id: 06351102
dt: j
an: 2014f.00459
au: Foster, Colin
ti: Being inclusive.
so: Math. Sch. (Leicester) 43, No. 3, 12-13 (2014).
py: 2014
pu: Mathematical Association (MA), Leicester
la: EN
cc: E30 E40 G40
ut: inclusive definitions; mathematical language; way of speaking; mathematical
logic; consistency; mathematical vocabulary; polygons; quadrilaterals;
elementary geometry; shapes
ci:
li:
ab: From the text: “A hexagon has five sides." True or false? ‘False’,
you might say ‒ ‘a hexagon has six sides’. But if it has six
sides, then it certainly has five sides. If I have ten pound coins in
my pocket and somebody asks me, ‘Do you have two pounds?’ then I
should answer ‘Yes’, shouldn’t I? If I didn’t want to give them
my money, and so answered ‘No’ on the grounds that I had ten
pounds, not two pounds, you would think that a bit dubious, wouldn’t
you? To protest that ‘They should have asked me whether I had “at
least" two pounds!’ sounds a bit hollow. So a hexagon has five sides,
a square has three right angles, a rectangle has one line of symmetry
and a triangle has two vertices. I think this is how pupils sometimes
feel when we ask them to accept ‘inclusive definitions’. We show
them a square and ask them if it’s a parallelogram, and they say,
‘No, it’s a square, stupid’, with the ‘stupid’ perhaps
implied rather than stated. And we think, ‘Oh dear. They don’t
realize that all squares are parallelograms’. But maybe they do but
they are just trying to answer more accurately.
rv: