[math-fun] Distributive law without +? (6th Grade)
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
Come to that, in what sense is that equation a "simplification"? Schoolteachers of mathematics who are themselves weak at the subject (in my experience, most of them) almost inevitably approach it as formalists: the manipulation of symbols, according to apparently arbitrary and externally meaningless linguistic rules, becomes their only consideration. As a schoolboy I took no interest in school mathematics, discovering an aptitude for the subject instead through fascination with Archimedean polyhedra leading to compulsion to calculate and build models of them; and I gather a number of other contributors to this list arrived here in a similarly accidental fashion. As a parent, I watched my own children's pre-school interest in the subject swiftly extinguished by mediocre teaching. As a universtity teacher, I time and again encountered students lacking any capacity to relate formal manipulation to what I understand as an underlying conceptual reality. As a grumpy old man, I realise that despite regular attempts by able mathematicians and educators to remedy the situation, nothing has changed. It occurs to me that Archimedes was doubtless to be heard muttering much the same sentiments a couple of millenia ago (in ancient Greek, presumably). Fred Lunnon On 4/26/16, Bill Gosper <billgosper@gmail.com> wrote:
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Can you provide more info about the source of this idiocy? I believe that most of the idiocies found in implementations of Common Core come from implementers of the standards, not the standards themselves. Jim Propp On Tuesday, April 26, 2016, Bill Gosper <billgosper@gmail.com> wrote:
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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com <javascript:;> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Oops, I see they want you to change the 9 into 10 - 1 and then use the distributive law. gosper.org/Holt McDougal Mathematics Grade 7, Common Core Edition.pdf --rwg My flame prompted Zack Chroman to exhume the classic: this textbook in texas <http://i.imgur.com/tDSX24E.jpg> . The typography matches an earlier series of texts given my young friend, which I thought were widely standardized. Has anyone seen this howler outside of Texas? Another foul emanation from the Texas School Book Depository? --rwg On Tue, Apr 26, 2016 at 12:09 AM, Bill Gosper <billgosper@gmail.com> wrote:
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
Now I'm even queasy about this Texas textbook howler. I can't source it beyond the imgur jpg mentioned in reddit. Someone suggested Algebra 2 by Glencoe, but I can't find it there. Is this just manufactured Texas ridicule? --rwg On Tue, Apr 26, 2016 at 4:45 PM, Bill Gosper <billgosper@gmail.com> wrote:
Oops, I see they want you to change the 9 into 10 - 1 and then use the distributive law. gosper.org/Holt McDougal Mathematics Grade 7, Common Core Edition.pdf <http://gosper.org/Holt%20McDougal%20Mathematics%20Grade%207,%20Common%20Core%20Edition.pdf> --rwg My flame prompted Zack Chroman to exhume the classic: this textbook in texas <http://i.imgur.com/tDSX24E.jpg> . The typography matches an earlier series of texts given my young friend, which I thought were widely standardized. Has anyone seen this howler outside of Texas? Another foul emanation from the Texas School Book Depository? --rwg
On Tue, Apr 26, 2016 at 12:09 AM, Bill Gosper <billgosper@gmail.com> wrote:
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
On 27/04/2016 18:44, Bill Gosper wrote:
Now I'm even queasy about this Texas textbook howler. I can't source it beyond the imgur jpg mentioned in reddit. Someone suggested Algebra 2 by Glencoe, but I can't find it there. Is this just manufactured Texas ridicule?
http://nseuntj.weebly.com/uploads/1/8/2/0/18201983/2.1relations_and_function... contains the offending thing, though I have no particular evidence that it isn't fabricated. It does indeed say "Glencoe Algebra 2" on its pages. -- g
This may have been discussed here before, but: Google the words in Images: division chart , and click on the first thing on the upper left. Then look at the yellow box. —Dan
On Apr 27, 2016, at 11:17 AM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 27/04/2016 18:44, Bill Gosper wrote:
Now I'm even queasy about this Texas textbook howler. I can't source it beyond the imgur jpg mentioned in reddit. Someone suggested Algebra 2 by Glencoe, but I can't find it there. Is this just manufactured Texas ridicule?
http://nseuntj.weebly.com/uploads/1/8/2/0/18201983/2.1relations_and_function...
contains the offending thing, though I have no particular evidence that it isn't fabricated. It does indeed say "Glencoe Algebra 2" on its pages.
This is what I get when I click on that chart (from Cornell): WARNING! The page you were trying to reach has been identified as unsafe; its content may put your computer and Cornell University operations at risk. ... -Veit
On Apr 27, 2016, at 2:51 PM, Dan Asimov <asimov@msri.org> wrote:
This may have been discussed here before, but:
Google the words in Images:
division chart
, and click on the first thing on the upper left.
Then look at the yellow box.
—Dan
http://www.rainbowresource.com/products/026355.jpg On Wed, Apr 27, 2016 at 1:52 PM, Veit Elser <ve10@cornell.edu> wrote:
This is what I get when I click on that chart (from Cornell):
WARNING!
The page you were trying to reach has been identified as unsafe; its content may put your computer and Cornell University operations at risk. ...
-Veit
On Apr 27, 2016, at 2:51 PM, Dan Asimov <asimov@msri.org> wrote:
This may have been discussed here before, but:
Google the words in Images:
division chart
, and click on the first thing on the upper left.
Then look at the yellow box.
—Dan
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Yikes! I hope it's safe. In any case I found the same chart in full here: http://www.rainbowresource.com/products/026355.jpg I hope that one is safe! Didn't cause me any trouble. (Yet.) —Dan
On Apr 27, 2016, at 1:52 PM, Veit Elser <ve10@cornell.edu> wrote:
This is what I get when I click on that chart (from Cornell):
WARNING!
The page you were trying to reach has been identified as unsafe; its content may put your computer and Cornell University operations at risk. ...
On Apr 27, 2016, at 2:51 PM, Dan Asimov <asimov@msri.org> wrote:
This may have been discussed here before, but:
Google the words in Images:
division chart
, and click on the first thing on the upper left.
Then look at the yellow box.
I tracked this down, and it looks like they fixed it. http://edupress.com/edupress/Math-in-a-Flashtrade-Wall-Chart-Division-EP2437... (vs http://www.rainbowresource.com/products/026355.jpg ) On Wed, 27 Apr 2016, Dan Asimov wrote:
This may have been discussed here before, but:
Google the words in Images:
division chart
, and click on the first thing on the upper left.
Then look at the yellow box.
-- Tom Duff. A safe, natural solution to your snoring problem.
The first thing that should be mentioned is that the one-to-one correspondence howler is not in the textbook per se, but in some accompanying guide. Gareth's link shows pages 5 to 10 of such a guide for section 2-1 of the book. I found an "answers" link for this particular guide which reproduces pages 5 to 9 as pages 6 to 10 (with answers) but replaces the offending page 10 with a page 11 that is different (subheading "Mappings" instead of "Real Number Relations and Functions") and makes no mention of the "correspondence". My guess is that the howler was in an early version of the guide that was subsequently replaced.
On Apr 27, 2016, at 2:17 PM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
http://nseuntj.weebly.com/uploads/1/8/2/0/18201983/2.1relations_and_function...
contains the offending thing, though I have no particular evidence that it isn't fabricated. It does indeed say "Glencoe Algebra 2" on its pages.
On Tue, Apr 26, 2016 at 3:09 AM, Bill Gosper <billgosper@gmail.com> wrote:
The simplification 6(9) = 6×9 is an example of (choose one) a) associativity b) commutativity c) distributivity.
Now that you've posted the source, we see that the source does not give this as a multiple choice exercise. What the exercise actually says is "use the distributive property to find the produce 5(31)". with the intended solution of something like 5(31) = 5(30 + 1) = 5(30) + 5(1) = 150 + 5 = 155. I don't see anything wrong with this.If asked to find, say 14 * 99, I would certainly do it by calculating 14(100-1) using the distributive law, rather than using the standard multiplication algorithm. The common core certainly has flaws. But it seems to be widely and unjustly criticized for its attitude that there are a multitude of ways to solve any given problem, and an understanding of what's going on can help you find an easy one, rather than simply mindlessly following an algorithm. Much of this criticism comes from people who were themselves taught to mindlessly follow an algorithm, and view any curriculum that teaches anything they did not themselves learn as a waste of time. Andy
participants (11)
-
Andy Latto -
Bill Gosper -
Dan Asimov -
Dan Asimov -
Fred Lunnon -
Gareth McCaughan -
Hans Havermann -
James Propp -
Mike Stay -
Tom Duff -
Veit Elser