||Description of the CMS-POW|
Cleveland Middle School Problem of the Week
Grover Cleveland Middle School, Elizabeth, NJ
The Math Forum is generally recognized as the exemplary web site for the support of K-16 mathematics education. Their Problems of the Week, known affectionately as "PoWs", are designed to provide an environment for students to engage in mathematical thinking and communication. Problems are posted on the Math Forum web site, and students submit solutions to the problems electronically.
The Cleveland Middle School Problem of the Week (CMS-PoW) is available at http://mathforum.org/cmspow, and is a customized PoW environment designed specifically for the students at Grover Cleveland Middle School in Elizabeth, NJ. A new problem will be posted each Monday at 12:01 AM and will remain 'open' for submissions through 11:59 PM of the following Monday, when it 'closes'.
There are two problem formats that will appear in alternate weeks.
MENTORED PROBLEMSMentored problems feature interaction with a professional mentor. After students submit their solutions, they will receive the mentor's comments and feedback via e-mail.SCAFFOLDED PROBLEMS
A problem is open for initial submissions for a week, but revisions will be accepted at any time until the revision period ends at 11:59 PM on the Thursday after the problem closes. Students are encouraged to engage the mentor in dialogue that results in their repeatedly revising their solutions until they are correct and complete. The goal is to get every student to successfully understand the mathematics imbedded in each problem, and communicate that understanding in a correct solution to the problem.
Highlighted student solutions and the mentor's comments about the problem and approaches to its solution will be available on the website on the Friday after the revision period ends.
Mentored Problem Schedule Summary:
- Problem Opens .......................... 12:01 AM on Monday of week 1
- Problem Closes .......................... 11:59 PM on Monday of week 2
- Revisions Accepted ........... until 11:59 PM on Thursday of week 2
- Highlighted Solutions & Mentor's Comments ... on Friday of week 2Scaffolded problems feature an interactive electronic environment that allows students to choose from three types of feedback after they have submitted some initial problem solving effort, even if it is not a full solution. We want to encourage them to practice beginning problem-solving even when they don't know how to get all of the way to an answer.
A sequence of Hints provides tips and key ideas related to the problem, and may include links to web pages of relevant mathematical content.
Check Answers enables the students to see if they are on the right track and to check their work against some key results.
Complete Solutions to the problem are also available for viewing. The idea is that students who believe they have complete solutions can immediately compare their work with other approaches, and reflect on their own work in a safe and private setting.
If students are confident of their approach and work without hints, that's great. However, if they need or want help, it's there. Of course, students must use the feedback prudently in order to get the full educational benefit of the scaffolded problems. Simply viewing a correct solution and then revising their own solution to mimic it or 'fake it' misses the point completely. (We actually do track the pages that students have viewed.) Students must engage the problem solving process for this to be meaningful. This includes their viewing the feedback and thinking about how it relates to the problem and their work on it. The format is truly an opportunity for students to practice being responsible for their own learning.
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