These standards don't actually say to teach that repeated addition is what multiplication *is*. If you can show where Devlin actually said that they should not notice or learn the repeated addition property of multiplication, then show it. Otherwise, quit making things up about what he or anyone else is saying on this issue who thinks it would be a good idea to have another model in play.
The burden of proof is now on you to prove that it would be a bad idea to show them the differences in the nature of the motion on the number line when comparing multiplication with addition, where one type of motion is proportional and scaling and the other type is not.
Perhaps you think that the kids at that age are too stupid to see something that is proportional and scaling, that, for instance, 15 is to 5 as 3 is to 1 - that is, that point 15 is three times further out from 0 than is point 5, just as point 3 is three times further out from 0 as is 1?
On Mon, Sep 10, 2012 at 12:52 AM, Wayne Bishop <firstname.lastname@example.org> wrote: > Also of interest is that he has almost nothing to do with the Stanford > mathematics faculty much less those whose children were in the Palo Alto > school district being exposed to New New Math watching the district's > enviable computational mathematics scores plunge from the low 90th > percentile to the high 60th percentile is a very few short years. That was > their motivation for writing the California Mathematics Content Standards, > still among the best in the nation. One of the Key Standards for 2nd grade: > 3.0 Students model and solve simple problems involving multiplication and > division: > > 3.1 Use repeated addition, arrays, and counting by multiples to do > multiplication. > > 3.2 Use repeated subtraction, equal sharing, and forming equal groups with > remainders to do division. Wayne > > > At 05:53 PM 9/9/2012, Paul Tanner wrote: > > On Sun, Sep 9, 2012 at 7:51 PM, Robert Hansen <email@example.com> wrote: >> >> On Sep 9, 2012, at 3:13 PM, Paul Tanner <firstname.lastname@example.org> wrote: >> >> Or are you now of the position that all those mathematicians who don't >> know how to each kids but who like you have had a problem with reform >> mathematics education at that level of teaching kids and therefore >> spoke up about it - and not only have you have agreed with them you >> are glad they spoke up - should have shut up and should forever stay >> shut up on this issue and other such issues? >>> >> I am of the position that Devlin knows neither mathematics nor the >> teaching >> thereof. Devlin is a populist writer. >> >> Bob Hansen > > And you, with your mere undergraduate physics degree, having taking > much, much less math than even one with a mere undergraduate math > degree like myself, know more mathematics than Devlin, a PhD in > mathematics, with all these accomplishments? > > http://www.stanford.edu/~kdevlin/ > > Quote: > > "Dr. Keith Devlin is a co-founder and Executive Director of the > university's H-STAR institute, a co-founder of the Stanford Media X > research network, and a Senior Researcher at CSLI. He is a World > Economic Forum Fellow and a Fellow of the American Association for the > Advancement of Science. His current research is focused on the use of > different media to teach and communicate mathematics to diverse > audiences. He also works on the design of information/reasoning > systems for intelligence analysis. Other research interests include: > theory of information, models of reasoning, applications of > mathematical techniques in the study of communication, and > mathematical cognition. He has written 32 books and over 80 published > research articles. Recipient of the Pythagoras Prize, the Peano Prize, > the Carl Sagan Award, and the Joint Policy Board for Mathematics > Communications Award." > > Consider: > > http://en.wikipedia.org/wiki/Crank_(person)