Maria made a comment a while back about new math and spiraling. I had to look it up. I’d heard about this thing called “new math”, but really didn’t know what it was. Math is math, as far as I knew. The thought also occurred to me that maybe this new math was actually was I was taught. Well, sort of. In addition to the traditional way for multiplication, I was taught The Lattice Method. It was kind of neat, but I didn’t really see the point except for those allergic to the traditional method. I commented at the time that it was math for people that preferred drawing pictures to doing math.
Anyhow, when looking it up, I ran across this site, which has a helpful video that outlines the new way that math is being taught:
With the exception of Lattice, I had never heard of it before as a bonafide method. Truth be told, though, it’s something that I have used in my head. Once you learn the way it’s really done, it’s pretty obvious. I’m not entirely sure what the rationale is for teaching it this way. The video gives a couple of explanations that don’t really make sense, but they’re critics so perhaps they are not giving the best reason.
In any event, I am glad that I watched the video because, it turns out, Arapaho is a “new math” state. Actually, they teach math both ways and let kids choose the method. It seems that everyone chooses “cluster math” over the traditional way. Cluster math, for those that don’t want to bother watching the video, basically says that instead of doing it the “normal” way (breaking, say, 38x27, down into 38x7+38*20), you reason it out your own way. So you might say “38x10 is 380. Okay, do that twice and you’re at 380+380. Since multiplying it by 5 would be half of that, you’ve got 380+380+190. So you’ve accounted for 25 of the 27. Simply add 38 in there a couple more times and 380+380+190+38+38 gives you your answer.
It was great that I watched the video because, when I was tutoring some kids, I would not have had a single clue what they were doing otherwise. This way I was at least able to get an idea of what they were doing wrong if they weren’t getting the right answer.
Cluster math seems most problematic because it is hugely error-prone. Kids try it out one way, hit a wall, then start over. Before you know it, they have multipliers or 38 written down all over the place and when it comes time for the final addition, they don’t know which counts. In the above case, his answer was over 2,000. He groaned when I asked him to do it in the traditional way, but he got the right answer.
So what is the appeal of cluster math? Why fix something that isn’t broke? I have a theory that teachers like to try new things out of boredom. I have another theory that teachers in general don’t like math, blame it on the way they were taught (the monotony of a single algorithm, to be precise), and so want to do it a different way. I can also understand a different appeal: it’s interesting to watch kids reason things out. It was much more interesting to watch him figure out all the ways to add multipliers of 38 to try to get to the answer. But on the whole, I am not impressed.
Notably, Arapaho’s standardized math scores are considerably less impressive than Delosa’s (once you factor racial demographics), but their reading scores are pretty good. I wonder if this is why.