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Blog: What's in a number?
How our lives are dominated by numbers yet we somehow get it wrong

10. Are We Creating a Nation of Dunces? The GCSE Sweet problem

A simple question has been posed in the 2015 GCSE maths exam which has stumped many of our little kiddies. Why are they such imbeciles? I don't know if it's more embarrassing that they can't solve the problem or that they feel the need to vent their frustration on Twitter.

The problem relates to sweets in a bag and simple probability. It is dressed up in simple English so that it is a "real life" sounding problem. As in all such problems the issue is to boil the English down to the mathematics. That is the power of mathematics. It cuts out the garbage. There is no supersticion, no belief in supernatural beings, no belief in aliens or horroscopes, just plain logic. The rules of logic are clear and easily memorised. What is the difficulty? I have no idea.

If you haven't heard by now, this the problem:

There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes at random a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet.

The probability that Hannah eats two orange sweets is 1/3.

(a) Show that n2 - n - 90 = 0

(b) Solve n2 - n - 90 = 0 to find the value of n

I won't give the solution, which took me less than 2 minutes to arrive at. You can go elsewhere for that if you really can't do it.

I think it's a brilliant problem as it has all the hallmarks of quality mathematics that I have encountered throughout my academic career. It is difficult for those who fail to see the point, and it is dead easy for those who see the route to the solution because they understand the basic material. Very few workings are required. Once you see the solution it gives you a positive glow!

For those students who took to Twitter you should be ashamed and embarrassed! Not only could you not solve a trivial mathematics problem. What does that say about your brains? Also, it demonstrates a lack of maturity. If you want to be treated seriously in the rest of your apparently sorry life, try not to be a spoilt child! You can't vent your frustration on Twitter every time you're a twit!

Congratulations to the puzzle formulators! The puzzle sorts the wheat from the chaff. The fact that so many people have vented their frustration on Twitter just confirms that. Brilliant! Please don't bow down to public pressure and water down future questions.

I do wonder if we are generating a nation of mathematical dunces. It has been suggested that our crappy measurement system is partially responsible (e.g. Dr. Metric). We have a system of mixed Imperial and metric units to the detriment of everyone. Some people (probably they can't solve the trivial problem above) prefer the medieval system of units that weighs our bodies in stones and our heights in feet and inches. The metric system is a proper coordinated system of units that facilitates mental arithmetic. Our kiddies are perhaps not getting enough practice at home in mental arithmetic as the mixture of units around them requires the need for calculators to make any quantitative sense of anything. For a long time politicians have argued that knowledge of both systems improves people's understanding. They themselves seem quite incapable of basic arithmetic. So I believe the opposite is true: mixed units causes muddled thinking and an inability to solve simple maths problems.

So the kiddies in their Twitter enthusiasm have missed the point. Why aren't they equally outraged that our crappy measurement system doesn't allow them easily to calculate important things such as body mass index, fuel economy of vehicles etc., the area of a space in acres (in what you might say...) etc., etc. Perhaps they are trying to acquire "qualifications" without an education. If they worried about getting an education first, the qualifications would follow and Twitter outrage would not be needed.

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Website revised by John Austin, 5/6/2015. © Enigma Scientific Publishing, 2015.