Maths exams and how we prepare
Recently I’ve been thinking a lot about the way maths is examined and the way we need to prepare for exams, and I’m not the only one. @bigkid4 has written a series of posts on it here: http://mylifeasacynicalteacher.wordpress.com/2013/06/03/how-would-i-change-the-exam-system-ks1-5/ Dave Gale (@reflectivemaths) has written about it here and has also discussed it with Colin Beveridge (@icecolbeveridge) on their podcast here. I’ve read and heard other things too, and had many conversations about this.
The main thing that got me thinking was “that” C3 exam last week. It was really hard and seems to have thrown the vast majority of A level students across the country who sat it. When I first read it I thought it was ridiculously hard. But then I worked through it and realised the the main reason it looked so hard was that some of the questions were phrased differently to previous years. I actually enjoyed working through it, and realised that the students had all the tools to complete it, but if they had relied too heavily on past papers for revision they may have been thrown. Last year I tried to include more open ended maths questions in my lessons, and found some real beauties on some old A level and O level papers dating back to the sixties (when calculus still held it’s rightful place on the O level curriculum!). My year 13’s (among others) loved those questions that I threw in, (one said enthusiastically one lesson: “sir, these questions where you have to work out what maths to use are my favourite!”) and I’m going to build many more.
It’s clear to me that exams are moving this way, and I think it’s right that they are doing, especially at A level. Dave Gale mentions on the podcast above that S1 questions start “using a binomial distribution”, and I know S2 ones do the same with poisson etc, and this seems too easy. But as I say, I reckon the c3 exam is the first step in a move away from that.
This is a trend we are also seeing in GCSE papers. When my HoD and I went through last Friday’s calculator paper is seemed every other question we were saying things like: “that’s unusually phrased so may have thrown some of them”. I hope (and think) that I already am teaching the maths, and not just the methods to pass exams. But I intend to work on this even more to ensure in future that my pupils are ready for anything that gets thrown at them come next May/June time.
While listening to the podcast above I thought the real life use of solids of revolution to derive the volume of a frustum shaped plantpot was superb, and I’m going to use this when c4 comes around. I also liked the challenge question they asked and enthusiastically answered it afterwards (see below). I think questions like this will be key to fully developing future mathematicians.
Question: an equilateral triangle and a regular hexagon have equal perimeter. The area of the triangle is 2 square units, what is the area of the hexagon. The picture was my initial solution, but I did then realise I could have done it quicker and more simply using similar shapes…