Wow!  What an amazing three days I spent at the NCTM annual conference in New Orleans!  I can’t believe how much I learned (which actually never amazes me and always humbles me – one of the many reasons I love going to these conferences.)  I also hate leaving and knowing that I missed at least 20 sessions that conflicted with ones that I did go to, so now I’m catching up and trying to email the speakers that I didn’t quite get to see or get in contact with while there.

One of my major a-ha moments was in Gail Burrill’s session on logarithms.  You’d think that after 25 years of teaching that you’d understand how much you understand about logs right? Oh, no!  So she had us all have a very large number and we were doing an exercise where we had to put a post it note with that number (mine was 72, 753) on a scale of powers of 10 {10, 10^2, 10^3, 10^4, 10^5…}, her argument being that one of the main reasons to teach logs is to have a different scale for very large numbers.  So after all of these teachers did this, we analyzed where all of our numbers were on the scale – particularly between these numbers.  Since my number should’ve been between 10^4 and 10^5, I knew I put it in the right place – but oh no, I had it in the wrong place relative to the middle.  She asked us to calculate the middle of those two – 10^4.5 which was 31,622 and yes, I admit that’s very close to where I put my post-it.  I could blame the person who put their’s up first which said 75,289 and I just put mine by there’s but I won’t.  I just didn’t really think.  But I know this was a light bulb moment for many of the teachers in the room.  Students don’t really understand how a logarithm is an exponent in the first place and we were doing this exercise without even using the word “logarithm.”

Then we went down to the section below that was between 10^3 and 10^4 and checked some of those numbers.  They were very off too and Gail asked us what number we expected to be in the middle.  At this point, some of us pulled out our calculator (yes, I admit, I did) but some of the smartees in the room just said “3,162” and I finally got it.  By just dividing by 10 and looking at the scale in this nonlinear way, students would be able to make the connection between the algebraic properties of exponents and what a logarithm was.  I thought this was an amazing way to introduce logs.  Has anyone done this before?  Thanks so much Gail!!  I think I’m going to write a problem for my curriculum about this, it’s such an insightful experience.

More reflections to come – just can’t do it all at once – catching up on school work!