Wow!\u00a0 What an amazing three days I spent at the NCTM annual conference in New Orleans!\u00a0 I can\u2019t believe how much I learned (which actually never amazes me and always humbles me \u2013 one of the many reasons I love going to these conferences.) \u00a0I also hate leaving and knowing that I missed at least 20 sessions that conflicted with ones that I did go to, so now I\u2019m catching up and trying to email the speakers that I didn\u2019t quite get to see or get in contact with while there.<\/p>\n
One of my major a-ha moments was in Gail Burrill\u2019s session on logarithms.\u00a0 You\u2019d think that after 25 years of teaching that you\u2019d understand how much you understand about logs right? Oh, no!\u00a0 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\u2026}, her argument being that one of the main reasons to teach logs is to have a different scale for very large numbers.\u00a0 So after all of these teachers did this, we analyzed where all of our numbers were on the scale \u2013 particularly between these numbers.\u00a0 Since my number should\u2019ve been between 10^4 and 10^5, I knew I put it in the right place \u2013 but oh no, I had it in the wrong place relative to the middle.\u00a0 She asked us to calculate the middle of those two \u2013 10^4.5 which was 31,622 and yes, I admit that\u2019s very close to where I put my post-it.\u00a0 I could blame the person who put their\u2019s up first which said 75,289 and I just put mine by there\u2019s but I won\u2019t.\u00a0 I just didn\u2019t really think.\u00a0 But I know this was a light bulb moment for many of the teachers in the room.\u00a0 Students don\u2019t really understand how a logarithm is an exponent in the first place and we were doing this exercise without even using the word \u201clogarithm.\u201d<\/p>\n
Then we went down to the section below that was between 10^3 and 10^4 and checked some of those numbers.\u00a0 They were very off too and Gail asked us what number we expected to be in the middle.\u00a0 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 \u201c3,162\u201d and I finally got it.\u00a0 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.\u00a0 I thought this was an amazing way to introduce logs.\u00a0 Has anyone done this before?\u00a0 Thanks so much Gail!!\u00a0 I think I\u2019m going to write a problem for my curriculum about this, it\u2019s such an insightful experience.<\/p>\n
More reflections to come – just can’t do it all at once – catching up on school work!<\/p>\n\n