I agree, Hilarie. In either case they skip a few steps, so there really is no right answer. 6(9) = 6(9+0) = 6*9 + 6*0 = 6*9 + 0 = 6*9 or 6(9) = 6(9*1) = 6*(9*1) = (6*9)*1 = 6*9. I don't think Common Core is typically idiotic, but this may be an example.* I think the exaggerated opposition to it is an example of mob hysteria. For example, using different kinds of bracket for nested parentheses is a visual aid to avoid pairing the wrong parentheses. Insisting on proper fractions for final answers actually makes sense for getting an idea of a fraction's approximate value. —Dan ——————————————————— * This is a pervasive problem in math testing: not considering other equally valid interpretations of the same question.
On Apr 26, 2016, at 12:07 PM, Hilarie Orman <ho@alum.mit.edu> wrote:
You can pick a or c: 6*(9*1) or 6*(9+0)
I mean, what do you tell a 6th grader who is struggling with order of operations and by carefully following the rules, comes down to 6(9) ? Did you previously prove "parens around singletons can be thrown away"? How?
Common Core the standard says that students should understand and be able to use the distributive law. The textbook implementing Common Core may be idiotic, but the same idiocy existed before Common Core.
I don't think anyone knows very much about the psychology of math. There's no easy pathway to the circuits and programming of it. This makes it difficult to teach, in general. So much can go wrong if the student gets off track. Maybe square brackets are a useful crutch for most people, I don't know. Auto close of parens wouldn't have been invented if nesting wasn't so confusing.
Hilarie
From: Bill Gosper <billgosper@gmail.com>
The simplification 6(9) = 6*9 is an example of (choose one) a) associativity b) commutativity c) distributivity.
"Answer": c. Has anybody ever seen this usage of "the distributive law"? This is from the same Common Core idiots who outlaw "improper" fractions. They also insist that parens enclosing parens be changed to square brackets. --rwg
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