Autumn 1999
Math 130: Arithmetical Problem Solving
Tips for Write-ups

• Speak out during large group discussion to get other groups' ideas. Make them explain their ideas to you, so you can explain them clearly to me in your problem report.
• Address every question: even if you do not know the answer, at least acknowledge that and perhaps guess at it or suggest a strategy for finding it.
• Problem reports will ideally all have one or two key sentences which hit upon exactly why the answer you provide is true. For example, in a write-up analyzing the game Tic Tac Toe, a sentence or two which says something like, "Go first and choose the center. On your next two turns choose two adjacent squares (a corner and the center of a side), so that you have two ways to win --- diagonally and straight across or down --- and your opponent can do no better than a tie," hits the nail on the head.
• Sometimes you may not be able to explain the complete solution. In this case, try to pinpoint the difficulties you are having, and even try to solve a simpler version of the problem. You get partial credit for this, and it may even give you insight that helps you make the leap to solve the original problem. If there is a problem with your solution, point it out clearly, and, if possible, give special conditions under which your solution still works.
• It's better to take a stab at an answer (i.e., to guess intelligently) than to throw up your hands and say, ``I don't know.'' Try to eke out as much of an answer (again, maybe only a partial answer) as possible, and say why you believe it.
• If something relevant comes up in small or large group that is interesting, you might want to tell about it in your report, even if it is not necessary for the solution (however, it should at least be relevant). Report ideas that did not turn out to be correct as well as those which did, if they help you to understand the pitfalls in solving a tricky problem.
• Write a conclusion that actually draws a conclusion, rather than simply rewriting your introduction. The overall flow should be ``here's what I'm going to tell you about, here I'm telling you about it, and this is what we can come away with'', not ``here's what I'm going to tell you, here I'm telling you about it, and here's what I just told you''.
• Use paragraphs --- one for each idea. It's not a rule, but you usually should have more than one paragraph per side of a page.
• Is order important? There is no unique formula for writing a problem report. Use your judgement to decide the best order in which to present your report of what your group did and your argument for your solution. They may even be mixed together, if you find that useful.
• Have a friend read the report. Can s/he understand it with no help from you?
• A good problem report is exhaustive yet not verbose.
• Read your report out loud to hear how it sounds!