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Assessment (Dick Lesh's talk)
Posted:
Jun 29, 1993 7:25 PM
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Dick Lesh, one of 150 PhD's currently doing research for ETS, has come to
the Geometry Institute at Swarthmore (see geometry.institutes for more
information). He is knowledgeable about instruction, psychology, higher
level mathematics and the world of technology, making him an ideal
candidate to be reassessing assessment as it is currently visualized
within the sphere of mathematics both by ETS and by many teachers,
students, and parents. An outline of the talk he gave us this afternoon
follows.
Some themes:
--A single number cannot accurately characterize a student.
--Mathematics is a growing field in a changing world; teaching strategies
tend to view both as excrutiatingly fixed. Questions involving systems
(telecommunications, marketing, etc) have become more relevant then
questions involving addition of oranges.
--(a related thing item) We need to pay attention to a broader range of
abilities than we currently tend to do. Searching for more abilities
results in finding more people with more abilities. Dick talks of how
time and time again he has heard very sophisticated problem solving
techniques from students who had just about been given up on. This
broader range need not leave mathematics, but ought to focus on more
aspects of the huge mathematical discipline that aren't ordinarily
touched upon at the precollege level.
--Students need to know who is asking a question and why: context is
key. (Example given: "How do I get from Swarthmore to New York?" is not
a straightforward question. It provokes more questions or several
answers: "Is time important to you?" "Is scenery important to you?"
"Is money important to you?" / to what degree?, etc. ) A suggestion for
finding such questions is to have students look for newspaper articles
which involve math and to have them construct questions based within the
context of a given article.
Now for some more information more directly related to Assessment
--activities in assessment should also be learning experiences. One can
simultaneously learn and document learning.
--assessment as a giving of information to decision makers:
1) who are they?
2) what decision?
3) policy makers?
--assessment should not occur entirely at the end of a course: it should
be going on continuously from the beginning through the middle and end of
the course.
--we need to get kids talking about what they are learning and then use
what they say to judge where they are.
--What exists and how this may change:
__Traditional testing__ __Instructional assessments__
Testing = ordeal Examining = studying closely
Measuring = partitioning into equal Describing = generating a
multi-dimensional
fragments (units), measuring verbal portrait
general intelligence
Evaluating = assigning a value Assessing: taking stock, getting
oriented
(one dimensional and uncon- (give profiles of the sort used
by
ditional) businesses instead of a single
number)
Goals:
Make tests more credible Make assessment more authentic
(It should be noted that Dick Lesh came out strongly in favor of the
methods described in the second column.)
In many situations, tests are not the best means available of assessment.
Reports and group projects should be described in a portfolio set up by
the students, and noted on a resume. The projects should undergo some
sort of official process that will document their existance similar to
that undergone by the reports and projects of professionals.
Lesh especially stressed the importance of current trends in psychology,
most specifically how cognitive psychology lends itself to math
education. People map information onto images. Often problems arise
when children (and I would extend this to anyone learning new things)
have heard presented information, but don't know what to do with it, as
they are unfamiliar with the framework of the ideas and models. Many
young children, when asked to construct a cube, make something that looks
like:
.__.
.__|__|__.
|__|__|__| (hope this came out okay. to me it looks like a box with
|__| unfolded edges. rather cubist, really)
And he showed us the following
.
. .
. and asked us what we saw. Then he connected some dots.
. .
.
He showed several different patterns, among them, the following:
.
./ | \.
| \ | / | The first time we saw this I think most of us saw it as
an asterix
| / | \ | within a hexagon. After seeing a few more images, we
were amazed
\ | / to see a cube.
'
People often need to be trained to see things in different ways. (Just
as I would imagine, assuming this posts nicely, that those of you more
accustomed to character graphics will have an easier time understanding
the above image than those of you to whom this may be a rather new way of
seeing.) Lesh feels that for learning to occur the most important and
relevant models must be stressed.
We did an activity in which given a quadrilateral and a point light
source (such as a candle), we had to deduce whether a square shadow could
be produced. (The given shapes were: a square, an isoceles trapezoid, a
kite, a rectangle, a rhombus, an irregular quadrilateral, a concave
quadrilateral, and a parallelogram.) This is one of the activities which
has elicited very impressive solutions from D students in math.
Lesh finished by proposing a teaching unit beginning with "model
construct". This would occur during an activity like the above. (For
students unused to this sort of activity, the activities don't really
tend to work effectively until the third try at them. Lesh has found
that it takes this long for them to stop looking to the teacher for the
"right answer" or for more specific instructions as to how to proceed. )
The second part of the unit would be "model explore." This is more pure
math and deals with situations to which the model can be applied. The
unit finishes with "model apply" in which real world applications come
up.
ETS is working on 10 such units, which teachers can adapt to fit their
own time constraints. The units need not be used as a block.
Look for participants in our geometry software institute to be airing
their reflections.
Bye
-Beth
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