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."