Common Core = Government Logic   --  Gene From: Hilarie Orman <ho@alum.mit.edu> To: math-fun@mailman.xmission.com Sent: Tuesday, April 26, 2016 12:07 PM Subject: Re: [math-fun] Distributive law without +? (6th Grade) 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

I'm a very good mathematics tutor. A classroom can be much trickier with students of varying a) abilities, b) background knowledge, and c) communications skills (reading, listening, articulateness both orally and in writing). But I love classroom teaching as well. But one on one, I think the key is to initially figure out where the student is coming from with respect to a), b), c). That's important to assess initially just by interacting with the student. Then just go on from there, expressing things in language the student will understand — at once in speech and writing — going only as fast as the student can follow, and getting copious feedback from them on their expressed comprehension, both oral and written as they tackle problems. Concrete examples are indispensable. I've always enjoyed teaching the smartest students at the highest levels, but found teaching motivated students at any level to also be amazingly gratifying. My favorite tutoring experience came recently with 3 siblings in grades 1, 3, and 6, each with their own shtick, but all eager to learn. As for the ones who have no interest in learning and cannot be wheedled, coaxed, cajoled, persuaded, or bribed to feel otherwise: meh. —Dan

On Apr 26, 2016, at 12:07 PM, Hilarie Orman <ho@alum.mit.edu> wrote:

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.