At the Wisconsin Math Council conference I heard a great problem from Dave Ebert's presentation that sets the tone for all my problems; it was simply a video of a cheetah running down an antelope and the following question:
A cheetah and a gazelle are on the African plain, does the cheetah catch the gazelle?
This question requires the student to do all the things we want from them. We all realize a cheetah runs faster than antelope during a burst but for a short duration, it requires a piece-wise function in my opinion. Otherwise all gazelle would be caught!
But students are going need to be taught that the above problem is math versus doing 1-25 odds on page 666 (and parents too). And that will be the really hard part.
So I am working on a list of milestones with deliverables for when I first assign problems like the cheetah problem this coming year. Otherwise someone, a mini-Scott, will simply answer "sometimes" to the whether the cheetah catches the gazelle. (My penetence for being a smart-a** in HS is teaching them all now.) What we want is just too different not to guide the students at first. I am initially thinking it is a 4 week assignment, where I will guide students through stages of the projects.
This is not set in stone and will be evolving on a Google doc, but right now I have the following milestones:
1) In a reflection explain what the answer to the problem will look like.
2) Define an “entry point” on the problem (by e-mail?, combine with #1?)
3) Define unknowns and things to research
4) Gather knowns from research (be sure to cite and check)
5) Create solution
6) Test solution
8) Prepare final document
Also a sampling of problems:
A bridge is being built across the Wisconsin River, what gap should be left between sections.
You are following a car on the interstate, you pull off to use the restroom at a wayside. How long will it take you to catch up again?
Determine whether global warming is occurring in Juda?
Determine the amount of money saved by the solar array at the school for July 2013.
Again I see these problems working in tandem with on-line practice, using every minute of every period for concepts/practice versus students "starting homework" and as integral part of a class that uses PBL to deliver the required curriculum.
I know this is not easy, I know students will "fight change," people always do. But I also know that solving problems is the skill the separates people in the world - and at the least my students will have practiced that skill.