Sir, – I can't help but notice that there appears to be an error in the "Share and share alike" question ("Dr Maths solves problemof how to make subject fun", Science, October 13th).
The problem was stated thus: “Four children were given a packet of sweets. Julian said: ‘I am the eldest, I should have half.’ Dick said: ‘If that’s the case, I am next so I should have a third.’ George demanded a quarter and said that Anne should get a fifth. Anne said: ‘If that’s the case, then we’ll need another 15 sweets.’ How many sweets were there in the packet?”
The answer given was that there were 60 sweets in the packet.
However, if they were divided out as per the question the split would have been as follows: half to Julian equals 30; a third to Dick equals 20; a quarter to George equals 15; and a fifth to Anne equals 12. This gives a total of 77 sweets and thus an extra 17 sweets would have been required and not the extra 15 as stated in the article.
In fairness, the mathsweek.ie website appears to also have the wrong answer. – Yours, etc,
KENDRA JACKSON,
Rialto,
Dublin 8.
Sir, –The answer I got was 77, not 15 more than 60. Have I missed something? – Yours, etc,
PADRAIG McGINN,
Carrick-on-Shannon,
Co Leitrim.
Sir, – The article “Dr Maths solves problem of how to make subject fun” rightly suggests the key to an engaging maths lesson is word problems. However, word problems fall into two conflicting categories, only one of which belongs in the enlightened classroom.
The ideal word problem is the application that motivates the theory. If the teacher gives clear and accessible examples from the get-go, the pupil will better see what the theory “means” and more easily remember and apply it. Once the theory is understood, a problem that once seemed inaccessible is reduced to a routine exercise.
However, all too often the theory is decided in advance, and the “applications” are contrived specifically to justify it.
Take as an example some artificially selected tidbits of information on how a bag of sweets is to be shared between five children. We are asked to use fractions to calculate the total number of sweets. A moment’s reflection shows this problem is completely impractical. If such a situation arose for real, a pupil could always just count the number of sweets, obviating any need for a knowledge of fractions, or the specific pattern of knowns and unknowns given in the question.
Both types of word problem have an abstract mathematical exercise at the core. Both have stories built around that exercise.
The first story is a bridge between the real world and the abstract world of mathematics. But the second story is only a barrier between the pupil and the mechanistic mantra of “how do I do this sort of problem?” – Yours, etc,
DARON ANDERSON,
School of Mathematics,
NUI Galway.