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.
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.
The educational industrial complex also figures heavily here. Textbook manufacturers and the people who design curricula both have to make money; “new teaching methods” mean that the old perfectly serviceable textbooks and teaching aids get thrown out on a regular basis and replaced with new ones. Whether kids learn or not is not the point.
That’s why California leads the country in educational fads (and is at the bottom of the educational performance table.) We have the most kids in public school, ergo, we are the richest target for the textbook publishers to make their money on. Sometimes our stuff gets thrown out every year and replaced with “new, better” textbooks and learning aids.
My girl never learned how to move ahead in math until she learned how to memorize her times tables. But they wouldn’t teach it to her at school; she had to learn it on her own.
Same with phonics. She didn’t learn to read until she was in the fourth grade. We sent her to a tutoring franchise and they taught her phonics (at thousands of dollars expense.) It wasn’t all the school’s fault–we learned after sixth grade that she had ADD–but it was partly their fault.
The good news is that she made the honor roll again this quarter! Last year in sixth grade she was a D student. From a D student to the honor roll. Some of that was from having me home to make sure she did her work and help her study, but it was mostly the Concert, IMHO. That’s why I believe in ADD where other people poo-poo it.
Comment by Maria — April 26, 2011 @ 11:11 am
Sorry, that should have been “It was the Concerta,” above. Not the “Concert!”
Comment by Maria — April 26, 2011 @ 11:12 am
Teachers like to be thought of as creative professionals, but the most effective way to teach the broadest swath of students is often via a rote, by-the-numbers approach. The U.S. military has done that successfully for ages. A similar approach was found to be somewhat effective in K-12 teaching (”Direct Instruction”), but I don’t think it appealed to most K-12 teachers.
Comment by DaveinHackensack — April 26, 2011 @ 5:19 pm
I mentioned DI favorably in my “Learning By The Metric System” post. Some months later, I’ve actually used DI material. I can understand why teachers hate it. It’s pretty soul-sucking, as though it were uniquely designed to make teaching miserable.
That being said, it’s been shown to work, and I haven’t seen countering evidence. The question is the degree to which it would remain successful with a lower caliber of teacher. It’s one of those odd things where the boosters say that teacher quality does not cease to matter (and therefore if it drove good teachers out of the profession, that would be bad) and critics say that it’s designed to weaken the position of teachers (by making teacher quality irrelevant, which makes me think it might be the way to go!).
I have a post on this I’ve been meaning to write.
Comment by trumwill — April 26, 2011 @ 5:45 pm
I would probably break 38*27 down to 38*30-38*3…
Nevertheless, there is nothing like tried and true 8*7=56, carry the 5, 3*7+5=26, etc…
The last time I had to multiply 2 2-digit numbers together by hand was literally more than half a lifetime ago, and I can still do it without thinking.
Comment by Mike Hunt — April 26, 2011 @ 6:37 pm
Cluster math seems most problematic because it is hugely error-prone. Kids try it out one way, hit a wall, then start over.
And waiting for the kids to figure it out probably takes a huge chunk of time that could have spent on teaching the children math properly. It’s almost as if teachers like it because is squanders considerable time…
Comment by David Alexander — April 27, 2011 @ 12:34 am
The problem is, “Cluster Math” is essentially dropping a bunch of numbers in front of the kid, making them get frustrated, and then eventually hoping they reach the point of the usual algorithms on their own.
The point of traditional math is that it breaks things down to where you have (a) a defined number of steps for any problem and (b) the number of steps is kept to a relative minimum.
A kid wondering where he messed up can go back, with the traditional method, and check steps. With “cluster math”, the chance that the kid can re-check their own work (by going back and trying again with the same approach) to understand their error is minimal at best.
Comment by web — April 27, 2011 @ 7:18 am
I forgot to mention, I’m shocked that they let you teach anything at all. When I was in school, the job of the sub was to hand out worksheets and make sure that we didn’t misbehave too badly. No actual teaching went on…
Comment by Mike Hunt — April 27, 2011 @ 7:52 pm
Maria, I think a better way to sell textbooks is for the makers to simply lobby for laws that require that they be replaced every x-years. That was the case in Delosa. Because a ten year old book on American History from 1600-1861 is obviously woefully inadequate.
Comment by trumwill — April 28, 2011 @ 9:28 am
The problem is, “Cluster Math” is essentially dropping a bunch of numbers in front of the kid, making them get frustrated, and then eventually hoping they reach the point of the usual algorithms on their own.
Well, not exactly. At least not in Redstone, where they show both. The kids seem to really prefer Cluster Math. It makes sense, I suppose, because it keeps things simpler (at the expense of efficiency, though).
With “cluster math”, the chance that the kid can re-check their own work (by going back and trying again with the same approach) to understand their error is minimal at best.
If my (limited) observational experience is relevent, they don’t check their work. Hit a wall, start over. Two or three times before finding something that works for them.
Comment by trumwill — April 28, 2011 @ 9:32 am
Mike, things veer that way at the high school level. In K-6, and to a lesser extent 7 and 8, they let me actually teach. I think it’s one of the reasons I am more enjoying my early-school assignments more than my high school ones.
Comment by trumwill — April 28, 2011 @ 9:33 am