I love the Aha! moments

Statistics today was filled with several aha's! I can almost hear all the cogs clicking in their brains.  I gave them three data sets and had them make a box plot for each as well as find the mean and median.  Then I asked them about the shapes and the comparison of the mean to the median.  The first example I gave them was clearly symmetric with mean = median (always start with the easy ones first!)  Then they had to decide between skewed left/right for the next two.  There was a lot of shouting going on as each student thought they were right.  Then the "why that?" explanations.  I love these moments.  In some brains, you can tell there is a backflip happening as they have to redirect some previous thoughts.  It's as though they are re-categorizing their thoughts, while some are glib about their correct choice the first time.  So, of course I have to challenge their thinking some more.  I offered them 4 histograms with 4 box plots.  They have to match them, and it's NOT EASY.  While two of them are actually fairly obvious, the other two are difficult to match.  There was SO MUCH discussion.  I can't wait for tomorrow!  Just when they think they have it right, I will challenge their thinking AGAIN!  I have to enjoy this now, because once we get past this unit, they are smarter and it is more difficult to get them.  Boy, do they grow SO MUCH!

Continuity and limits to infinity were the two topics today.  Mooculus helped them look at graphs of infinite limits.  But when they went to paper problems, their struggle increased.  Deciding continuity and how to fix removable continuities is pretty abstract at the moment.  This will take another day for sure.  Especially because we don't offer piece-wise functions too much in Pre-Calc.  Even remembering graphs of rational polynomial functions, radical functions and logarithmic functions has gotten lost in the recesses of their brain. Note to self: the summer assignment needs to contain more graphing of all types of functions, including piecewise.  This needs to get lodged back in their brains before school starts. I'm looking forward to "the workout" tomorrow!