Oh, So That's Why?

A minute-and-a-half into an introduction into introductory geometric (triangle congruence) proofs, it comes - the interruption - the question, this time accompanied by a look of genuine curiosity (and, dare I say, intelligence?) rather than the usual eye-roll and skeptically sour tone: “Why do we need to learn this?”

 

An attempt at a well-thought-out, pseudo-philosophical, at-times-bordering-on-existential, and probably-mostly-bullshit response:

 

You don’t.  I know it’s not the sort of response that someone expects from a person that peddles this stuff for a living, but there it is.  You simply don’t need to learn this.  There is a very short list of things that you do need to do - among them are breathing, eating, drinking, and sleeping (and somewhere, I remember hearing a line about taxes) - but learning mathematics is most certainly a choice.  Now, there are some obvious consequences to not learning this, but it is still your choice whether or not to suffer those consequences.  Your question is easy to respond to because it is accompanied by an underlying assumption that just isn’t true: that I’m here in the trenches teaching you mathematics because I think it is necessarily something you need. 

 

Food for thought:

Consider your education, course-by-course.  How much of what you’ve learned is need-based?  Is the goal of education to fulfill needs?  Do we need poetry?  If the works of every great poet who ever lived were to disappear along with every living poet, would you up and die, cease to exist, lay lifeless in your tracks without the will to go on?  Poetry is not a need - it enhances and enriches our lives and the lives of those who write it.  Education is about offering us things that have the potential to enhance and enrich our lives, and it goes way beyond satisfying our basic needs - it gives our lives purpose. 

 

Let’s put mathematics and education on the back burner for a moment and talk about some of the things that we enjoy pursuing, that stimulate and entertain us, that we may even feel we need.  We watch movies, read books, play sports, draw, paint, sing, dance, travel, visit museums, stand in awe before great works of art.  We do these things because they enrich our lives, rarely considering whether or not we need to do them.  We don’t place these things under the why-do-I-need-to-do-this? microscope because they entertain us.  Mathematics, however, does not receive the same treatment because, for so many, it falls desperately short of entertainment.

 

So…education is a choice.  We have the right to choose which parts of our education we embrace because education is not about fulfilling base needs, but about offering us things that may (or may not) enhance our lives.  I believe we’re at a point where it is appropriate to rephrase the original - ‘Why do we need to learn this?' - question.  I propose, “Why should I learn this?”

 

Food for thought:

Is it possible for our lives to be enhanced and enriched by things that don’t stimulate and entertain us (at least not in any of the conventional ways), that may even bore us at times?  Is there life-enriching value in acquiring the ability to focus our minds on the abstract, the mundane, the boring (disclaimer: I’m aware that I’m giving math a bad rap here and these are not my own feelings and opinions about mathematics.  They are merely suggested as the sort of feelings a why-do-I-need-to-learn-this-type-question asker might have about mathematics)?

 

So, how will mathematics enrich your life?  Or better yet - Will mathematics enrich your life?  The truth is that I don’t know.  That isn’t a question I can answer.  I can’t speak intelligently about your needs and I don’t know what will enrich your life going forward because I’m not you.  But honestly, I’m not sure that you can answer these questions with any degree of certainty either.  There’s just no way to know what the future holds for you.  We’re always operating on best guesses and, sure, we have an idea of where we hope life is taking us, but life doesn’t always behave according to our desires. 

 

Food for thought:

If education really is about offering us things that have the potential to enrich our lives and each of these things may or may not actually do so and we have no definite way of knowing what the future holds, is choosing to embrace some part of our education an act of faith? 

 

I’ve noticed that people who embrace every aspect of learning seem to be - on average - successful, happy, fulfilled, wealthy, and so on.  Could it all just be a numbers game?  If I tune in, without question, to everything I’m being taught, then it is unlikely that a potential future life-enhancer will pass me by.  Sure, there will be some waste; some not-so-useful knowledge may creep in, but there’s not much harm in that.

 

The reason I chose to teach mathematics is simply because I love it and I’ve always loved it.  If I’m being honest, then I think I love mathematics more than I love teaching.  Teaching, however, is a profession that allows me to share a small part (and often the less interesting elements) of the field of thought that I love.  I teach, not because I think my students need math or because I think they have to learn it, but to give them the opportunity to fall in love with it, to embrace it, to see the same things in it that I did at their age, to allow it to do for them what it has done for me, all the while knowing full-well that, for many of them, it will not.  And that’s just fine with me.  Teaching mathematics is about small victories and if I can get even a few students to understand its value in the context of their own lives, then I am satisfied. 

 

I don’t want this response to become all about me, but I’m trying to answer the question, “Why should I learn this?” and the best way to show you what mathematics can do for you is to try and explain what it’s done for me.  I’ve discussed, in detail, the fact that the role of education is to enrich and enhance our lives.  I think it is important to discuss another role of education that is intimately linked to the one previously mentioned.  Education is about making the world a little less unpredictable (forgive the double-negative), a little less scary.  As adolescents, we inhabit a space that is defined by preparation (Perhaps this is the reason for the faulty notion that everything offered to us by more experienced adults is something that we’ll eventually need.  Since so much of preparation is usually about fulfilling needs, it’s easy to overlook the fact that our elders wish to provide us with things that go beyond need and ensure that we’ll live good, high-value lives.).  And what are we preparing for?  To the best of my recollection, it’s a phase of life that offers experiences that are both new and mysterious.  It is exciting and it is terrifying.  It is from the terrifying nature of the inevitable unknown that education gains its power and its usefulness. 

 

And what part does mathematics play in all this?  How does it enhance one’s life and subdue the fear instilled in each one of us by the new, the mysterious, the unknown world?  I think that it’s difficult for many to see the value of mathematics in this role because they focus too much on what is being learned rather than the process.  Almost all of what we gain is in the process.

 

Break this process down and what do you get?  We’re asked a question.  We’re provided information.  Information that is vital to identifying a solution is withheld.  Here, the process truly begins.  A series of logical deductions allows us to make connections between the information provided and the information needed.  The solution presents itself. 

 

Mathematics offers us the stuff of life in its most basic elements - lines, curves, angles, shapes.  The products of human existence are presented as data, figures, number.  We are taken way outside of our comfort zone and challenged to find our way back to the familiar; to draw connections between these abstract things and what we experience in day-to-day living.  This is not an easy thing to do.  This takes practice and training.  Mathematics is one of the few areas of thought that presses us to use our minds to these ends, pushing us to the limit of our cognitive ability. 

 

Food for thought:

Is there anything to be gained from this?  Will training your mind to think at the very highest level about the most abstract concepts serve you over a lifetime?

 

I’ve spent four years studying mathematics at the university level, ten years teaching the subject, and I am a lifelong learner always seeking to expose myself to areas of mathematics that I have not previously explored.  One thing is clear: Once you have studied mathematics at a high level, learning anything else becomes simple in comparison.  Put simply, if you can do math, you can do almost anything.  I really believe this.  Possibly the most important thing that mathematics has given me is a tremendous sense of pride and esteem and confidence about what my mind is capable of - a sort of intellectual swagger.  This is a benefit of education that is often overlooked - how it makes us feel about ourselves - and few things make us feel as smart as being really good at mathematics. 

 

I hope that I’ve made one thing clear: We do not study mathematics now so that, later on, we’ll be able to do mathematics.  We study mathematics now so that, later on, we’ll be able to do anything.  I know it’s not obvious or easy to understand how the mathematics we learn in school relate to life experiences that have nothing to do with mathematics.  It’s possible that you won’t make the connection for years or decades.  It’s possible you may never see it.

 

Food for thought:

When the original question was asked, I was introducing the concept of a proof.  I can say with near certainty that you will never encounter a proof anywhere outside of a classroom.  You may, however, find yourself one day being interrupted by a young person with a challenging and thought provoking question - one that is not easy to answer.  Because you wish to offer an equally thoughtful response, you decide to organize your thoughts on paper.  This response must be elegant and convincing, with a precise logical structure.  You’ll be making statements and claims and they’ll need to be supported by evidence and reason.  You will need to draw on information this young person already knows and create connections to new ideas and information.  Ideally, each thought must be concise; it must derive its relevance from the previous idea and flow seamlessly into the next idea.  If this flow - this logical structure of interconnected ideas - breaks down, your argument will become ineffective and confusing.  You are, after all, attempting to prove something.  I wish you success in this endeavor and all others.  Now, grab a pen and listen up.

 

 

Reviews

[Babe]

Yh its alryt. It was good and flowing thru out

[Wendy Seames Garner]

Well this does may me more inclined to like mathematics.

[Shep]

Love the Idea and how it tells a story with such flar and it grabs the mind. In a good way. Awesome write.

[Jack Isaac]

How much calculus must the brain perform during a simple act of walking? And this story is a neat attempt at answering the nagging question "why do I need to know that?" There may be only one correct answer: In order to live, we need to grow, and for that, we must _____. And, you fill in the blank. So you enter, "eat" but then you need to know where to find food. Eating is proof that you can find food. This story is proof that you can find food for thought. Moreso, you will find the answer to that nagging question --and I think this works quite well!