M360M/396C, Fall 2004

# GUIDELINES FOR PRESENTING SOLUTIONS IN CLASS

One of many important skills for a prospective teacher to learn is how to explain mathematical topics to other people. You are expected to practice developing that skill in this course.

When you obtain a solution to a problem in this course, you're not done with the problem. You need to think about how best to explain your solution to others.

If you have no previous experience at the blackboard, you might want to do some rehearsing before coming to class. You will probably be nervous at first, but remember that most of your audience is just as inexperienced as you, and those who are more experienced were beginners once, too, so can sympathize with you. You also might try to contact me before class to see if I can reserve a particular problem for you to present.

Bear in mind that presenting a problem solution in this class is not like a formal presentation of a project or a report. Your solutions will be discussed and critiqued. I will often ask questions such as the following while a student is presenting a solution:
•  Do you agree with that step? (to the class), or
• Why is that true? (to the presenter)
(I might also ask you to slow down if you are going too fast.)

Other students may ask for further explanation as you talk, or question whether or not a statement is true.
I may often ask the class similar questions after you have finished your solution:
• Are there any points you don't understand?
• Are there any mistakes?
If there is a mistake, sometimes you or the class will be able to patch it up, and sometimes you will need to "go back to the drawing board." That's all a normal part of the process. Sometimes other students will have ideas that together with your ideas can be put together to make a solution that works.

I will usually ask you (if you haven't given this information already):
•     How did you arrive at your solution method?
Then I'll usually ask the class,
•    Can anyone do it another way?
If so, that student will present their solution and we will discuss it. I'll probably ask if anyone else has still another solution. After we've discussed each solution separately, we'll compare and contrast them.

When you present solutions to the class, keep these pointers in mind:
• Remember that your audience is the entire class plus the instructor. Don't speak just to me.
• Try to mention what motivated the main steps of the solution.
• Make good use of the fact that you can talk, write, and draw when presenting solutions at the board.
• Watch out for the word "obvious". All too often when someone uses this word, they either have made a mistake, or don't really understand what they are talking about, or haven't thought enough about how to express it, or have acquired an unfortunate habit of putting others down. You will probably, however, find at times that something really did seem obvious when you did it, but when you try to explain it, or someone else doesn't understand it, it all of a sudden doesn't seem so obvious.