There’s been a lot of talk on social (and other) media about “that maths question”. A problem in last week’s GCSE Maths paper that stumped a whole cohort of candidates.
I suppose the resultant Twitter storm is the modern day equivalent of sitting outside the school gates discussing the exam that we had just taken.
I always tried to avoid these discussions, and am still not an advocate of them.
Exam post mortems are rarely useful, and are never going to change how you have answered the paper. They either make you feel bad because you didn’t spot the answer that your friends did, or make your friends feel bad because they didn’t spot the answer that you did.
The difficult question started like this:
A bag contains an unknown number of sweets. Six are orange; the rest are yellow. Hannah took two sweets from the bag and they were both orange.
So far, so good. It’s looking like a standard probability question, and the next bit is going to ask “what is the probability of this happening”.
Except … it wasn’t. The next bit was:
The chances of this happening are 1/3
Prove that n2 – n – 90 = 0
Do what? I can see why this caused such confusion. It looks like a non-sequitur. OK, once you have worked out the equation for the probability, it cancels down to this quadratic equation, but maybe there should have been an intermediate step to tell the students to do this.
I spent a few minutes working this out yesterday. My first attempt went off at a tangent, and I filled a page of A4 with equations that proved that 12 = 1 – not a whole lot of use, other than to provide amusement to my tame maths teacher.
But then I got there:
Initially there are n sweets in the bag of which six are orange. So the probability of picking an orange sweet is 6/n.
There is then one fewer sweet in the bag, and only five orange ones. So the probably of picking second orange sweet is 5/n-1.
Multiply these together, and you get the probability of picking two orange sweets:
We’ve been told that this is 1/3, so:
Multiply both sides by 3:
Multiply both sides by (n2-n)
And finally subtract 90 from both sides
W5 (WWWWW – Which Was What We Wanted). Or QED (Quite Easily Done), if you prefer.
Apparently the next part of the question was to solve the equation – having been given the quadratic equation.
So not rocket science. Not even algebra, in my book – it’s simple substitution.
“In my day we were expected to know the quadratic equation.” Though we probably weren’t as it would have been in the Tables Book (which don’t exist anymore as calculators do it all) along with the rest of the formulae that we might need.
“Come on, Page 8, the refusal formulae” was the familiar cry from Ratty Saunders when we were faced with a trigonometrical problem.
“Why do you call them the refusal formulae?” we once dared to ask. “Because generations of schoolboys have refused to learn them” was the answer.
Was the old O-Level paper easier?
I dug out my O-Level paper to see what sort of probability or algebra questions we were expected to solve.
A number is chosen at random from the numbers 2, 3, 4, 5, 6, 7, 8, 9. What is the probability that it is divisible by 3? What is the probability that it is either a prime number or divisible by 3, or both?
w = (x – y) / 2a. Express x in terms of a, w and y
After modification, a car will do 25% more miles to the gallon. Calculate the resulting percentage saving in fuel for a given journey.
Solve the inequality 5 – 3x > (x / 2)
These don’t look particularly more difficult than today’s GCSE questions – in fact, it could be argued that these examples are easier, as it specifically tells you what you need to do.
We can only realistically compare exam papers if they are assessing the same syllabus. Maths is a huge subject, and topics drop in and out of the syllabus more frequently than … fill in your own metaphor here.
Still carrying your “Little Oxford Dictionary” ?
I took O-Levels in Maths (in year 10) and Advanced Maths (in year 11), followed by A-Level Maths and (for a while, until I saw the light (or, rather, I couldn’t)) Further Maths. It’s all a bit of a blur as to which topic was covered at which level.
I know we did matrices at O-Level – they are not in the current syllabus (but even back then, the syllabus differed between exam boards. A friend didn’t see matrices until he got to university – where he studied maths). But we didn’t do the Circle Theorems, which are.
Also, technology has moved on in ways that we couldn’t even imagine back in my schooldays. My mobile phone (still a dumb-phone by the way) has a more comprehensive spell-checker than the “Little Oxford Dictionary” that I used to carry round. It has a better calculator than my TI-33 too. Pretty much everything is available on the internet at the click of a few buttons.
Schooling today isn’t so much about remembering facts; it’s more about knowing where to find the facts and assessing their usefulness. It’s not so much about knowing stuff; it’s more about knowing what you need to know and where to find it.
I was once told that children don’t go to school to learn; they go to school to learn how to learn. That’s still the case – but how we learn things has changed. For all of us, not just schoolchildren.
Note: Back to Hannah’s sweets, here is the solution by Rob Eastaway, author of Maths for Mums and Dads.