Post by Ian/Cath FordOK, I always fall for these. What is the largest possible answer?
And how do I talk about it to a nearly 4 year old?
Is this him asking, or you trying to teach him? If the
latter, then of course you don't [but you already know that, in
your capacity as a teacher]. Does he *really* want to know, or
is it a displacement activity to defer bedtime?
You can usually pass it back to him. "What do *you* think
it might be?" "A million million million million million." "Then
how about a million million million million million and one?" "OK,
a bazillion gazillion illion illion ... *and* *one*." "A bazillion
gazillion illion illion ... *and* *two*." He should soon realise
that you can always add one to any actual number. At that age, you
can usually divert to "I can count faster than you can." "No you
can't" "Yes I can" "OK, race you to a hundred" [if he knows that far,
and if not, you won't have had the millions and biggest number stuff
yet]. While he's gabbling through the numbers, you go "One, two,
skip a few, ninety-nine, a hundred"; gives him something to tease
his friends with.
If he's *really* good, and *really* interested, he may come
to the realisation that "infinity" is not a counting number, so that
you can add one to it [or double it, or square it] and still have the
same number. Or he may think up some infinite games, like "My dad
has more than your dad". And then there are the infinitesimals to
think about. If you find yourself in this territory, and it's a
genuine interest for him [which it probably won't be] -- don't you
*dare* try to teach him about it -- pass him on to me.
The important thing from my point of view is that you are
"correct" and "honest". The vast majority of children are not very
interested in maths, and you can just answer arithmetic questions
["Dad, I'm stuck, how do you do 111 take away 22"] in the same way
you'd answer any questions by a child. The only different thing
is that there are several ways of laying out most calculations, so
you will get "No, Dad, you don't understand, Miss Jones says we
have to do it like *this*", and no amount of "But it doesn't matter,
we'll get the same answer" can overcome the teacher's authority.
But just a few will want to explore, esp in areas like
infinity. I'd much rather you explained reasons and/or admitted
ignorance than said things like "There is no largest number" that
block off the area without satisfying curiosity. Good teachers
know that, of course; the problem is that most teachers are so
scared of maths and of seeming ignorant that they give blocking
answers anyway.
--
Andy Walker, School of MathSci., Univ. of Nott'm, UK.
***@maths.nott.ac.uk