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[arrowedumbrella]

I am having a really hard time understanding how something "can't be explained."

A speaker this morning at the NCTM (National Council of Teachers of Mathematics) gave a cute example of a kid's interpretation of the prompt, "Write a story problem whose answer is 5*(7+3)". The kid wrote,
Tim went to the candy store to bye (sic) some chocolate

Comments

[theojf]

A separate debate seems to be whether as a teacher it's _better_ if I emphasize stated knowledge or enacted knowledge. Even if a skill can be transmitted both ways.

[leech]

For this particular example, it seems that articulating the precise expectations of such a story problem would be much more difficult than demonstrating by building up examples. That may be an argument against assignments that rely on such intangible verbal subtleties, but I think the target audience's limitations must come into play in deciding how much to explain and how much to handwave.

[mollishka]

"enacted" knowledge?

[arrowedumbrella]

... Something I still am struggling to understand. Hence the quotes. :)

[oxeador]

I am mostly with you. However, when I read "the teacher would have a hard time explaining..." I do not read it as "it is impossible". If it is possible, but it requires the teacher to work one-on-one with the student for a full hour building from smaller problems and requiring the student's full collaboration (which the teacher, no matter how good, will not always have), then we might as well call it "impossible" for all practical purposes.

I often find myself trying to answer a student question and thinking in my head "I think I know how I could make this crystal-clear to you, guiding you to help you realize each step of the way on your own, so that it makes sense to you, but it would take five hours, which we do not have" so I have to go for a suboptimal shortcut.

[arrowedumbrella]

A few weeks ago, hauptmoduln and I had dinner with a friend who works now as a journalist. This journalist friend is rather well-versed in math and science, and at some point wrote an article whose investigations into a major company required a sophisticated understanding of statistics

[cityofgates]

It's pretty easy to explain: Ask the kid if he felt like he was taking a clever shortcut by writing the story he did. Kids can usually tell when they're bending the rules. Then shoot the teacher for asking such a ridiculous question.

[arrowedumbrella]

Haha!

It's true, students can often tell. Although sometimes, kids bend the rules in an attempt to satisfy an assignment in letter because they don't understand the spirit.