## Thursday, September 5, 2013

### Open-Ended Problems Resources

We have a team challenge, involving the development of an environmentally friendly bus fleet for a school district. This is a real-world, open-ended problem with different approaches that can be taken, and no single 'right' answer!  Complex problems hound us in all fields in real life, so being able to attack such problems and develop reasonable solutions is a skill set that is necessary in the 21st century. You are going to have to collaborate, do research to find reliable resources of large data sets, use technology to assist the process, communicate your work, use more advanced thinking and problem solving skills (such as developing a mathematical model), make predictions that can be tested against a real world sample, develop creative solutions, and so on!

To assist you, here are various resources that will hopefully be helpful for you and your team:

Check out other open-ended, complex problems from the COMAP High School Mathematical Modeling Contest (HiMCM) and the Moody's Mega Math Challenge. The home pages are: HiMCM and Moody's.

Problems from past contests are: HiMCM and Moody's.

Exemplar papers from Moody's.  This includes an ETHS team paper that took 5th place nationally!!!  See what a good paper looks like.  See how teams took a problem and broke it down into simpler pieces, and what assumptions they made.  See how a mathematical model was developed, and what math techniques went into the model's development.  See how they explained their work.  See how they used the model to make predictions that could be tested against real data and other information. See how they determined and explained the weaknesses of the model.  Might as well learn from some others who did a good job with this process!

Judge's perspectives from Moody's can be found on this page, and for COMAP on this page (pages 17-35).  These are especially useful because they point out what makes for an average solution paper compared to an outstanding solution paper!  Are you doing these things for your solution paper?  If not, why not?  How can you re-adjust and make the solution better?  If you had more time, what would you focus on to try and improve your solution proposal?

Teams might consider drawing out a flow chart early on in the process that outlines key components and assumptions you want to make.  Get a visual picture of what this all looks like, and think about what is connected to what.  Do you expect direct or inverse relationships?  Linear or non-linear?  What factor or parameter, when changed, will have an effect on other parts of the model/solution?

We hope these all help you in this process.  Good luck, and have fun with it!