Sunday, October 26, 2008

How would you mulitply 11 times 29?

Does it matter what way you work 11 times 29 if you get the correct answer?
  1. One way would be to multiply 10 times 29 which is 290 and then add another 29 which is 319.
  2. Another way would be to multiply 11 times 30 and which is 330 and subtract one 11 to get 319.
  3. Another way would be to add 11 plus 11 plus 11 ... and so on until you have done it 29 times.
  4. Another way would be to use the column method. See below.
  5. How about using a calculator?
Usually students are drawn towards the method that is easiest. Furthermore, students want what is easiest for them. Reviewing different methods is an excellent way to have students buy into a quicker method. So often I make the mistake of showing one way to do a problem. I think that I'm cheating some of my students when I do this because they lose out on the opportunity to add to their toolbox of methods of solutions. I think that by only showing one method, I'm sending a message that the way I cover is best, and whatever way you used to solve this problem is not as good.
So I think that I need to work harder at showing multiple methods to solve a problem. I need require my students to find multiple methods of solving a problem. At the high school level, it is more about how students are thinking to solve problems. I know they can get a solution. More importantly, how did you come up with it. Justify your thinking.
So, yes it does matter how you solved the problem. The way you solved it might just help me understand it a little bit better.

Friday, October 17, 2008

More on When Students Teach

I received an email this week from a teacher Susan McKay that gave an excellent suggestion.
She calls it "Teacher, Student Pair"
  1. Separate your students into pairs
  2. Have them designate one person a teacher and one person a student.
  3. Now give the class a problem for the pairs to work out.
  4. The designated teacher can only explain how to do the problem and the designated student can only write the solution to the problem. With these rules the pair must try to solve the problem.
  5. Remember, if you have the pencil, you can't talk. If you don't have a pencil, you can talk.
  6. Now give the class another problem and the pair will switch roles.
I can't wait to try this in my class. Thanks Susan!

Friday, October 10, 2008

When You Teach, You Learn

I have been a firm believer of the idea that when you teach something, you actually learn it better than you would if you just learned it traditionally. I have an example for you. A student today was explaining to another student how to find an equation of a rational function and stopped in the middle and said, "I don't know why there is a 3 in the equation." She realized that she had found the answer, yet didn't know why she had done something. In the middle of "teaching" it, she had to learn more herself. I thought, that was excellent. She taught herself by teaching someone else. Is it accountability? Maybe it is the idea that you genuinely want to help someone else do something correctly. I'm not sure. But it works.
I have been trying to have my students teach each other. Lately, when a student gets done with a math problem, I tell them they must walk around and help others arrive at the solution. By the time I have 3-4 other "teachers" helping me, the whole class catches on to the idea of the problem.
Give it a try. Students love to help others. Give it a try.