"Daddy, ask me a math problem."
"OK. What's 18 plus 6?"
"See, I just keep the 18 and then add 2 from the 6 to get 20. That leaves 4 from the six, and 20 plus 4 is 24."
"Right. Good work."
"Hey, SteelyKid. What's 120 plus 180?"
"I just added the hundreds to make 200, and then 80 plus 20 is 100, and then I add them all together to get 300."
"It takes a little while, though."
"Yes, but you keep practicing, and getting faster."
"Practice makes perfect!"
"That would take ten minutes, which is... six hundred seconds."
"Very good. How did you know that?"
"Well, I know that five minutes is three hundred seconds, and ten minutes is five minutes plus five minutes, so three hundred plus three hundred is six hundred."
"I'm very impressed, honey."
There's a lot of traffic on social media these days from disgruntled parents venting about their kids' math homework and how they hate the way math is being taught these days. This is mostly blamed on the Common Core standards, which were put together in response to a genuine need-- it turns out the math standards were written in part by a physics major a few classes ahead of me at Williams. (I didn't interact with him at all, as far as I can recall, and my main association with him has nothing to do with physics or math, but that's a different matter...) Parental anger about the new standards, mostly generated by the incredibly dumb way they were rolled out in a lot of places (and brilliantly spoofed on Twitter) is predictably causing politicians to flee them as fast as they can run while carrying fat sacks of cash.
Anyway, as a mild counterpoint to the massive parental ire, I thought I'd share the above conversations with SteelyKid, all from the last week or so. She's very into math-- to the point of demanding extra math problems with some regularity-- and I have been extremely impressed with her math reasoning skills, as illustrated nicely in the above. She doesn't just know a rote algorithm for adding numbers, but actually understands the meaning of the process, and cheerfully explains her reasoning. In fact, when I told her the "trick" for multiplying by ten of just adding a zero at the end, getting from 60 seconds in one minute to 600 in ten, she was unimpressed, preferring her method where she understood the steps.
Now, I don't actually know that this has anything to do with Common Core math per se. I can tell you, though, that it's not anything I taught her. This all comes from school, or possibly the after-school program at the JCC. We try to encourage her interest in math by making up problems on request, and pointing out cool math things when the opportunity arises, but haven't been doing any formal instruction at home.
So, whatever it is that they're doing in math classes these days, I'm all in favor of it. She's in first grade, and confidently adds two- and sometimes three-digit numbers, and is basically doing proto-algebra (with the "five minutes is three hundred seconds..." business, and regular problems of the form "27 minus what is 22?"). I've seen entering college students struggle with this level of stuff, because they know algorithms but don't understand the meaning.
So, anyway, thanks Common Core. More like this, please.
I think it's great that Steely Kid has such a good grasp of arithmetic.
I think the math part of Common Core has gotten such a poor reputation because of the change in terminology from what most of us adults are used to. Disclosure: I have a degree in Applied Math. Several years ago I looked at CC problems (6th grade level) and the description of how to solve them was obtuse. Probably not if you had taken grades K-5 before, but really weird abounding to someone who might have been taught by Euclid's pupils.
I do agree that there should be national standards for math and science (less so for Social Sciences), but the "optics" of Common Core was poorly handled.
CC is a set of standards that tie math concepts to grade level. "Must be able to multiply 1-digit numbers in their head by the end of grade 3" "Must understand reducing fractions by grade...", etc. It is a standard. It is not a teaching methodology or curriculum. All it says is that if a kid finishes 4th grade in Louisiana, his family can move to Minnesota and he won't be light years ahead or behind the rest of the class. It doesn't suggest any specific tools for the Louisiana teacher to use to get that kid to the right level of knowledge. All those extra techniques the kids are being shown to multiply numbers, etc. are not CC math. They are just the way some teacher has chosen to teach math. Hopefully their method leaves the kid at the standard expected by the CC at the end of their grade.
But folks need to stop blaming CC for making math look unusual.
Thank you for this post. I look forward to having more students in my college math classes with the depth of understanding that your daughter is already displaying.
In response to Jay, I should say that I have a PhD in Mathematics, but it wasn't until I started working with K-12 teachers that I began to appreciate the intellectual work of teaching math to children, as well as the deficiencies in the math education of many adults; the "terminology" we were taught may not have been effective in the long run. I often wonder if some of the complaining parents are made uncomfortable at the thought that some of their own mathematical knowledge is limited to procedures rather than the underlying concepts. Yes, depending on the state, the roll-out could have been better (Vermont is doing okay; New York not so much). Making things worse are the pre-existing odious NCLB testing requirements. But the fact remains that the CCSSM are a huge improvement.
Part of the problem with common core is people look at a specific curriculum they don't like, pull out the example of how to do a problem in a certain way, and then go "LOL, too many steps!"
Well, yeah. A teaching example of the standard algorithm (of whatever) is going to take up an entire page and look like a bajillion steps as well. It just LOOKS simple because you already know how to do it.
You should consider the very real possibility that the obtuse "CC problems" you saw SEVERAL years ago predate the CC standards, which were only released in 2010 and not adopted until a year or two ago in my state. Those were quite likely to be problems from one of the bad books out there.
Peter, you are correct that standards and curriculum are different things. I'd like to point out that CC and the curricula used are, hopefully, linked (but not always). The framers of the common core math standards wrote them to encourage number sense - not just how but why. The good curricula that are actually aligned to the CCS will help teachers teach what SteelyKid appears to be getting.
The third piece of the puzzle is teacher training (pre-service and in-service). That's a whole other bag of worms.
The distinction between curriculum and standards is an important one-- roughly speaking, the curriculum is the tool you use to attempt to meet the standards. I think the specific curriculum used in SteelyKid's school is Singapore Math (tm), for what that's worth. Current curricula are supposed to be aligned with the Common Core standards, which are somewhat different than the previous local patchwork of stuff.
The switch to Common Core was in most places accompanied by a change of curriculum, and in everyday usage, those two things have sort of been lumped together. But the general trend of looking for greater "number sense," namely an understanding of why you do particular things when adding or subtracting is a result of the standards, and common to most curricula.
The big problem in most places is that the change to Common Core and its aligned curricula was done extremely stupidly. One teacher I spoke with recently described being told in mid-August that they would be using a new curriculum starting in September. Lots of places also implemented the changes wholesale, in all grade levels at the same time, rather than phasing them in, meaning that students in upper grades suddenly found themselves expected to know things that they would've been taught in a lower grade, but hadn't learned under the previous system.
Both of these moves are idiotic, and even more frustrating for teachers than parents. They're sadly typical of a lot of what goes on in education policy, though.
"Both of these moves are idiotic..."
"...They’re sadly typical of a lot of what goes on in education policy, though."
Why? Things don't happen at random, mostly.
Thank you so much for this! As a math teacher who fully supports the CCSS, and have to admit I think I was teaching this way before the standards were introduced, we need more parents like you who have seen this improvement in the problem solving process in their children to speak up. Thank you again!
Thank YOU for this post!
For years I thought I was bad at math, but it turns out I'm really hot shit at arithmetic and I do it just like Steely Kid. I've been asked if I'm a lightning calculator and I'm much faster at basics than punching it in to a calculator. This has earned me the privilege of figuring out tips and how to split checks for all my friends. Tell her if she keeps practicing she *will* get faster and all her friends will appreciate her forever.
The controversy surrounding Common Core is not necessarily around the curriculum, or the roll out. Rather it is a concern with the circumnavigation of the American National Standards Institute (ANSI) which has an established protocol for writing standards.
According to ANSI the process of setting standards must be transparent, must involve all interested parties, must not be dominated by a single interest, and must include a process for appeal and revision. Common Core has failed in all of these aspects.
I may be wrong, but it appears to me that Common Core is simply an attempt to abscond with public education money and put it into the hands of the for-profit testing industry.