# Discussion: Keynote Part 2

 posted by: Jane-jane Lo on May 21, 2003 at 4:26PM subject: depth of the understanding
 I have a hard time separate the mathematical and pedagogical reasonsfor this case. Mathematically, three-fourth of a dozen is not much different from the3/4 box of a crayon of 24, yet psychologically, they felt verydifferent. They each provide different challenges on connectingbetween symbols, words, and the meanings. In the first day's lessons, the questions were sequenced from theeasier to the harder one to help students move from the more familarsiutaitons and fractions to the less familar ones. the progresionitself might hide certain unclear reasoning, as this case seemed to be. Without revisit it head-on, it's not possible to discover theconfusion.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, butmathematically added the opportunities of exploring multiples ofanother number.
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