But the recent discussion is just so nicely coincident with the
dissertation I am just finishing, where there is one chapter about what
_children_ think is learning (and real learning). I'm basing it on
interviews with seven-year-olds with whom I talked about maths/ /counting/
/arithmetic and how kids learn that kind of stuff -- basically one
interview in the beginning of first grade and one in the end. And I'm not
assessing _how_ they learn, but trying to understand what they think maths
learning is. Although this can naturally also be used as a sort of
metacognitive assessment, as what they voice and act out in the interviews
varies so that I can say that some ways are more advanced than others. I
have (finally) six categories in this chapter.
The simplest accounts are those where learning coincides entirely with
being taught: someone says something and someone else repeats it, and this
is learning. The Swedish language affords this way of thinking, as the same
word (l=94ra) can be used for learning (grammatically reflexive) as well as
for teaching. I have nicknamed this category "being taught" (yes,
=46rancoise, that's new).
In the next type of account learning means just that you _begin_ to be able
to do something or you _begin_ to know something: you try and it just
works. And this you can recognize in retrospect as learning. What you
(possibly) do in the domain _before_ the first time it works doesn't seem
to count as (real) learning. I have nicknamed this "beginning to know".
These two categories are common in the school start interviews, and the
first one almost disappears in the end-of-year interview.
Then there are the accounts where you learn (to count or to do sums...) by
working on it. By practicing many times. By working in your books and
finishing one book after the other. I have nicknamed it "learning through
working" -- what you work with is _fixed_ number facts that you certainly
should not tamper with by "transforming" them -- although you can very well
re-cycle them: use them on the next page.
And next there are the accounts where just filling the books (with
handed-down solutions) isn't enough. You don't _really_ learn unless you
think-for-yourself without being told everything. I have nicknamed it
"working mindfully". (There's a very nice example from a girl who acts as
teacher's-little-helper (sigh...) and who tells me how she tries to get her
peers to solve minus problems by suggesting that they think of "the plus
that would make this").
Both these categories are present at school start, but as you can imagine
there are more kids in them at the end of the year...
Then there's a problematic one, which I finally placed lowest in my system:
the accounts where "learning" seems to be the name of some school activity.
The process of studying, one might say -- the problem being that the kid's
don't see any connection with an outcome (of becoming more able, or knowing
more). I have nicknamed it "doing work". The product of the process rather
seems to be those filled books, and other neat things made in the maths
lessons. Again this is, I think, afforded by how we use discourse on
learning with kids. And I'm told that in Chinese it is a perfectly
legitimate meaning of the most common word for learning. Indeed, there are
many kids talking in this vein, but then also giving some more advanced
account. But there are also a few (more in the end than in the beginning)
whom I cannot coax into any other corner in the interview.
And last there is a category of accounts where learning again (as in the
first two categories) takes place in an instant. The difference is that
here this "instant of learning" is what is seen as _real_ learning. The
drudgery of practice is _not_ learning. I have nicknamed it "grasping
instantly" and I can sense in it both an affinity with the "aha"-erlebnis
and with the romanticism of brilliance.
So. What I get back from these kids is that they are, already, living in
the available value patterns of tension between transmissive learning and
transformative learning (and between apparent learning and real learning)
although the transformation of basic number facts seems very heavily to
have to be a re-constitution of the same age-old patterns...
Eva