it. The zoo? They think zoos are boring. Jeez, man, what do they like? TV and golf. And so, you see, NYC, one of the most exciting and fun places on earth, was excruciatingly boring for them, and they would have much rather sat at home watching reruns of Full House.

IMO this is why you have to study mathematics, among other things. If you are a person with no interests (and I’ve met way too many of them,) then you sit at home and watch semi-amusing TV 7 nights a week, and you play some golf on Saturday, and on Sunday you mouth a few lifeless prayers asking for eternal life, and after 52 weeks a year over a few decades, it’s a wonder you haven’t killed yourself already. If you’re a person who has learned to be excited by learning, then you can drink from the bottomless well of human culture all your life.

-Ben

Because mathematics allows a deep, rather than a superficial, understanding of a vast number of other subjects.


peas on earth

So, what you’re saying, Mooney, is that I’m a nincompoop? I’ve been called worse, but if you can’t comprehend the need to convince a disaffected, disillusioned student why the skill and knowledge to grasp mathmatics is necessary, then I’m not the only nincompoop in this thread.

To the rest of you, thank you for your input. Please, keep piling it in. I’ll be checking out the Algebra thread in a bit.

BTW, as for mathematics per se, I’d suggest you read some of Martin Gardner’s books on recreational mathematics, particularly his later ones (where he moves away from puzzles and more into math per se.) I think it’s a real shame that more teachers don’t make math cool the way he does.

-Ben

It is my only motto. It is the only main constant upon which I base my core belief system:

There is nothing that is not worth knowing.

It’s a simple motto, but it contains something universal that I like. There is nothing I have ever felt that I don’t want to learn. This is a value that is lacking in many of our students, and one that, if you truly believe, precludes one even ASKING a question like the O.P. The key to convincing students that math (or history or science or foreign languages or whatever) is worth learning is to instill this one value in them.

There is nothing that is not worth knowing.

Ultimately, the problem is not convincing a student of the utility of mathematics, it’s convincing them of the joy of learning. If you place a utility value on a subject matter liek mathematics, then there is a reason not to learn it. If you can say to a student “You need math for X” then the student can say “X is not important to me.” Rather, to instill in the student an unconditional love of learning, then no reason is needed to learn anything. To learn for the selfish enjoyment gotten from learning itself is to truly be educated. If we learn for the purpose of accomplishing other goals, then we are limited in our learning insofar as we accomplish these goals. What is the point of learning more than we perceive to need to accomplish the goals we have set? If, on the other hand, learning itself is a goal, then can there really be any bounds to our desire to be educated?

Christ, I sound like John Dewey. I haven’t read him in months, really. Seriously, the answer to the O.P. is:

There is nothing that is not worth learning.

Another reason:

It is very important for scientific and technical work. It would be a shame to deny anybody the opportunity to pursue this because they didn’t have a strong enough math background. A friend of mine never got an adequate math education because, where she went to school, girls didn’t learn things like that. She regretted having those career paths closed off from her.

While I was researches my line of argument fo the* Does something have to rhyme to be considered poetry? * thread here, I ran acrossed a couple of term paper online sites. As an extention of the math question–why is anything important when you can get the answers, and the term papers, on line?

THe answer to this is–the most importnat part of learning isn’t the facts, it’s learning to think for yourself. Mind you, not all schools subscribe to this theory.

THis is an Orwellian thought, but it is possible to have a populace so used to not thinking that they will believe anything that Big Brother says. We may be rapidly approaching this now. It would explain alot–Gore, Bush, Britney Spears…

Don’t think math is important? Ok, let me exchange your $20 with the value of silver per ounce in London today.

THere are good reasons why mathematics should be taught in schools. The problem with why people tend to view mathematics as difficult, goes back to the way how people were taught in schools. We studied mathematics in elementary schools subsequently to high schools, knowing the techniques and ideas but never understood why it worked this way.

Mathematics encompasses the set of reasoning tools which allow us to think in everyday life. One might not realize that they were using such tools when they were trying to figure out things. Mathematical logic and Statistical reasoning are the very tools which allow us to make physical models from the very reductionistic mode (simple systems) to the very holistic modes (complex systems). For example, physics used a lot of mathematics, and allows us to have a good approximation to the physical reality. Different modes of reasoning, stemming from inductive and deductive reasoning are very essential to understanding things. Inductive reasoning, is the inference of certain facts from a set of assumptions based on the criteria, that there is no contradictory cases in existence (and all sciences are inductive by nature, since experimentation is used to verify and falsify hypothesis). Deductive reasoning is totally different, we start with a set of correct premises, and we work out the consequences which is logically consistent to the axioms.

One could appreciate the beauty of mathematics by understanding the history. I recommend reading two classics, the first being “Prelude to Mathematics” by W.W. Sawyer and the second being “How to Solve it” by George Polya. In addition to read an account of historical understanding on some problems we learned in high schools, for example why the square root of 2 is an irrational number, and how the Greeks figure out the geometry of the plane, and how the Arabs divide the land by using algebra techniques, like completing the square. One can Boyer “A history of mathematics”.

I strongly believe that a basic introduction of mathematics to students is important, because it exposes the child to different modes of reasoning, should he or she would go further in his/her education, regardless whether he or she would end up studying natural sciences or social sciences.

yours,
Prodigal

I used to be a professional poker player. Day in, day out, my job was to play with people who didn’t know mathematics and take all of their money.

Here in Canada, we have a serious problem in that people without mathematics backgrounds are being hooked on video slot machines and losing all their money. They think they are just unlucky and will get it back, because they lack the mathematical understanding of how the games really work.

On a larger scale, our entire society is built on a foundation of mathematics. To go through life without understanding it is to live in a fog of ignorance. There is great joy in simply being able to understand how the things around you work. If your kid is uneducated, he’ll live in fear of the nameless, faceless forces that control his life. The computer guy at work, the technician who came in and installed the cable, the guy at the bank who makes you sign papers describing complex financial relationships you can’t understand, etc. You’ll have to spend your life trusting all these strangers, because they are necessary and you lack the ability to understand what they are doing.