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Assessment
Posted:
Mar 15, 1995 3:17 PM
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My experience this morning relates, I believe, directly to what some people
are interpreting as "mathematical power." I would appreciate your
comments. If the list moderators fell this is out of line for the list,
please direct your messages directly to me.
I was an invited participant at a two high school joint scoring of this
"open-ended problem" done by all students, grade 9-12, in the two large
high schools. I invite your comments on this item and its potential
scoring. I have the "essence statement" and rubric which were
predetermined for the item. I also participated in the "calibration"
process in which actual student exemplars were used to get all equivalent
scoring by all participants. The teachers were inclusive off all faculty,
not just math, in the high schools and middle schools in the district. At
some point I will bring those out in a message.
It is important that you first "work" the problem in whatever way you deem
best before you comment. A cursory reading will not bring out the
important details.
The problem is to be scored on a 1-4 point rubric. (1 - Student usually
can fog up a mirror. to 4 - Wow, this is good stuff.)
First the directions (No clarification of the problem statement was allowed.)
"Use a #2 pencil.... Your score on this question will depend on how
well you communicate your understanding of mathematics.
1. Communicate your thinking by a "*combination*" (the quotes and
*bolding* are in the instruction) of written, symbolic (computation)
or visual means (graphs, diagrams or charts).
2...
3. In your response, demonstrate how you can arrive at the solution in
various ways."
Next page:
"To fully accomplish the purpose of this task, make sure your work
communicates your thinking process clearly.
THE STRING OF PEARLS"
[A picture of a string of pearls is shown.] "Mr. Smith is buying Mrs.
Smith a gift for their 33rd anniversary. He has found a necklace with 33
pearls for her.
On this string of 33 pearls, the middle pearl is the largest and most
expensive of all. The first pearl on the right end is worth $80 more
than the first pearl on the left end. Starting from the right end and
working toward the middle, each pearl is worth $10 more than the one
before. From the left end and working toward the middle, each pearl
is worth $15 more than the one before. The string of pearls is worth
$6,075. What is the value of the middle pearl?
Showing all calculations, demonstrate how you arrived at the price of
the middle pearl. In addition, explain in writing how you proceeded
in solving this problem."
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Richard Pilgrim Director of Mathematics Testing and Placement
University of California, San Diego
Internet: rpilgrim@ucsd.edu Voice: (619) 534-3298 Fax: (619) 534-1011
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