Why we learn math (or anything for that matter).

As babies, if we never learned to walk, could we still survive in this world?  I think so.  In fact, it is much easier to keep your balance on four legs rather than two.  It is hard to learn to walk, with all the falling down, the trial and error, and mostly error at the beginning, all the bumps and bruises, the tears.  Why do we even bother to teach our children to walk?  Well, walking does make life a lot easier, and maybe in the long run it's worth it.  For instance, it is much faster to get around on two feet, rather than crawling.  When getting around in the street, all of our clothes and hands don't get dirty, only the soles of our shoes do (again a convenience created for "walking people").  Also, it is much easier to carry something while walking rather than crawling (multi-tasking).

If I didn't know how front crawl, I would have to doggie paddle to get to the other side of the river.  If I didn't know how to drive, I would have to take the bus everywhere or walk.  If I didn't know how to use pythagoras, I would most likely have to draw a scale diagram for any sort of construction or wood working project, and estimate the numbers.  If we don't know (advance) math, obviously we won't use it.  However, if it's in our blood, our second language, we will find places to use it at every corner, everyday, even in our sleep.  Math is a way to organize the world around us, and with more advance tools (such as exponents, logarithms, trigonometry), we can organize more and more. 

Teaching advance math is like teaching a baby to walk.  Of course, it is not absolutely necessary, and we could get around with only arithmetic (and many people do this).  As teachers, however, we should realize that the world is desigend for people who know advanced math, and instead of crawling, with the skills of math our students can get up on two feet and run.

Submitted by bogusia on Mon, 05/28/2007 - 21:23

Hope you liked the post. Please do me a favour ...

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Comments

Submitted by Linda F
on Sun, 06/10/2007 - 00:57

This is one of the most cogent and well-reasoned explanations I've ever encountered.  I'm sending the link to it to my Physics teacher listserv.

Submitted by bogusia
on Tue, 06/12/2007 - 03:51

Thanks for the complement - I'm glad you agree and understand my point of view.

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Submitted by bogusia
on Fri, 05/06/2011 - 16:33

Thank you so much Evelyn! I am a humble teacher, but sometimes I have some opinions, and this medium (blog / internet) is the perfect place to share it... get some feedback from the rest of the world.

Submitted by Joshua Hornick
on Mon, 06/11/2007 - 17:11

     I used to teach math and physics.  I love advanced math.  I believe that, as you suggest, my knowledge of advanced math helps me see all manner of phenomena with a broader eye.

     The broadening of perspective from understanding math is similar to the broadening of perspective that comes from learning to draw, understanding genetics, Shakespeare, poetry, physical fitness, story telling, economics, colonialism, hip hop music, video games, and--well frankly--anything.  Whenever we learn more, especially when we understand something deeply, it broadens the way we see everything.  It's one of the miracles of our lives.  (I think that you acknowledge this in the title of your post.)
     All of us have different propensities.  For some, advanced math is not the right portal into a deeper understanding of the world.  Many students grow to hate the study of mathematics and shun the use of it later in life because they are forced to learn it when it is simply not necessary.  It's a lot like Latin was in the 1920s; the study of Latin was an arbitrary portal required for academic advancement.  Now algebra and advanced math play that largely arbitrary role.
     Study of advanced mathematics can be fabulous.  When we teachers are at our best, we encourage our students to pursue the studies that will be most fruitful for who they are.  We who love math must be careful not to force math on those for whom it is not the best path.  

Submitted by bogusia
on Tue, 06/12/2007 - 05:21

Joshua, thanks for your comment and the well thought out response. 

I also teach math, and have tutored the weaker students a great deal, and so I do understand that learning advanced math is not an easy task by everyone.  Many students, as you say, hate math and avoid using it later in life.   I understand their pain and try to show all the tricks to get them through high school math, allowing for no depth of understanding the math, but instead helping in the survival of the math course.  These students however, are going to be significantly disadvantaged in their lives (I believe), because, unfortunately (or fortunately for people like us) the world today is highly technologically based, and math can be used every step of the way. 

Let me give you one practical example.  My husband is not a teacher, but has a background in computer science.  However now he is working as a project manager (completely unrelated to programming).  Thanks to his computer science background, he has automated all his reporting, and when his predecessor took a week to produce a particular report, it only takes my husband a few hours to run his program to create the report.  Even though the automation wasn't necessary, it made life so much easier for him, and he has more time to contemplate how to make other things work better.  Without his math/computer science knowledge, he would be hanging back at work, working on the weekends to finish the reports before the meeting on Monday. 

This is a very basic example, but if you take even a handful of such examples, life just becomes so much easier for the math savvy person, and harder for the "loathing math" student. 

 

All in all, I agree with you: advanced math is not necessary, but knowing it makes life so much easier.  (Maybe knowing Latin made life easier in the 1920's Wink.)

Submitted by Anonymous
on Wed, 07/04/2007 - 23:36

Sorry, but your example does not really show how someone can benefit from learning advanced math. Learning how to program or manipulate a computer does not require advanced math knowledge.

Submitted by bogusia
on Thu, 07/05/2007 - 03:46

One discipline builds on the other. In order to learn basic algorithms for computer programming, one needs the foundations of mathematics - advanced mathematics (combinatorics, number theory, numerical methods, etc.). If you know any computer programmer, then you will know that they are extremely adept at mathematics, especially because they need to use the beautiful "organization" of it. Of course basic manipulation with a computer, or programming in HTML (not that that's even considered programming) can be done without math - but real programming is impossible without math!

Submitted by Ms. Tate
on Thu, 09/03/2009 - 18:54

Whilst it is good to expand one's horizons, it is also good at some point in one's pre-career days to get focused.

No one can do it all all the time.

Yes, if you are looking to be promoted to higher levels of expertise, then one should definitely become adept at more advanced math.

However, for some of us, doing so will take time from the real path we wish to follow, becoming an expert at what we do best.

It is a matter of our own instincts AND encouragement from others in what they see our talents to be.

We simply cannot do it all in one lifetime, and it is sad when the law student finally reaches the point of the bar exam and fails it, then takes his life.

I hire a plumber to do my plumbing, and I don't need to know very much about it except to understand how to turn the water off when there is a leak.

I am much better off to concentrate on meeting the needs of my family and students, whatever that may be, and even there I am specialized only in certain fields.

Submitted by MathMentor
on Wed, 05/12/2010 - 19:50

I wish the law student didn't take his own life. Realizing that she has wasted her life up to that point should be a glorious release -- the person should be happy that they didn't lose more time :)

Joking aside, it really depends what "advanced" math is, or advanced plumbing. Some people don't know how to turn off their water supply, other people know how to change a toilet, and others would know how to run new pipes. The pro plumber would not consider any of those to be very advanced, but most homeowners will use any of those three levels of knowledge at some point.

People don't seem to need the skills they don't have!

Submitted by bogusia
on Wed, 05/12/2010 - 21:09

I really like your comment... "People don't see to need the skills they don't have!" Sometimes, they probably don't even know that the skills exist, until they have them, and only then can they use them. Thanks for this insight!

Submitted by Janet S. Tiger
on Mon, 03/23/2009 - 01:58

Although I am now a playwright, I was good at math and still enjoy numbers. I homeschooled both children - my son loves math and is going to be an engineer, but my daughter, well, that's another story.

From my daughter, I learned that math is not fun (my sister also hated math, but I just thought she didn't want to) and she is now going through polynomials. Please tell me why the world is designed for people who know polynomials! I have lived 53 years and never needed one - except for teaching them. I do my own taxes, I work with insurance forms - none of these involve algebra. They do require a good understanding of basic arithmetic - percentages and division and all the items being left out while algebra is pursued.

So please let me know how you figure this - I know doctors and chemists and engineers need to get algebra, but do people in the arts? (Unless they want to, of course) And in the future, calculators will be even smaller and more accessible, so algebra will be solvable like arithmetic is now.

Thanks for clarifying!

Submitted by bogusia
on Mon, 03/23/2009 - 18:56

I can't say I'm an expert in this subject. I can give you my opinion, but of course that's all it is - you can agree with it or not.

As I already stated, advanced math is not necessary to live in our world - even a fullfilled life, like in your case. I think of it more like learning a language. If you know it, more doors open for you in different countries. You can communicate with more people. However, if you don't live in that country (or in this case if you're not an engineer, scientist, accountant, etc.) you will have no use for it, and it will be wasted on you.

The only thing is that math is a very important language, and many "countries" have it as an official language, and lots of people "speak" it.

Polynomials might be useless for your daughter if she decides to pursue the arts / theatre as yourself. But if she falls in love with biology (and just this year, I have encountered many students like this), she will need the "stupid" polynomials to do some other math courses that will allow her to enter the university of her liking in order to take the dreaded "calculus courses" of first year university. Unfortunately, this calculus would be very useful for her to understand fundamental biological processes.

Submitted by Anonymous
on Sun, 05/09/2010 - 21:11

I think polynomials and algebra could be considered the basis of science. Algebra is essentially making predicitons of what's coming next. It's basically looking at patterns in the world and trying to figure out a coherent formula to predict. It answers questions to "what would happen if".
We've been learning about algebra since preschool, but back then we called it "patterns". In this world, a lot of our focus in academics is on trying to figure out the world and predict what happens next. In psychology, the study of human behaviour, they strive to predict behaviour by looking at behaviour patterns that in the past. A comedian has to predict whether a certain joke or punch line will cause the audience to laugh. The ones that can, tend to be successful. Maybe eventually they'll come up with an algebraic equation to predict laughter. It's far fetched, but that's essentially what algebra is.

Now, in response to the question "is advanced math or algebra involving polynomials necesary to the non-scientists?". I would have to say that it's not necessary, but it's beneficial. Algebra and math in general is very logical, systematic and requires both organization and creative thinking. Most Arts degrees require all these skills.
These skills come into play even for everyday things like putting together a simple computer. You would be surprised to see how many people who I work with cannot put together a computer. I think a lot of math indirectly supports skills that are beneficial to allow you to be independent.

Submitted by vedic mathematic
on Fri, 03/26/2010 - 07:15

Yep maths is the basic needs like food,Clothing and shelter as nobody could live without it.Without maths it would be impossible for the human being to get the exact calculation.Thanks for such a reminder article.Keep posting.

Submitted by vedic mathematic
on Tue, 04/12/2011 - 07:55

its true that maths comes everywhere you can't ignore it
but thinks it as music its really like "lets take a walk"
its really working for me and i dont know how but.... music and maths are co-related
the instrument that works for me are piano and cello you should give a try.
thanks for wonderful information.

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on Tue, 04/12/2011 - 08:15

Maths is a basic need in everyone's life.
Without Maths, nothing is possible.

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Submitted by erikahiggason
on Thu, 05/12/2011 - 13:16

God made the integers; all else is the work of man." Probably one of the most famous mathematical quotations of all time. Its author was the German mathematician Leopold Kronecker (1823-1891). Though sometimes interpreted (erroneously) as a theological claim, Kronecker was articulating an intellectual thrust that dominated a lot of mathematics through the second half of the nineteenth century, to reduce the real number system first to whole numbers and ultimately to formal logic.

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