Thursday 10 October 2013

When Will I Use Algebra in Real Life?

There is one question my students ask me that I hate far more than all others. Far more than "Why are you just a teacher?" and "Do you have a boyfriend? What's his name? What's his job..." etc.

That question is: "When will I use simultaneous equations/ the laws of indices/ completing the square in real life?"

A good maths teacher, of course, would have a bank of answers to such questions. "Satellite dishes are in the shape of a parabola!" etc. Urgh.

Even though I do happen to know a few applications of algebraic principles to "real life" (picture me making air quotes with my fingers), I never tell these to my students. I refuse. 

First of all - real life? I'm sorry, are my maths lessons not real? When you enter room 204, are you entering some kind of alternate universe? Is a  maths lesson merely a state of mind? Some kind of lucid dream that looks real and feels real, but can't possibly be real because instead of English the teacher is speaking in an alpha-numeric jumble?

Secondly, where did students (and, for that matter, teachers) get the absurd idea that everything one learns has to have some kind of practical "use"? Can't we simply enjoy learning maths for its own sake? Does everything we do have to have a useful purpose? What kind of depressing life would that be?

Maths is beautiful. It is deep and interesting. It is a language. It is an art. It is a self-contained world with its own rules, patterns, and mysteries. So don't try to spoil my beautiful maths with your ugly "applications". 

I will leave you with some profound quotes from mathematician G H Hardy: 

"Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics". 

“Imaginary’ universes are so much more beautiful than this stupidly constructed ‘real’ one; and most of the finest products of an applied mathematician’s fancy must be rejected, as soon as they have been created, for the brutal but sufficient reason that they do not fit the facts.”

"I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."

Of course G H Hardy was wrong with that last one - his work was actually widely applied to genetics and thermodynamics. But the point is, that wasn't why he did it. And he didn't need these applications as motivation for producing this work.

Do you agree with me or are you someone who sees maths as a "tool" with which to get things done?

Emma x x x


  1. I totally agree. I used to make an effort but it never went well, even the genuine 'real life' applications I could come up with tended to be met with "well, I'm not going to do that when I'm older, can't someone else learn it instead?" or other smarmy answers that annoyed me and wasted time that would otherwise be spent learning. I don't even tolerate that question off 6th formers anymore - you chose to be here so don't expect me to justify your choice to you! So now I am totally unabashed about this with my classes so when students ask me "Miss, when will I use [insert awesome maths thing here] in my day to day life?" and say "probably, never. That's not the point of learning it". I have found this developed kudos for having such a hardcore love of my subject.

    If actually answering it seriously, I will say:
    *Maths is more about skills than applications.
    *A lack of mathematical literacy leads to a lower quality of life (I read this in research ages ago) e.g. these people are more easily swindled of their money and convinced into ridiculous financial decisions.
    *Just because something doesn't seem useful now doesn't mean it won't be later (e.g. factorisation -> encryption)
    *Maths comes in handy in the randomest of ways that just makes life better and more convenient. E.g. 2 years ago I knew I could get my enormous sofa round an awkward corner, through the front door and into my flat because I worked out which were the critical lengths to measure and used pythagoras. The other day, I created a super accurate scale diagram of my new house and all my furniture so I could see what would fit where and decide layouts before hand and decide an ordering of what got moved when so we were supermega efficient on moving day.
    *Maths qualifications means you can get paid lots (if you don't go into teaching!).
    *There is great joy to be had in doing maths. It's equipment- and cost-free and cheers up any rainy day! :)

    1. Totally agree with everything you just said! And that last bullet point made me particularly happy. I am now picturing myself snuggled up on the sofa with a cup of camomile tea, notepad and pencil, and cosy blanket, with the rain beating down outside, and a good maths problem to attack. That is my happy place. *warm fuzzy feeling*

    2. Great post Emma and Elizabeth.

      In your list of real reasons Elizabeth don't forget that Maths teaches you to solve problems, and that we need to solve problems every day!

      Personally, I can never be bothered with it and just ask student's "Why did you get up this morning?"

  2. I've loved many of your posts, but this may be a favourite :)

  3. Thank you for this post :)
    It is SO nice to hear you saying this.
    I always feel a pang of guilt (as well as annoyance!) when I get this question, but now I shall hold my head high and think of this post instead!

    1. Glad to have reassured you! Yes, hold your head up high! Remember: you are a mathematician. You are above such trivialities as "real life applications"!