Attending a thoroughly engaging class has the same effect on me as reading a thoroughly engaging book. I carry its voice with me for a while.

In CSC 140, Java, yesterday we heard and saw a meticulous explanation of how object reference variables work and how important it is to understand that the variable name holds an address, not data (as primitive variables would). I think I’m going to make a pencast from my notes to entertain myself on my commutes, and perhaps sharing it, which would mean figuring out how to make a PDF from Livescribe and finding my jou8rnals… but it’s *not* an easy find.

… and it’s having an impact. It’s easier for me to explain, one (or seven) more time(s), that “raising i to powers works like raising -1 to powers,” and showing it, instead of getting the “dang it! Don’t you know this yet?!?!? I *told* you it was important!” edge in my voice. If the student is down here, they’re trying to learn it. Dragging fresh paint over the rotted wood is only a temporary fix.

More than that, though, it means that I’m working in concept-building interactions more often. When the student wants to know how to set up “what are two consecutive odd integers whose product is ____?” I remember that one of the more insidious conceptual potholes is lack of understanding that “x stands for a number — and could be any number until we put constraints on it,” and I’ll walk through examples of “next even number” so they figure out that it’s 12 + 2, 30 + 2… and I’ll mention that since it would work for any number in the universe, we can just say “x + 2.” (Now to figure out how to do that so it’s not just me talking…)

I am deeply appreciating approaching learning from “this is what you need to understand to prevent bad mistakes later,” instead of “DO NOT MAKE THIS MISTAKE! DO NOT MAKE THIS MISTAKE!” as Salman Khan’s “lesson” on exponents does, in which he tells us many, many times that it is NOT 6 x 8, it is NOT 48, though it is 6 and 6 and 6 and 6 … (exactly the same language he uses when explaining multiplication), and he never actually calculates what 6^8 is… I want to understand how and why to figure out how to make a Class, so I’ll be performing the process that gets to a good answer, instead of plowing through the important concept so quickly that I simplify it, and then finding out what mistakes that taking short cuts cause (but not why), and trying not to make them, but having to figure that out at every level, having no fun, and becoming convinced that I shall always be making mistakes.

We heard two or three examples, and were implored to get colored pencils to make the visual descriptions (oh, yes, did I mention use visuals and not just words?) ourselves… I shall henceforth call this “Conceptual Frontloading” and because it has a jargon name, it is therefore meet and right.

And, henceforth, I shall endeavor to figure out how to do it for operations on negative numbers, because students are out there bein’ knocked upside the head with them right now, and … yes, we tear through “adding negatives is more negative — so two negatives don’t make a positive’ (except in a way they do, in that if you’re writing down what you’re doing you’re going to + the two absolute values)…. and we do kinda give it the “DO NOT MAKE THIS MISTAKE!” and “here’s a trick so you don’t make the mistake” approach instead of “let’s totally get this, so you can understand how *that* would be a mistake.”

*cognitive resonance, Java, visual math*

Kate MacInnis

September 20, 2013

Yes! I think this was what was missing from your discussion of the Nix the Trix site. It’s not that we don’t want students to not have things that would make their life easier, it’s that we know that people are teaching the tricks to avoid dealing with students that don’t have the conceptual understanding– or sometimes because the person doing the teaching doesn’t have the conceptual understanding either.

I’ve seen most tricks go wrong so many times that I really don’t think they’re worth anything. I taught developmental math for four years, and it was so common to have a student remember a trick, and try to apply it in the wrong situation. Sometimes they would say things like “Hey, I loved that boom-boom-fizzle shortcut. What’s that for?” They would remember the trick but not understand anything.

And as far as getting them to do the talking about consecutive odd numbers, try getting them to list off a few pairs. Then make them say, if x is the first one, then what would the second one be. (If that confuses them, change examples, and say if your two numbers are 20 and 30, and if x is 20, then 30 would be x + 10. Then go back to the pairs of numbers that the student generated.) Be prepared to take a lot of time with this, and let them have time to think. If they get an impatient vibe off of you, you can make it worse. But I suspect you know that, since you write about your students with such obvious respect.

xiousgeonz

September 20, 2013

Thanks 🙂 🙂 Yup — that’s pretty much exactly what I do, almost word for word… we also have a big ol’ number line taped to the table in here. so I can show how, odds or evens, they are jumping the same way — but they started in a different place.

The thing that was so gratifying about the class is that he was giving so much time — which was really helping me — and it *wasn’t* ‘developmental.’ It was, simply, important enough to do.

xiousgeonz

September 20, 2013

(and I have a kiddo that keeps asking me, “is this where I can use the around the world thing?” which is what he calls changing a fraction int o a mixed number. And you’re so right — once a trick is nailed nailed down… it’s hard to pry it open …)