On Oct 27, 2012, at 10:31 AM, kirby urner <email@example.com> wrote:
> You may not be aware of Caleb Gattegno's way of teach "algebra first" > using colored rods (Cuisenaire) and color-coded letter expressions.
> He had empirical / measurable success with his system, published a > series of books, did studies and was influential.
I cannot reply to this statement better than you did with the statement above this statement.
Newton was influential, and we all know of Newton.
> I think if you're looking at 4th grade materials and seeing lots of > algebra, you are maybe seeing some of Gattegno's influence, even if > the approach is different.
It is the same fallacy. Gattegno saw the mathematics in colored rods, he had a PhD in mathematics. His students saw a game. And note, I have given Cuisenaire rods a whirl. They were influential in helping me see this fallacy. During the "activity" I recognized that a key element was missing. Mathematics. Hasta la vista colored rods.
> > You may scoff at the idea, but remember the human brain is capable of > mastering complete human languages at that age.
And the obvious conclusion is that mathematics and language are very different beasts.
> > I don't think we really know what humans are capable of, given > intelligently designed learning materials.
We know what they are capable of. I don't know of any subject that has been more thoroughly tested than math. I think what you mean is that we don't know if a curriculum can be improved. At this point, the biggest improvement (overwhelmingly) appears to be to drop the pretense that it can be improved. That is my conclusion after studying dozens of curriculums and classes and noting which students make it into the "club" and which do not.