Teaching is hard. Teaching for a second year is mostly easier than the first, but some things have been tougher.
I’m doubling down this year on teaching for understanding. Seems obvious, but on a day-to-day level, it’s not easy. I came upon a striking example of its challenges teaching scientific notation over the last few days.
Scientific notation is a pretty interesting concept. Using it and doing multiplication and division with it are pretty simple if you have a strong understanding of multiplication, division, exponents, and the base ten number system. But it can also be oversimplified into a few facts to memorize: move left, move right, add 0s, etc.
I started the unit off by just going for it: both to and from scientific notation, positive and negative exponents. I could have broken it down into smaller pieces, but I think the connections between these topics are critical. Maybe I was too ambitious, but I framed the unit by saying that it would be tough, people would get confused, but if they stuck with it, they would figure it out.
For most kids this worked pretty well. But still, some kids insisted on internalizing scientific notation as a set of rules for when to move left or right, or worse, a set of rules for adding or subtracting 0s to a number. I think this is a destructive mindset to have towards math.
But the fundamental challenge I had was how to deal with this during class. A student gets a simple question wrong. I probe their thinking, and they say “I moved the decimal left because that’s the rule when it’s negative”. I have two choices. I can correct quickly, saying “whoops, when the exponent is negative, the decimal actually moves left”. Kid gets the question right, maybe gets the next one right, and moves on. Or, I can try to break it down — talk about big and small numbers, powers of ten, and multiplication.
Option two takes time. Option two makes it tough to manage the other students. Option two is sometimes ignored, as students just want to know whether to go left or right. Option two is also where I went the vast majority of the time last year.
I’m trying really hard to avoid it. I don’t think it leads to any meaningful learning of mathematics. But it leaves me feeling powerless in class. Students are stuck, and because their understanding is so far from complete, I struggle to figure out where to start while still doing their learning justice.
This is the best kind of struggle, and I’m learning a ton from it, But, compared with my approach last year, it’s much harder to be in that room, in front of that kid who’s confused, struggling to help them understand.