Exponents, Products and [my mathematical] Powers

"Everyone who beats Mrs. Lahey on this problem set will earn extra credit points."

Oh, dear. Extra credit points will be flowing like New Hampshire spring runoff thanks to Mrs. Gorman's misplaced faith in me.

When I decided to return to Algebra I in order to get over my math anxiety, I knew I'd have some catching up to do. I stumbled into class on the last day before a unit test, in the last week of the second trimester. I paid little attention in Algebra I the first time around, and that was 30 years ago.

Helpful hint: If you plan to return to Algebra I in middle age, start on the first day of a unit, not the last.

I did my best to catch up with the kids, and Alison Gorman is the best math teacher I've ever seen, but if you glance back up at the scan of my first practice set, you can see how badly I tanked. The red "C" in the middle of the sheet was the one problem I got right on the first try. I had totally forgotten what to do with exponents, could not remember what the distributive property was let alone how to use it, and my hand cramped up about four pages into my notes.

That one correct problem turned out to be my only correct problem. But it reveals I learned at least one new thing yesterday, and that's good, right?

The students loved it. My students taught me. One taught me about domain and range, another explained why you add exponents when the bases are multiplied, another whispered the number of the problem we were supposed to be working on when I missed Alison's instructions. Hey, come on, I was taking notes. It's hard to listen to write and listen at the same time. I will try to remember that next time I start talking when my students are still writing.

I can't attend Alison's class every day because my teaching schedule overlaps with some of her math classes, so a fair amount of confusion is to be expected. But that first day was just silly.

Today was better, though. The class started a new unit, "Exponents, Products, and Powers," so I stood a fighting chance. We were all on the same starting line, give or take thirty years. As we moved through the exercises, I started to see it. I have my list of properties - power of a product, product of a power with equal bases, power of a power, power of a quotient...and on and on - and I have to refer back to them, but they are slowly sinking in.

I got some insight into my basic issue with math when I proudly told my son Ben about my day. We have a tradition at dinner - "high, low, funny." The best thing in our day, the worst, and the funniest. My best and my funny were both math class, but Ben provided the worst. I recounted the properties I'd learned, and told him how proud I was of myself for remembering that when you multiply variables raised to a power, you simply add the exponents. Ben looked at me like I was an idiot and said,

"Well, that just makes sense. Of course you add the exponents."

And there you have it, ladies and gentlemen, the difference between my brain and the brain of someone who naturally gets math. I can't see it. I can repeat the steps if someone shows them to me, I can replicate the process, but I don't think any of my teachers spent much time explaining the "why" of the process to me.

For example, we did this problem today:

Look at the one without all the scribbles and crosses through it. I have no problem leaving the exponents well enough alone when they are next to an X or a Y, but put them next to a number, and they call out to me. The 12-year-old in me has to DO something with them. Create something. Find an answer, multiply all those threes, no matter what. That's the part under the big cross-out. I made mistakes because I solved for all sorts of unnecessarily large numbers. 

Must. Multiply.

But today, the grown-up, rational teacher in me had a breakthrough. If Alison, teacher extraordinaire, hands her students a problem where the exponent is higher than 3 or 4, and she's not letting them use their calculators, and she's not particularly in the mood to torture them, she probably does not mean for them to do the multiplication. She's probably hinting that there's a simpler method. 

So, two things. I learned two things today. 

But now I have to head out to the dining room table. I have a lot of homework and a teenage son to impress.

Part IV of my math odyssey can be found here