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‘Real Life Maths’

September 30, 2014

Ok. Time for a minor rant.
“Sir? When are we ever going to use this?”
“You’re not. Apart from in the exam maybe.”
And then:

IMG_4251.JPG
I spotted this in a text book and it’s pretty obviously a lie. Every day graphs? Hardly. I don’t think I’ve ever used one of these outside of maths education. Apparently Mike is the kind of person who meticulously monitors his route to library. It’s a damn convenient 1000m from his house and he took a very precise 15 minutes to get there. No he didn’t because Mike doesn’t exist, this library is fictitious and this graph is not even remotely ‘every day’. Some books might well have this in a chapter called Real Life graphs but that’s also pretty much a lie as well. I think my life if fairly real and I don’t use them. I literally can’t think of a circumstance where this time/distance to the library graph would be useful to me. I doubt you can either.
At A level, I teach statistics which sits firmly in the camp of applied maths. I’m pleased to be able to say to my students “For everything we do in this course, you will be able to see why it might be useful for someone to be able to do this.” That’s great. There are absolutely areas of maths that have practical applications and obviously mechanics and decision maths fall into this too.
However, there’s also pure maths. Maths for the sake of maths. Doing things with abstract thinking just because we can. Pure maths contains some of the most truly beautiful parts of maths and a wonderful proof has a great feeling to it. You get the ‘Ah!’ And ‘Aha!’ moments as Rob Eastaway calls them in How Many Socks Make a Pair? Now, don’t get me wrong, I really love statistics but I wouldn’t refer to it as beautiful in most cases. Pure maths has beauty.
This graph however lies somewhere in between. It’s an attempt at applied maths but evidently fails that. It’s not pure maths otherwise we wouldn’t be pretending there’s a context. I think this falls into what Dan Meyer would call pseudocontext. If the maths isn’t interesting enough to be done in its own right, then this is a poor attempt to pretend it will be useful. Students do not fall for this and I pity any teacher that thinks otherwise. Trying to pretend there’s a context here actually makes things worse.
There are certainly other areas of GCSE maths that can’t really be claimed to be useful. Fractions (and especially dividing them) are rarely helpful. Sure a basic quarter of something perhaps or maybe “let’s split this cake in thirds” but rarely are precise fractions needed. Scale drawings and loci often have the whiff of pseudocontext to them as well. “A goat is chained to a barn on a sliding rail…” No it isn’t. And if it was, nobody would care how much grass it could eat anyway.
I think I may well be currently trying to work out why we force everyone to do maths. I hope it’s because it’s good for the brain to be thinking in abstract ways (although I don’t have any evidence for this) but I fear it’s under the pretence that it’s useful for later life. Ask most grown ups that have taken GCSE maths and they’ll tell you that it hasn’t been useful. I suppose it’s really rather difficult to get a sense of whether the abstract thinking has helped them but I am confident that most of them will have not had much of a glimpse of the beauty of maths throughout their studies.
That is a shame.

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13 Comments
  1. Yep, I’m totally in agreement with every single thing you say here Dave! http://wp.me/p2z9Lp-9R

  2. Yes, we need to do some spring cleaning and think what really makes sense to teach. I’ve been thinking on similar lines:
    http://followinglearning.blogspot.fr/2014/08/harder-sums.html

    • I certainly agree about the spring cleaning. I’d lose constructions with compasses and ruler pretty quickly.
      Your blog post is interesting. However, I’m not sure about this point: “Telling the story of a maths idea by talking about its discoverer will help the kids to go further with it.”
      I’m not against explaining some context and history but I’m not sure that it’ll help students go further.

  3. Definitely pseudocontext, though there are some kiddos whom I could imagine enjoying making graphs like these about ordinary things.
    I also suspect that there’s another “grey area” where if we weren’t such a math-averse culture, we would use graphs or math… but mathematical and even arithmetical thinking is really not that common.

    • Indeed. Even if we were a more mathematically comfortable nation, I still can’t see that graph being particularly helpful.

  4. Astounding, but true, that Maths remains poorly aligned with needs and the real world. How can a teacher draw endless triangles with angles marked and lines intercepting and not even attempt to explain why? Of course, understanding is easier from a need, so starting from a real world scenario is optimal, but even the real world does not deal with triangles very much.

    I adored maths at school, so this is no anti-maths polemic.

    I wrote this to try to instil a tangible, meaningful, real world grasp of the matter of basic feel of numbers :

    http://www.educationreform.co.uk/Live/index.php?Id=415

    It illustrates how easily maths teaching can go adrift – many primary school teachers are not comfortable with maths so tend to teach by rote.

    • Ah, I feel we’re going to disagree 🙂
      ‘Starting from a real world need is optimal’ is pretty much what I’m suggesting is the problem. Most interesting maths wasn’t started from a real world need. The fact that we keep trying to pretend to students that that is the case is part of the problem. There is also a difference between “basic numeracy” where I think practical things (like sweets) may well help and more advanced maths where they don’t. Sharing sweets is fun. What about if they were your sweets and you didn’t want to share them equally?
      The ‘linking to the practical’ idea is why I have little doubt that using pizzas or cakes for fractions is why lots of students tell me you can’t have 5/4.

  5. Dave permalink

    Perhaps we need to be careful when we say “real life”. I don’t think they were trying to imply that people draw line graphs when they plan a trip to the library. They are just telling a simple story about visiting a library, and relating it to the rather abstract concept of line graphs. It’s “real life” because everyone has visited a library and they can relate to the story, even if some aspects of the story are unrealistic.

    I do agree that we should be honest when telling students how they might use mathematics in the real world. Some people get along quite well with only simple arithmetic. It is impossible to predict what mathematical tools will be useful to someone in the future, but mathematical problems can arise in surprising contexts. For example, I was recently trying to figure out the best way to divide a class into small groups, and this has led me to study combinatorial design theory.

    • I agree that we need to be very careful with the ‘real life’ label. The entire library thing is ridiculous and I’m afraid that if that’s the best someone can come up with to relate to the abstract concept of a line graphs then they really should be looking at some science examples.
      I’m not suggesting that we should only teach people the maths we think they’ll need (it’d be a short course). However, your example of small groups in classes suggests you’ve probably gone into more depth on it than was actually ‘needed’. (I assume without knowing the context of course.)

  6. Adam Atkinson permalink

    If you’re saying this particular graph is implausible, I can only agree, but graphs per se seem real life enough. You see graphs of stock prices and temperatures in newspapers, numbers of cases of Ebola on Wikipedia, and so on. Even graphs of CPU load on computers and whatnot seem pretty real life.

    • Hi Adam. Ok, that might be a fair point. I think that making use of newspaper examples is probably a good idea. CPU computer graphs probably are quite useful but I still don’t think they’d fall into ‘every day’ for most people.

      • Adam Atkinson permalink

        I see graphs (well, barcharts.. near enough?) of percentage of delayed trains at my local railway station. I think this is because the train company has to give refunds if the percentage is too high. I could imagine people trying to lose weight might draw graphs of their weight to see how their progress is looking (a not entirely implausible non-passive example of use of graphs in real life). Certainly a graph would seem more useful in the weight loss case than a list of numbers. It would also seem like a good time to drag in something like moving averages. Graph the 7-point moving average of the readings rather than the raw values, sort of thing.

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