\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2014f.00459}
\itemau{Foster, Colin}
\itemti{Being inclusive.}
\itemso{Math. Sch. (Leicester) 43, No. 3, 12-13 (2014).}
\itemab
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.
\itemrv{~}
\itemcc{E30 E40 G40}
\itemut{inclusive definitions; mathematical language; way of speaking; mathematical logic; consistency; mathematical vocabulary; polygons; quadrilaterals; elementary geometry; shapes}
\itemli{}
\end