Been a rough couple of weeks. Lost my dad to a too short battle with cancer and then found out a dear friend from my FLA days died just last week. Both were too young to go.
So, I’ve been trying to focus on the day to day and look for triumphs right now. There are a few to be savored. In Calc BC we are studying Differential Equations and I was proud of both of my classes this week. I posed the following challenge to them. Suppose I leave the dorm this morning with a cup of coffee (with a lid) in each hand. I place one of them on the sidewalk and take off the lid. I bring the other to my classroom and remove its lid. Now, sketch what the temp v time graph would look like for each. We noticed and wondered for awhile (I”m not good at using that language explicitly, but I am pretty good at generating some noticing through careful questions) and we decided that the slopes were in some ways related to the difference in temperature AND that there had to be a horizontal asymptote. We had a good conversation about the difference between the theoretical and the measurable temp differences between the room and the cup of coffee. We talked about the relative size of the surroundings versus the size of the object at hand. We got hung up on whether the initial temp of the object was all that important in the end. We realized that there was a proportionality constant to be accounted for (one student pointed out that the specific heat of the object mattered – I was impressed and I think he even used that lingo accurately) and we finally arrived at Newton’s Law of Cooling. I’m not naive enough to think that many of them will remember the exact conclusion, but I am pretty convinced that many of them will remember the process. The conversation that gives me hope about this is one I had in AP Stats today. We were introducing the idea of probability distributions and talking about finding means and standard deviations of random variables. We had to look at the ugly standard deviation formula and try to remember what it all meant. In each class kids were able to contribute meaningful memory of our earlier conversations and I even got a great challenge question from one of my students who doubles in BC and Stats. After we decided that we wanted all the differences between scores and the mean to be positive (so that they don’t all sum to zero) this student wanted to know why we bother squaring the difference between a score the mean score instead of just looking at absolute values. I was able to have a nice conversation about the differentiability of the square and square root functions and how they just behave more ‘nicely’ than absolute value functions do. I was just so pleased that there was such good memory about conversations we had weeks and weeks ago.
I’m also finding inspiration from blogs and tweets these days and it feels like something might be big brewing in the back of my head. Don’t have it together yet, but I’ve been so inspired lately by tweets from @gfrblxt, @JustinAion, @wwndtd and others by blog posts from Michael Pershan, Gary Johnston, Sam Shah and a slew of others, by the Nix The Tricks project that Tina has organized, the list could go on and on.
I’m so thankful for all of the inspirations I find in my daily contacts with family, friends, students, and colleagues for all the inspiration I find in my inbox and through my tweet deck, I just hope that I’m adding to that good karma in my own way…