Solving algebraic equations is, I’m thinking right this second, one of the “gateways within the gateway courses” that lots of folks don’t get through.
It’s definitely a ‘thing’ that I reveled in when I learned it. Learning that “of means times” … bang! Suddenly I could figure out percent problems and all kinds of other things… and fractions made so much more sense. “Half of 20” was 1/2 x 20…
… so when I started teaching, it was one of the topics where I was mystified when people didn’t get it and, I’m sure, often thought they did when they didn’t.
I’m pondering… is this one of those topics that’s complicated enough so that things we don’t really think have anything to do with understanding actually … have a lot to do with getting things right enough times to see the connections and get understanding?
I’m thinking specifically of the way that as soon as some of us see “4x = 20,” motor memory kicks in and we make pretty fractions on both sides, cancel, and voila!! … and that the motor memory is part of why when we see 20x = 4, it’s not as big a deal to realize that we do the same thing… and our answer is a fraction.
I’m thinking of the way our students are much more successful when we set them up to solve the equations vertically instead of the way texts do, so that it’s visually obvious whether or not we’re doing the “same thing to both sides.”
Drawing a line down the equals sign *really* helps with figuring out what to do with
4x + 5 – 7x = 2(x-4) + 11x – 1,098
and weird stuff like that. (That’s not a real text problem.)
… and I still share student frustration with the problem with the temperatures or altitudes where you add in the subtraction problem except when you don’t, you subtract in the addition problem except when you don’t, and then you have to remember that in the subtraction problem the answer will always be positive because we always answer “how much less” or “how much more” with a positive number, only next semester if you take 072 you have to say negative when it’s negative.
And somebody else uses Connect for their music course and … yea, it’s garage band software. Full of weird stuff and glitches requiring “just click everywhere, and … this might nto mean anything.” There’s a page where it says “question 1: ” and “Score — 0 points” — only … erm… THERE IS NO QUESTION ANYWHERE ON THE PAGE. Well, I could at least tell the student that Connect was flawed software so it probably wasn’t a thing he had to do.
… oh… and a small victory perhaps yesterday on getting Modumath to the masses!!!!! And I am thinking of creating my own little independent Canvas “sign up for getting cheered on!” course for those folks.