On Dec 23, 2013, at 4:02 PM, Clyde Greeno @ MALEI <email@example.com> wrote:
> If their research says anything at all, it is that educators had far better be looking at the alphabetics of the numerals, than supposing children to know something that they cannot.
The real question Clyde is how did these ?researchers" miss such a simple observation that even a mom who has been home schooling for a few years knows?
It?s always a combination of the following...
They're not very smart. They?re not very scientific. They've not studied the process.
And in this case, it appears to be all three.
But it is especially troubling that they haven?t studied the process. At the very least, even if these researchers aren?t very bright, that is where they should have started. By teaching children and taking them on the actual journey through mathematics.
Place value is like any other mathematical (and non mathematical) notion. It grows on you over years of example, exercise, discussion and contemplation. It?s that last element we have so little control over. What is the student thinking? A good teacher has a sixth sense in their ability to know what the student is thinking, unless the student isn?t thinking at all, and a good teacher will know that too.
As far as testing whether the young pre-formal student is getting the math of place value rather than just its syntax, the best way I know of is mental arithmetic. But don?t expect miracles. Without formal thinking skills, an actual theory of place value (as you suggest) is a ways off. But an informal and intuitive feeling for it is quite at hand.
So why are education researchers almost always wrong, beyond the causes I listed above? Because teaching is an art, not a science. Art is something you know when you see it but cannot fully explain. You can talk to it, you can talk of it, and you can even share it, with fellow artists, but you cannot fully explain it. It is served by the sharing of experiences and conventional wisdoms, with fellow artists, not the scientific method. And unfortunately, these experiences and conventional wisdoms can only be shared with fellow artists.
Having a discussion with a non-teacher about teaching is like a musician having a discussion with a non-muscian about music. Challenging. But education research is like two non-muscians having a discussion about music. Absurd.