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When will I use this?

June 4, 2019 Leave a comment

Recently I read a rather interesting article from Daniel Willingham about whether there were people who just cant do maths. It was a very good read and I hope to write my thoughts on it later, when I’ve had more time to digest the material and form some coherent thoughts, but there was one part that set me off on a train of thought that I want to write about here.

The part in question was discussing physical manipulatives and real life examples. Willingham said that there is some use in them but that research suggests this can sometimes be overstated as many abstract concepts have no real life examples. He then spoke about analogies and how they can be very effective in maths of used well.

This got me thinking, earlier on the day a year 12 student had asked me “when am I ever going to use proof in real life?”. This type of question is one I get a lot about various maths topics, and my stock answer tends to be “that depends what career you end up in”. Many students, when asking this, seem to think real life doesn’t mean work. A short discussion about the various roles that would use it and that its possible they never will if they chose different roles but that the reasoning skills it builds are useful is usually enough and certainly was in this case.

It does beg the question though “why do they only ask maths teachers”? Last week when a y10 student asked about “real life” use of algebraic fractions I asked him if he asked his English teachers when he’d need to know hiw to analyse an unseen poem in real life. He said no. I asked if he thought he would. Again no.

So why ask in maths?

The Willingham article got me thinking about this. There has been, throughout my career, a strong steer towards contextualising every maths topics. Observers and trainers pushing “make it relate to them” at every turn. But some topics have no every day relatable context.Circle theorems, for instance, are something that are not going to be encountered outside of school by pretty much any of them. So maybe thats the issue. Maybe we are drilling them with real life contexts too much in earlier years, and this means when they encounter algebraic fractions, circle theorems or proof and don’t have a relatable context the question arises not from somewhere that is naturally in them, but from somewhere that has been built into them through the mathematics education we give them.

Maybe we should spend more time on abstract concepts, ratger than forcing real life contexts. Especially when some of those contexts are ridiculous – who looks at a garden and thinks “that side is x + 4, that side is x – 2, I wonder what the area is?” (See more pseudocontext here and here).

What do you think? Do you think we should be spending more time lower down om the abstract contexts? Please let me know in comments or via social media.

Real life problems

April 6, 2014 9 comments

“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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