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Real life problems

“Lewis played a game of space invaders, he scored points for each spaceship that he captured.

He scored 140 points for his first spaceship, 160 for his second and 180 for his third. The points he scored formed an arithmetic sequence.”(C1 paper, Edexcel, Jan 2013)

This question is a great example of the stupidity that has crept in with “real life questions”. It’s ridiculously convoluted and is not real life at all. Firstly, space invaders was old in the 1980s, and my pupils hadn’t heard of it. Secondly, when you play space invaders, or other such games, the computer works out the scores for you! You play to get the highest score, not to try and reach a specific number of points. And even if you did, the computer would do the maths for you.

This example is not the only one, that c3 paper had the ridiculous question about Katie needing to cross a road to take a photo of a marathon runner.

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This is a ridiculously confusing way to ask a relatively straightforward alternative form question, and has absolutely no “real life” benefits. No one would see a marathon runner, think “I need to take a photo”, then think “if I assume my speed is a function of the angle I walk and can be modelled the reciprocal of rcos(theta-alpha)”. That would be ridiculous, so why ask a stressed 17/18 year old to do it in the most high pressured exam series of their life?

Someone, at some point in recent history, decided that mathematics needed words to contextualise it, and since that point examiners and teachers alike have been shoe-horning ridiculous contexts into their maths questions.

I’m not against wordy questions, or even real life ones. But they have to be appropriate and they have to have a use, the examples mentioned above don’t and the exams would have been better without their ridiculousness. The computer game question could be reframed, you could set it in the context of the programmer, not the player, and say he wants bonuses to drop at a certain score, so after how many spaceships is that? That would be a better question. The alternative format one would be better if the examiner had actually found out what is modelled by functions like that post school and asked around that.

Modelling is a great skill, and I would like to see that offered at alevel, perhaps as a project, perhaps even as a separate qualification. Maybe there’s scope to use the EPQ that way?

GCSE exams tend to be more realistic with their context, questions around the amount of paint you need to paint a room, how many boxes of grass seed to seed a lawn and whether someone has enough ingredients to bake something all have uses for the pupils post school. However, even they are sometimes silly. Edexcel’s June 2013 paper had a estimation question which asked something like “Mary had a goat, it produces 28.1 litres of milk a day for 280 days, estimate how many half litre bottles she could fill.” It isn’t really something they’ll ever meet!

On Friday one of my colleagues was off, and I was timetabled into a room immediately after his class and the ten ticks sheet that had been left as cover was entitled “real life questions”. There were some crackers:

“Bobby is worried that there might be a salad cream shortage so he goes to the supermarket and buys 42 bottles, each bottle contains 285 grams, what’s the total weight?”

WHAT? That’s not a real life problem, that’s a ridiculously convoluted way of asking “what is 42×285?”

“Sam has a catering pack of ketchup containing 412 mls. His job is to put it into 17ml sachet. How many sachets does she fill?”

Again, WHAT?!

I understand the need to set worded questions, and the need for students to be able pick out what info they need. But if you are going to call it “real life”, then make it “real life”! And make sure their is a point to the question! Obviously, I count things that happen in fantasy worlds, such as the Marvel Cinematic Universe, Game of Thrones, Discworld etc as “real life”….

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  1. April 8, 2014 at 9:08 pm

    That is maybe the worst math problem in the entire world.

    • April 8, 2014 at 9:30 pm

      The one with Katie and the runner? I can’t recall seeing a worse one!

  2. April 8, 2014 at 9:12 pm

    I’ve spent some time searching around just now and don’t quite have a handle on what “EdExcel C3″ means. I know that UK’s GCSE’s are their summative year-end exams and quite important. EdExcel is the Pearson subsidiarity that administers the test. Can you explain what “C3″ means?

    • April 8, 2014 at 9:29 pm

      Sorry, I should probably explain for non UK folk. C3 is an A Level module. A levels are studied by students after GCSEs, they normally pick 4 or 5 subjects. Maths is currently modular, although it it moving towards a terminal summarise exam. They sit 4 core modules and chose 2 applied from a variety of stats, mechanics and decision based choices. the core modules have a lot of algebra, geometry, Trigonometry and calculus on them C3 is Core 3 and includes a lot if stuff in functions (graphing, domains ranges, modulus, Ln, exponentials) trigonometric identities, polynomials and some calculus!

  3. April 12, 2014 at 7:27 pm

    Reblogged this on The Echo Chamber.

  4. Taco
    April 13, 2014 at 1:29 am

    These ‘real life’ questions are appalling. Wouldn’t be much better with Game of Thrones thrown in, as it still buys into the assumption that maths should be ‘fun’.

    • April 13, 2014 at 1:52 am

      That’s a strange choice of words. I find maths incredibly “fun”! In fact, I was just a little bored so proved Heron’s Formula to prove to myself I could, and I had fun doing it.

      I think I know what you’re getting at though. I think you mean that “fun” that is added in (such as these perceived hooks) shouldn’t get in the way of the maths? (do correct me if I’ve got the wrong end of the stick)

      I’d agree, but context used correctly does have a place. Pupils may want to go walking when they grow up, so a grasp of bearings in context could be important, and whether that context comes from a map of the Yorkshire dales, or from the fictional “seven kingdoms” is by the by, the maths is the same and the skills they develop will help if they choose that as something they want to do in later life.

  5. igb
    April 13, 2014 at 8:55 am

    Hardly a new issue: Feynmann excoriated it in the 1960s (http://www.textbookleague.org/103feyn.htm)
    “Finally I come to a book that says, “Mathematics is used in science in many ways. We will give you an example from astronomy, which is the science of stars.” I turn the page, and it says, “Red stars have a temperature of four thousand degrees, yellow stars have a temperature of five thousand degrees . . .” — so far, so good. It continues: “Green stars have a temperature of seven thousand degrees, blue stars have a temperature of ten thousand degrees, and violet stars have a temperature of . . . (some big number).” There are no green or violet stars, but the figures for the others are roughly correct. It’s vaguely right — but already, trouble! That’s the way everything was: Everything was written by somebody who didn’t know what the hell he was talking about, so it was a little bit wrong, always! And how we are going to teach well by using books written by people who don’t quite understand what they’re talking about, I cannot understand. I don’t know why, but the books are lousy; UNIVERSALLY LOUSY!
    Anyway, I’m happy with this book, because it’s the first example of applying arithmetic to science. I’m a bit unhappy when I read about the stars’ temperatures, but I’m not very unhappy because it’s more or less right — it’s just an example of error. Then comes the list of problems. It says, “John and his father go out to look at the stars. John sees two blue stars and a red star. His father sees a green star, a violet star, and two yellow stars. What is the total temperature of the stars seen by John and his father?” — and I would explode in horror.
    My wife would talk about the volcano downstairs. That’s only an example: it was perpetually like that. Perpetual absurdity! There’s no purpose whatsoever in adding the temperature of two stars. Nobody ever does that except, maybe, to then take the average temperature of the stars, but not to find out the total temperature of all the stars! It was awful! All it was was a game to get you to add, and they didn’t understand what they were talking about. It was like reading sentences with a few typographical errors, and then suddenly a whole sentence is written backwards. The mathematics was like that. Just hopeless!”

  6. May 17, 2014 at 12:35 am

    We were planning to write a lesson next week on the math of telephoto lenses — why do only long lenses have vibration reduction? — but the one about Kate crossing the road is MUCH better. Thanks for the tip! :)
    Great post. It’s sad that someone would consider “how many salad dressing bottles?” an authentic, real-world math question. The more we (mis)represent this as “real,” the more students will decide that math isn’t for them. Unless, of course, they love salad.

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