# First Day

I know I’ve been truly negligent about writing. If you know me, you know my philosophy around blogging is do it when you’re inspired, do it for yourself. And recently I just haven’t felt like it. That being said, today was finally our first day back with kids. We’ve had a week and a half of meetings without kids, but today was the first day with kids.

And I had my first class with each of them. Each class was only 30 minutes. It was designed so we could get a taste of them and they could get a taste of us. We have bonding activities for the next three days, and then academic classes will be in normal full swing the following week.

This year I’m teaching the same courses as last year (precalculus, calculus, multivariable calculus). Normally I start off the first day jumping straight into math — but it’s always been kinda boring math. Kids take notes, we have nightly work, we go to it. But this year, I wanted to mix things up a bit.

In Multivariable Calculus, I gave them an optimization problem that we do later in the year, and literally had them make a guess, we recorded the answers that their guesses gave, and then I broke them into groups and they were trying to come up with ways to solve the problem. I gave them nothing. It was interesting to listen to their conversations. Some were intuitive and geometric, others were going straight up algebraic work, and others were playing around with a mixture of both algebra and guess-and-check. I basically said they have until Monday (when we next have our class) to do whatever they can to make progress on the problem.

What’s so powerful about this is that I think I can parlay this discussion into a discussion of big ideas in multivariable calculus because they are already nudging their way towards level curves. It’s like three layers below what they were talking about today, but I think through our discussion I can dig it out. I have never really thought of multivariable calculus as a discovery based course… I don’t have enough of a command of the material (or the time) to actually do that. But heck if I myself can’t see glimpses of what that might look like. From just 30 minutes today.

The other amazing thing about that class was that I have in it a number of students I taught in my first year of teaching — they were sixth graders then, and they are seniors now. How amazing is that?

In calculus, I did something I’ve been wanting to do for years — a “3 Act” with my calculus kids. What’s been hard about this is that I always want to do them later in the year, and I always stop myself because I’m nervous I won’t do it justice, and also because I always feel like I don’t have time to spend. But today I got a taste of doing it, and I’m hooked. I did the taco cart problem which anyone from late middle school on should be able to solve. But what’s nice is that the kids seemed to get into it. And I’m not terrible at facilitating them (even though I did tell kids when they were right before we did the great reveal — which was soooooo dumb of me)! I can see this becoming a more regular part of my teaching. I already am planning on using the toothpicks 3 act in Precalculus in a couple weeks.

Precalculus was the class I was least imaginative with, because I did what I did last year. I had kids start to expand $(x+y)^n$ for various exponents, and then start to identify patterns. Kids were noticing stuff that I hoped they would, but one kid took things way further and saw Pascal’s Triangle (kinda… he saw the pattern in the coefficients) which was so lovely. The other classes I know a good number of kids from previous years, but this class is all people new to me! I’m nervous about learning their names.

Being back at school — now that kids are here — is putting me back in a more zen place, because they helped me remember what I love about teaching so much. The start-of-year-meetings are done and gone, long live the kids!