Wednesday, August 27, 2014

Is it possible for standard deviation to equal zero?

Such a great question: Select only four numbers from the numbers 1 through 10, such that the standard deviation is the smallest.  Repeat to find a standard deviation that is the largest.  Is there more than one choice for each set?

I love this question.  It gives the students a real chance to experiment to see what happens.  They were all positive about the fact that there were multiple solutions to the first part, but we had to experiment to determine the second.  Then they explained "WHY?" to me.  Hopefully that is all the explanation they will ever need to have that concept.

I felt like I was getting more correct responses as we reviewed material today.  I had assigned a problem set  before giving them formal definitions about resistance or how mean compares to median in skewed graphs.  So as they read off their answers I heard some say, "well I know that answer is wrong now, so I'm changing my answer".  I like that!  Although I would love to think that they are doing some extra research on their own, outside of class, in order to get the right answer, at least they can spot right away that their answer is wrong after the class discussion.  They are spotting their own mistakes.  Can't ask for more than that!

In Calc today we went over a problem that I gave them that was a real "brain buster".  I explained that mathematicians are still alive (no they are not all dead) and that we don't wake up and know all the answers.  Sometimes we have to explore and look for patterns, and this problem would be a good example of how I could do that.  So we went on an exploration of what happens with limits if you get 1/0 or 0/0.  No formal definition, just an exploration.  I want them to know how exploration works and can lead us to discovery (even in math)!  I was expecting to hear "is this going to be on the test" and I was shocked, but I didn't!  Maybe I am going to be able to turn them all into Christoper Columbuses or Ferdinand Magellans!

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