Problem of the Problem of the Week

In the past week, I have received two e-mails regarding best practices for using non-standard problems-of-the-week. Thus, it seemed only appropriate that I use these e-mails as a way to request input from others who have found successful ways to get students to explore these problems.

E-Mail #1 from S.W. (Lake Washington):
"Thanks for putting these problems up every week....doing one of these problems each week has helped me remember why I wanted to become a math teacher..... I also give these problems to my advanced algebra class for extra credit. I get a few responses back from inspired students, but no correct answers so far. Any tips on using these in high school classes? I’m cautious about doing a lot of scaffolding, both because of time and because I think it takes the fun out of it."

E-Mail #2 from D.K. (Seattle):
"...I have been giving my 8th graders POW's. I know it's the final weeks of school, but I liked the idea so much that I thought I would try it out. I have taken them from your MathNEXUS page and they have really stimulated some great conversations among my students. I'm wondering how you use them with your students and how you would suggest assessing them? Do you grade them based on attempting the problem? Do you give them the answers? So far, few students have been able to solve them on their own and I usually end up giving credit for various strategies attempted. The students talk about them in class but very rarely do they feel the satisfaction of solving them. If they get some parts of the problem, I sometimes give hints but I don't want to give them the answer. There seems to be a fine balance between giving them problems where they feel success in the completion and problems that leave them hanging, and then when they are left hanging, some of them end up thinking more on them and others seem to give up out of frustration. Suggestions?"

So, here is the problem for this week....how would would respond to these two mathematics teachers? Theye raise great concerns (e.g. credit, assessment; help)...and need your creative-yet-practical advice.

Please send me your responses, and I will post them on this web site. So far, no one has submitted a response or any ideas....Please think about it and help out. THANKS!