Tuesday, April 8, 2014

Tuesday: I was going to talk about statistics today, but I'm kind of tired, and so instead I'm going to talk about something else.

Elastica!

Yeah, I know.  "Who?"  They were a band in the 90s, and I was reminded of them last night, which led to me looking to see what they have on youtube, and then buying their albums off of amazon.  Yay the instant gratification that didn't exist twenty years ago.

Anyway.  Wikipedia gives like 19 genres for them, which basically says how little a genre means now-a-days.  Let's go with "British post-punk," as that's probably the most descriptive.  Quick 2-3 minute songs with wonderful bass lines and catchy tunes.

This was the first song of theirs that I heard:


Nice driving beat:


How odd, I also hate waking up in the morning:


I had never seen the video to this song until this week.  It is kind of brilliant:


I was going to say that more music videos need to be done in stop motion, but I haven't seen any recent music videos in years, so maybe they are:



And here's why.  First, let's copy just the question, and get rid of Jeff's scribbles:


Ok.  So we're using a number line to represent subtraction from 427 by an amount 316.  Jack (the fictional student) arrived at the value 121, and Jeff shits himself talking about how his BS in EE, which involves differential equations and "other higher math applications" tells him to "simplify things" and does the subtraction the standard way.

But what Jeff doesn't fucking understand is that he knows how to do that because he knows that the 4 represents 400, and so he needs to line it up with the 3 that represents the 300.  However, if you're a kid, someone telling you "stack things up, and then subtract the columns" doesn't really impart any underlying knowledge.  It's the plug-and-chug method.

What the question (and I guess Common Core) is trying to teach is that you can rework the question (427 - 316) into the "complicated" form (427 - 300 - 10 - 6).  Then, you can further expand into (427 - 100 - 100 - 100 - 10 - 1 - 1 - 1 - 1 - 1 - 1).  So, if you don't know what (427 - 316) is, you can take it in steps, and do simpler problems that you can do.  The number line structures that into clear steps.  You start at 427, and subtract the first 100.  Repeat this for the other terms, and you should get the correct answer.  Jack (the fictional student again) fucked this up because he forgot to take the step that subtracts off the 10.  He did the hundreds, and the units, but forgot the tens.  

Why would you want to do this?  Because what would happen if we were subtracting 318 from 427?  Jeff (the asshole) would say that you have to take 1 from the 2 and append it to the 7, so you subtract 8 from 17 which is 9.  Why? Because plug-and-chug.  The number line method shows that after you subtract the 310 from 427 (so we're at 117 now), you just take 8 steps down, which decrements from 110 to 109.  Now, if you want to do the calculation and get an answer, the standard way is going to be more efficient.  However, understanding the number line method motivates why you borrow the 1.  You're pre-emptively decrementing the tens place that you know you'll have to do.  It's functionally equivalent, but you have a more physical thing to think about while you learn how math works.

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