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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.

Revenge of the real life questions

May 21, 2015 7 comments

Last year I wrote this piece discussing some of the worst pseudo-contexts that I’d come across in maths exams. You know the ones, the ridiculous made up contexts that are supposed to give a real life twist to a question but Ard actually anything but. Well this year’s C2 Edexcel A Level paper has two of the worst I’ve ever seen!

Exhibit A

image

Aaaaaaaarrrrrrggggghhhhhh!!!!!!

“Figure 1 shows a sketch of a design for a scraper blade. The blade OABCDA consists of an isosceles triangle COD joined along its equal sides to sectors OAB and OCD of a circle with centre 0 and radius 8cm. Angles AOD and BOC are equal. AOB is a straight line and is parallel to the line DC. DC has length 7cm.”

There are a few issues I have with this question. Firstly we have a whole paragraph that is entirely unnecessary! The only purpose this paragraph would serve was to test the ability to sketch or visualise but this us completely negated  by the diagram. One of my year 12s asked, “what’s the point in that writing on the sectors question? It just described the picture.” I had to agree.

That wasn’t the worst bit though, the worst bit is there at the beginning .

“Figure 1 shows a sketch of a design for a scraper blade”

I can imagine the examiner’s meeting now: “I’ve got a great sectors question, it uses area, arc length, cosine rule, sine rule for area…. it’s a classic.” “Great, but we said that was going to be a real life question this year.” “Oh b@#@##ks, what can I do?” “Just make it about a scraper blade!”

What even is a scraper blade, and why do we need this question be about one?! This was actually a great question, or would have been if it had only one of the picture or the paragraph and no stupid mention of a scraper blade.

Exhibit B

image

“A solid glass cylinder, which is used in an expensive laser amplifier, has a volume of 75pi cm^3.
The cost of polishing the surface area of this glass cylinder is £2 per cm^2 for the curved surface and £3 per cm^2 for the circular top and base areas. Given that the radius is r cm…”

Show that the cost is, then find the minimum.

This question is pseudo-context at its worst. A part for an expensive laser amplifier will be the required size for said amplifier. It will need to fit abd as such it’s length and radius will be far more important that it’s volume, do there’s no way at all that they would design the laser around the minimum cost of polishing a cylinder with a certain volume! Why would you create such a convoluted, nonsensical, bogus context?! If you want to ask questions in context fine, but please make it a believable one!

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