A couple of weeks ago, I read Craig Barton’s post – The art of teaching anti-functional maths – and I wholeheartedly agree with the sentiments expressed there. In my previous job I had to teach Functional Maths at all the levels from Entry 1 to Level 2 and it wasn’t an especially pleasant experience. The students were great (and generally forgiving for being dragged through ‘yet more maths’) but the contexts used in the questions were either mind-numbingly awful, grossly oversimplifed to the point of nonsense, or just utterly irrelevant to the lives of your regular 16-19 year old.

Now, I didn’t think I would be doing much if any blogging this summer: the combination of needing to unwind, having a few trips planned, and a never-ending list of jobs that need doing around the house, doesn’t leave much spare time and, equally, I didn’t think I would have the inspiration. But today my life took a turn for the functional.

## Functional or Functioning

I would like to think I’m a generally competent mathematician. I understand enough of the subject at fundamental and at advanced levels so that I am able to teach Maths and Further Maths at A level. However, I’m pretty bad at mental arithmetic, often make stupid mistakes when adding fractions, and am generally rubbish solving any kind of traditional geometry problem beyond GCSE level. These weaknesses on low-level stuff don’t mean I’m bad at maths: more, they show I lack care and concentration with things that don’t capture my interest. Much more importantly, like any self-respecting mathematician, I also lack a significant amount of common sense in day to day life.

## A Functional Task

Today I decided to tick a job off my list: painting. Different parts of the house needed doing: the bathroom ceiling; a ‘feature’ wall in my bedroom which has been an awful shade of brown for the past 5 years; and the kitchen which has a patchy undercoat of white covering the baby blue that was there when I bought the place.

This is the stuff of functional maths examiners’ dreams: measurements to be made, quantities to be established, units to work with, prices to compare and total, even scheduling jobs if they really wanted to milk it!

So how did I tackle the situation as a functioning (rather than functional) mathematician?

Did I measure the widths and lengths of all the surfaces that needed painting, multiplying by the number of coats needed? Did I calculate perimeters of these surfaces to work out how much masking tape I would need? Add in a percentage to allow for overlap and wastage? Did I compare the cost-effectiveness of buying 2 x 5 litre tins instead of 1 x 10 litres? Woah, wait, litres? I must have converted my square centimetres into square metres into litres of coverage? Working out the change I’d get from a fistful of tenners? Rather disappointingly, the answer to all of those questions is a resounding no.

## A Functioning Solution

Don’t get me wrong, I’m not saying I went about this project in the most appropriate way. I am sure there are people out there who would answer yes to those questions. They’re probably the same people that haven’t spent the evening scraping paint out of their hair and off the bathroom tiles. But, looking back over the day, can I see the mathematician in me playing his part?

First up, I made a list. I quite like to see that as analogous to the hypotheses of a theorem. “If [I buy all these things] then [I will be able to do the job].” Ultimately, it turned out that my hypotheses were sufficient but not necessary. I never did use the sugar soap spray or mini-sized paint roller. Not entirely sure why I even picked them up. One-nil to you, B&Q.

Secondly, getting the shopping done. The maths I used here (bet you didn’t think of this, Pearson) was route-planning. How can I get my trolley around this shop so that I don’t have to keep doubling back on myself? Being honest with myself though, I think I solved this using a Monte Carlo method – ie, randomly.

Thirdly, choosing what to buy. I never knew there were so many varieties of masking tape. So what to choose? Some was branded ‘professional masking tape’ which I think ruled me out straight away. The wide stuff obviously meant better protection for the other walls when I was slapping the paint on. And, bizarrely, a 50 metre roll was cheaper than a 25m one. Would 50m be enough? To be honest, the question didn’t even cross my mind. B&Q is only down the road so I don’t need to solve a tedious problem. White paint also seemed very hard to find, but they had one shelf with massive tubs of it. I chose the cheaper of the two brands in the size I could lift without having had Weetabix this morning. (Sorry exam boards, both brands sell exactly the same size tubs; no price per litre comparison to be had here.)

Fourthly, a little Pythagorean inspiration meant I could use a dustsheet which originally seemed not quite wide enough. Folding it along a diagonal meant it went the whole length of the wall.

## Dysfunctional Maths

In case you hadn’t already surmised my main point here, it’s that functional maths tasks are rubbish in too many ways. Painting a bathroom ceiling won’t motivate teenagers and the kind of maths that an exam board would crowbar into the situation wasn’t even the kind involved in my ‘solution’. If you want them to paint a room, get them to paint a room. If you want them to do maths then give them a maths problem!

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