Great contribution, Peter.
In this case the undergrad, who is not assigned to the child, but ends up
with child X owing to many factors including interpersonal affinity, has to
work
from the starting point defined by the school system. Interpersonally she
induces the child (successfully in the second case, perhaps owing to
accumulated trust from first one?) to work with harder problem. But this
in no way comes close to the great system you observed in Russia. I believe
that similar meta discussions occur in some Japanese schools.
mike
On 5/1/05, Peter Moxhay <moxhap@portlandschools.org> wrote:
>
> Maybe this is a small footnote to the discussion, but the thing I was
> struck by was the used of color-coded math sheets corresponding to
> different levels of difficulty:
>
> > I noticed T was sitting at the same desk as before so I walked up to
> > her to see if she was working on math again. Sure enough she had the
> > blue (medium difficulty) math sheet. I exclaimed, "Blue again, common,
> > where's the green!" T looked up and smiled and then pulled out the
> > green (most difficult) sheet as I pulled up a chair.
>
> The point, for me, is that the problems have been differentiated into
> levels of difficulty not by the student, but by the teacher. So such an
> approach is unlikely to develop the child's reflective understanding
> of the boundary of his/her knowledge.
>
> In case it's of interest: In our math classes we use a technique I
> observed in Russia, where several different problems are put up on the
> board and the children are asked to vote on: (1) which problem is the
> most difficult, (2) which problem is the most interesting, and (3)
> which problem do I want to work on today.
>
> It is often difficult for children to rank the problems in level of
> difficulty because they will focus on empirical details of the problems
> rather on the mathematical relations they contain.
>
> After solving the problem of their choice independently and checking
> with a partner, a child or a pair of children present their solutions
> at the board, and the process they use to solve the problem is assessed
> and evaluated by the class as a whole.
>
> The remarkable thing is that at the end of the class the children vote
> once again on (1), (2), and (3), and what the children believe to be
> "difficult," or "interesting," or "do-able" will have changed during
> the course of the class. That is, the kids will have refined their
> reflective understanding of the boundary between what they can do and
> what they cannot do. For example, by the end of the class many kids
> will have concluded that they can attack problems that use algebraic
> instead of concrete numbers. And others will have concludes that a
> superficially "difficult" problem is actually one that they can solve
> easily.
>
> But all of this derives specifically from the levels of difficulty of
> problems NOT having been defined beforehand by the teacher.
>
> But perhaps such a technique is easier to implement in the collective
> work of a class than in a child's interaction with a single adult.
>
> Peter
>
>
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