on May 21, 2003
depth of the understanding
I have a hard time separate the mathematical and pedagogical reasons
for this case.
Mathematically, three-fourth of a dozen is not much different from the
3/4 box of a crayon of 24, yet psychologically, they felt very
different. They each provide different challenges on connecting
between symbols, words, and the meanings.
In the first day's lessons, the questions were sequenced from the
easier to the harder one to help students move from the more familar
siutaitons and fractions to the less familar ones. the progresion
itself might hide certain unclear reasoning, as this case seemed to be.
Without revisit it head-on, it's not possible to discover the
To add mathematical variaties, one can use a number such as a box of 30
crayons to bring in fractions of other denominators. Asking as 5/6 off
30 crayons should still be able to bring out the same confusion, but
mathematically added the opportunities of exploring multiples of