Mike,
Thanks for forwarding the math learning/teaching fragment as an instance of
creating a zoped. What's interesting for me is that the same interaction
could be analyzed as an instance of constructivist pedagogy. (I'm referring
here to strict psychological constructivism in the sense of Piaget, rather
than the newer social constructivisms that often rely on Vygotsky as well
as Piaget.) From a psychological constructivist perspective, the engine for
conceptual development is the cognitive conflicts one encounters every day
in the world when one's expectations for what should transpire in the world
(stemming form one's current, immature, conceptions) don't mesh with one's
experiences in the world. Thus, the constructivist teacher's role centers
on orchestrating a task environment to provoke transformative experiences
for the student. For constructivists, the student learns ONLY from their
engagement in the world. They do not learn from their engagement with
OTHER's ideas, as in a ZPD, except insofar as those ideas are translated
into world experiences.
In the fragment you forwarded (below), the teacher's interactions with the
student could be interpreted along the lines of the following
constructivist teaching method:
1. Observe the student's difficulties and develop a hypothesis about the
limitations of the student's current conceptions.
In this case, the teacher suspects that the student has conceptual
understandings about the relationship between subtraction and addition that
he is not bringing to bear on the current problem.
2. Develop a task environment for the student designed to produce
experiences that will challenge the limitations of the student's current
conceptions.
In this case, the teacher's strategy is to simply remind the student to
think about the meaning of subtraction by presenting a take-away situation
using magic markers that is juxtaposed temporally with the missing addend
situation the student is facing in his homework.
3. Observe the student's response to the task environment and assess the
success of the intervention. If it seems unsuccessful, go back and rethink
the original hypothesis and/or the task environment you've created.
In this case, the student's blank look convinces the teacher that the
intervention has not been successful. The student's blank stare is analyzed
as a problem with the task rather than the initial hypothesis. In
particular, the take-away situation is seen as too remote from the missing
addend problems the student is facing in his homework. The magic marker
task is reformulated as a missing addend problem for which the student
already possess a subtraction strategy. The teacher then successfully
supported the student's making an analogy back to the homework difficulty.
Any thoughts on why a sociocultural analysis might preferred to a
constructivist analysis for this teaching/learning fragment?
David
_____________________
David Kirshner
Department of Curriculum & Instruction
Louisiana State University
Baton Rouge LA 70803-4728
(225) 578-2332 (225) 578-9135 (fax)
dkirsh@lsu.edu
http://www.ednet.lsu.edu/tango3/coedirectory.taf?
_function=detail&Faculty_uid1=135&Users_uid2=135&_UserReference=59F4B47FBE3415E138CD68B2
Mike Cole
<mcole who-is-at weber. To: xmca@weber.ucsd.edu
ucsd.edu> cc: (bcc: David H Kirshner/dkirsh/LSU)
Subject: spontaneously creating a zoped
02/09/2002
10:35 AM
Please
respond to
xmca
Dear Colleagues,
Spontaneous zoped creation.
This fragment from a student tutor strikes me as a clear embodiment of a
clever way of creating a zoped for a student. This student first finished
all his homework with double digit addition, but had difficulty when given
a sum and one of its two components. This student then reports the
following:
delete now if uninterested)
mike
---------
As we sat down Ramiro took out a math worksheet that he had to finish for
homework. It was basic addition with double digits. For the first section
he seemed to have the hang of it for he didn't ask me for help and seemed
to be solving them quite easily. I did notice that he was thinking out
loud while solving the problem. For example, he would say the operations
of the problem, of how a number plus another added up to a sum and how you
had to carry over the one and so on. However, when he finished the first
section, he stopped and said, "Now, I need help on this section," referring
to the last section of his homework assignment. This part gave a number
and the sum and the object was to find the second number which would make
the given sum. I asked Ramiro if he had any ideas on how to solve this and
he gave me a blank look and said that he didn't. I thought for a bit on
what the best way might be to explain this to him. To my luck, there was a
box of markers next to me so I took out five markers and set them on the
table in front of him. I separated them into two and three markers. I
asked Ramiro, if I had 5 markers, and took out two, how many would I have
left? He answered with three. But he didn't have a look of revelation on
his face or anything so I could tell that he didn't see the connection
between that example and the math problem on the worksheet. So then I
tried to word it better and then asked, him if I had two markers and needed
to get five, how many would I need to get? He answered with three. I
asked him what he did and he answered that he just took two away from five.
I pointed to the math problem on the paper and showed him how it was just
like that problem. I think he got it because he then began to try the
problem on the worksheet with the method we tried with the simpler problem.
Every time he solved a problem, he would look at me for approval to see if
he did it right. Soon enough, Ramiro had finished the entire set. He then
packed his things and left.
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