It’s snowing in Columbia, MD. On March 12th. Should it snow in Columbia, MD in mid-March? No, it should not.
Temperature today is in the 30s (that’s Fahrenheit, looks like the 0s in Celsius… is that right?). Yesterday it was in the mid-70s (or low-20s C). I’m sure that’s fine. We live in hell.
Anyway, my Algebra journey continues, and I’d like to log in some of that. My return to Math has been going well, and it has also prompted some self reflection. I’ve been thinking about the lessons I seem to have missed, and from what I’m still struggling with, I seem to have completely missed how knowledge and processes build. Honestly, it feels a little silly.
In my high school days, our Math classes always had something we called “Word Problems”. I think they might still be called that, but I’m not in high school, so I wouldn’t know. But in these college level courses I’m taking, they call them “Applications”, and actually, I do prefer that. A part of me does find it a little stuffy and pretentious, but give the adolescent implication of the phrase “Word Problem”, I can live with that.
I find myself having a little panic at the start of every one of these. I’m trying to find the thing that I’m solving for and piecing together what bits of knowledge are dropped in it to figure out how to solve it. However, there always seem to be these keys that go entirely unnoticed by me. Stuff I do notice – square vs. cube. They are probably both dealing with lengths of sides but if the square problem goes beyond that, it’s probably about area. So your equations should be about length times width. Cube could also be about area, but there’s a good chance that if we’re talking about cubes, area is a stepping stone problem. Like, what we really want is the volume, and we don’t need to know the area to get the volume of a box – it’s LxWxH, right? Except what if you’re only given two of those dimensions and an area? Right, so now we have to setup an area problem, solve that for the missing variable, and then we can plug that into our simple volume equation.
I think I needed to write that out because, while that specific type of problem isn’t all that hard to put together, the biggest win from it is just how it informs, sort of previews harder problems. I need to find a way to remind myself of that as I encounter the more complicated stuff. Sometimes it isn’t even all that more complicated, I got thwarted by a surface area of a cylinder question the other day, but that’s not really that hard either, to be honest. But when I’m in the mindset looking for an A->B and not thinking of an A->B->C, then I’m likely going to get stuck just trying to remember some of the mid-problem math, like if it’s the pi or the r that gets squared. The implication of the materials trying to teach you to write, read, and interpret complex rational equations is that the technical world is chalk full of these types of problems.
I’m trying to put this all in perspective because I’m at least halfway through this online course, and the way it’s structured, I’d say I’m actually more like 3/4s through. I am feeling a lot more confident in my skills now, but I’m not 100%, and I need to lock in. I don’t want to jump to the next level still caring the baggage of decades of unlearned lessons.