[Maths-Education] use of counterexamples in primary classrooms

[romlins at rc.unesp.br]

Dear Dylan,

indeed,

> Interestingly the same "method" of division features in Abbott and
> Costello's "In the Navy".

which is from 1941 and is at http://youtube.com/watch?v=HLuhPBuy6-0 (the
short scene). Ma and Pa Kettle seems to be from 1949, according to
imdb.org.  Does anyone know how old this 'trick' is?

Anyway, I will show them both to my students!

Back to counterexamples. One could get Costello into possible trouble by
asking him whether 24 times 4 equals 24:

24
x4
--
 8
16
--
24

Fourteen such cases if multiplying two-digit numbers by a digit. If ab can
be multiplied by some c1 to produce ab, so can ba by a c2, and
c1+c2=11...! :)

That reminded me of a friend, an excellent maths teacher, Bigode, who once
asked his 5th grade pupils to add 2/3 + 3/5 and got back the (natural)
answer 5/8. Instead of "correcting" them, he then invited them to list
properties this operation had: associative, commutative, it has an
identity element 0/0 and so on. For homework he asked them to do some more
additions. One of them was 1/2 + 1/2. That solved the supposed problem: a
half plus a half can't be but one.

all the best
Romulo