Day: December 1, 2007

Honing intuition is hard work (but worth it)

I thought I’d kill birds with stones and (1) try using LaTeX equations while (2) explaining how I honed my calculus classes intuition. Granted, the idea is simple and I think most teachers teach it this way, but I didn’t and my students got confused. So on Day 2 of the chain rule, I had them come in and do the following right away:

Find the derivatives:

A1:
B1:
C1:

A2:
B2:
C2:

A3:
B3:
C3:

Bonus Problems:

D1: Find the derivative of .

D2: Find the derivative of .

And in fact, they were very successful. Instead of showing them a big equation and how to break it down, I instead started small and built it up. And showed them each part of what was going on. And by the end, my students were pretty capable chain-rule-appliers.

There are three things to say about this:

1. It is important to first introduce as because it makes the composition of functions easier to see. (Plus, really surprisingly and disappointingly, some of my students didn’t realize they were the same thing!)

2. There is something really exhilerating about writing really long answers to problems. They love it. I love it. It makes us feel important and like we’re doing something extraordinarily complex. Which we are (to some extent).

3. I think it’s important to polish off this whole chain rule business with something that shows the students that all these things that they’re doing works. Physically worsk. And are just like what we’ve been doing. So what I did after we worked on this worksheet is we went back to a derivative we had initially solved with the chain rule: . I asked them what the equation of the tangent line to this function was at a particular value of . And then I showed them that what we found for the tangent line worked graphically. They saw the tangent line hit the curve in front of them. At this point, there weren’t many gasps (they knew it was going to work), but I think it drove home that (a) hell yeah, it works! and i’m. not. lying. to. you. and (b) this is no different than everything else we’ve been doing. (We’ve been finding tangent lines to tons of functions. These functions are just longer and more gross looking.)

Happy hour. Let’s be honest: happy hours. many happy hours.

There’s a tradition at my school: teachers grab a drink after work on Fridays. I think it’s been happening for years, but it’s a tradition that has really come into it’s own recently. And normally on Friday five to fifteen of us go to a local watering hole and unwind. Stories are shared, annoyances are vented, and we get to actually enjoy each other’s company for longer than the frequent “how’s it going?” as we pass through the hallways of the school like ships in the night.

Each Friday around 1pm an email gets sent out by the “leaders” of happy hour which pokes fun at the school and the goings on of that week. This week, I accepted an invitation to be a guest writer:

Dear thirsty compatriots,Sam Shah, guest writer extrodinarie here. I thought in light of the school’s committment to self-reflection and goal-setting, that I would share with you one of my SMARTgoals.

Currently, as a first year math teacher, there are a number of areas in which I can improve: namely bring in more cupcakes. But that goal doesn’t quit fit any tenets of teaching. (But it is a tenet of being a good person.) Our plane would still fly whether there were cupcakes on the fold-down trays or not.

What would make the plane crash, literally and metaphorically, is if there was no fuel. And addressing that is my SMARTgoal. Keep yourself well-fueled. As the new school nurse said to the US this week, hydrate yourself. It wards off the colds that cause 2.2million days of school lost, and keeps you focused and attentive to help students out. (And bake cupcakes.) So my SMARTgoal is:

Be healthy. Drink copious amounts of beverages of all kinds in equal measure frequently. That means… well… you know where this is going…

[Bar Name Here]

Today. 4pm.

AND LET THE NEW HEALTH REGIMEN BEGIN!

Recently I’ve been going to happy hour and I have a better and better time each week. The bartender (she works every Friday) has gotten to know me well enough that she asked “hey is your crew coming today?” and then she gave me 2 free Guinesses! And afterwards, I went to dinner with three teachers.

The best part about all of this is that this is exactly the place where I feel like I’m becoming part of the community. It’s where we talk about things and (best of all) I hear gossip.

Gosh I love gossip.