No, I’m saying some teachers are teaching the NEW math poorly.
What statistical innumeracy?
I don’t think you need a strong math background to grokk this stuff. I’m not opposed to paying teachers more, in fact I am decidedly in favor of it. And its not a teacher’s job to be fascinated by elementary school math. its their job to get their students fascinated by it.
Why not both?
Common Core sounds like something that has been around for over a decade and we STILL have trouble implementing it. That sounds like a problem.
WTF??!?! How the fuck is common core a liberal thing? Just because its stupid doesn’t mean you have to take ownership of it.
Is THAT what’s causing this inexplicable defense of the stupidity? political tribalism?
I talked to the teacher. I talked to the principal. They both displayed a very obvious contempt for memorization as a form of learning. They both seemed to think that studying more than assigned was borderline cheating. My dedication to public education might not survive, I’ll probably still support it in principle but not dogmatically so.
Not just algebraic concepts, I’ve seen the occasional straight out algebra problem on 3rd grade math homework. And this isn’t some advanced class. My kid struggles with math.
When my kid started bringing home common core type homework in the 2nd grade, I was all WTF too. But then I made the effort to find out why they were teaching the way they were, it started to make sense.
The funniest thing about about the OP’s complaint is that something that he couldn’t grasp is “dumbing down” America. It’s really the opposite. Kids are being taught concepts that will help them when the math gets more advanced. How well this will end up working remains to be seen, but it sure isn’t dumbing down the subject matter.
Unless you think that all teachers taught old math well*–which would of course be a very stupid thing to think–the supposed disagreement you have with me is very stupid.
“New Math,” the song, is a little over half a century old now. There’s an animated version of it, and anyone who watches it who’s younger than Lehrer will be, if they pay attention closely enough, a little taken aback by the weird way they used to teach addition, as compared to the totally sensible methods he’s mocking in the song.
Same thing is going on here.
Story about how folks used to teach math: back around 2005 I visited my math-teacher friend one Friday evening, asked him how his day was. He blew out a frustrated sigh. He’d been teaching a remedial math class to elementary school teachers who sucked at math. One teacher close to retirement absolutely refused to accept what he told her about fractions. “I’ve been teaching for twenty years,” she said defiantly. “I know that 1/2 + 1/2 = 2/4: you add the tops and add the bottoms. And there’s no way you can persuade me different.”
He, of course, drew two halves of a pizza, and then 2/4 of a pizza, and asked her if they were the same thing. “No, of course not,” she said, “That’s a whole pizza. But that’s different.”
So any theory about how Common Core math is harder to teach, or results in poorer understanding by teachers, runs into a little bit of a problem with me.
I don’t understand the way my kids are taught to do math, but it’s very clear that they do and that they understand math considerably better than I, or my peers, did at a comparable age.
Well I don’t know that its particularly liberal, but the opposition against it sure seems to be strongest among conservatives. I think its a combination of, “this is the way I learned it so that is the way it is” close mindedness, and also an opposition to learning about evolution and an honest look at American history
Good. Memorization is a superficial way to learn. Far better to have a firm understanding of the concept involved than just regurgitation. As I said above, if all you want to know is what 7*3 is you can google it.
The schools I attended years ago had contempt for rote memorization as well: it was thought to be more important to understand the underlying concepts. This has been US pedagogy for decades. During the 1980s, Japan issued reports that their students did too much rote learning: they thought this led to uncreative workers later on.
As for studying more than what is assigned amounts to borderline cheating: wow, that does suck. My sympathies. That’s awful. Yes, yes, I’m sure they have their reasons. Still a bad thing.
The US education system isn’t great. Our elementary schools are getting better, our high schools are weak, our colleges are top notch. Our technological base is second to none, at least for the moment. All levels could benefit from continuous process improvement.
I had this conversation Friday with my students, where we watched a video talking about the brain science of learning maths (it was British). The video encouraged students to regard maths as a process of understanding, not of memorization.
Afterwards, I disagreed with the video.
Sure, it’s not enough to memorize that 6x7=42, because then you’ll have trouble contextualizing it in real-world problems, and in applying the principles of multiplication you’ve learned for whole numbers to other number sets. Model it with repeated addition, with arrays, with drawings of groups, with the area of rectangles; make connections; visually represent with arrays that 6x7=(5x7)+(2x7).
That’s all incredibly important.
But when you’ve moved on to solving problems like 372x648, where there are nine different multiplication problems embedded, you don’t want to be doing repeated addition for each one. You want to know that 6x7=42, without thinking about it.
Memorization, as I see it, is not the essence of math–but it is another cognitive tool, just like using a number line is a cognitive tool, or counting on your fingers is a cognitive tool. Add memorization to your toolbelt, and you’re gonna have an easier time following the three rules of choosing a method to solve a problem.
We started teaching our son math using Singapore Math before he started Kindergarten, mostly because he really liked math. Singapore math is the math curriculum they use in Singapore. It’s very popular with homeschoolers in the states. It’s not exactly common core–for example, multiplication and division start much, much earlier–but it is very “common core-ish” in the sense that it is very focused on core mathematical concepts–which includes a lot of mental meth approaches. We are a couple years in, and there’s never been anything about memorization–but all the mental math and conceptual thinking naturally leads to it. My son is not quite 7 and I think he probably has all his times tables to 5 memorized just because they get used so much–and he can deduce the bigger ones quickly because he’s been taught to build them out of smaller ones (like, “8*4 is two 16s, that’s . . .32” It’s not quite instant, but it’s really fast).
My son’s bright, but he’s not off the charts. The way Singapore teaches math is nothing like the “old way” here in the US. Common Core, near as I can tell, uses principals more more aligned with how the countries with more successful math programs teach math.
So my problem isn’t with Common Core, its with bad teachers?
OK, I can buy that.
However, these particular teachers seem to have drunk the cool aid on common core. When I explained that my kid (and several other kids in her class) was doing long multiplication and division, her specific comment was “I am not impressed that some child has been drilled to be able to do long multiplication or division, that’s not real learning”
She spoke of a “deep understanding of math” and proceeded to explain how these kids who could multiply and divide had no greater an understanding of even and odd numbers than the kids who couldn’t do multiplication. They didn’t REALLY understand what they were doing.
These kids are getting bored to tears drawing dots on graph paper and other common core exercises that seem geared towards the mathematically challenged.
The problem with the OP is that the problem "73=?" is badly expressed. If A=B and B=C, then A=C. Therefore 73=3+3+3+3+3+3+3=7+7+7=21, and both 73=3+3+3+3+3+3+3 and 73=7+7+7 are correct. What they meant was "how many 3s do you add together to get 7*3’.
AFAICT common core does not present a different way of reading. The vowels are still randomly scattered throughout the alphabet. Through, tough, plough, thought all still pronounce the “ough” differently and never the way you would think if you were just learning how to read.
History doesn’t seem any different (I don’t know where they are teaching history differently but having only ever lived in cities, I don’t notice the difference).
Life sciences seem to have more environmental stuff and more global warming stuff but the scientific method hasn’t really been fiddled with.
Math on the other hand is being taught entirely differently. There is a particular antipathy for memorization in math.
Memorization is one of the cornerstones of learning and knowledge. Sure critical thinking is important but you can’t reinvent the wheel every day.
This disdain for memorization is a bad idea. Just like muscle memory slows down a game and gives you the bandwidth to develop situational awareness and more time to think about what you are doing, “math memory” (or simply “memory”) allows you to see more relationships between numbers that you would take a longer time noticing because you are sitting there drawing dots on graph paper.
Apparently there are teachers who disagree with this disdain for memorization and are in fact teaching kids to memorize the multiplication table by renaming the multiplication table “math facts” to avoid the appearance of promoting memorization.
I don’t think the problem is necessarily too much rote memorization so much as it is too little critical thinking. And almost NO lateral thinking.
They mentioned it during the orientation. There is a pretty good magnet school in my area and admissions is largely based on a test. A lot of kids go to after school programs like Kumon from an early age. These kids get into the gifted program more frequently, they get into the magnet school more frequently. This is seen as a form of cheating because they are getting more than their share of seats in these programs. There is a slightly racist undercurrent to this antipathy, these programs have gone from majority white to majority Asian.
Of course. I don’t think anyone would disagree. I’m just not sure that having all the kids kids draw dots on graph paper for a month is an improvement in the process.
Singapore’s math curriculum is a little unique in Asia. Places like Korea, Taiwan and Japan have a lot of brute force memorization. They almost take it from the other direction. Rather than learning the principles and having the repetition of the principles develop into a memory of the tables, through the memorization of these tables, they start to internalize the relationships between the numbers. They extrapolate the principles from the rote memorization.
I will bet dollars to donuts that 100 random Taiwanese, Korean and Japanese students who have learned math largely through rote memorization (after being exposed to the principles and theories) will understand math better than 100 random US students who learned it the common core way.
I do teach my kids to fail forward–that making a mistake isn’t normally a big deal as long as you can figure out what went wrong, so you can try to avoid that kind of mistake in the future. And I make mistakes, and I reward kids who catch me at it (I have terrible memories from school of catching teachers making dumb mistakes and getting scowled at for correcting them).
I might make a mistake like that in front of the class. If I did, I’d stop and look at it. Again, I said:
6x7=(5x7)+(2x7)
I correctly remembered that I could break 7 into 5 and 2; that’s a great strategy. But I didn’t pay attention to my factors. I should have multiplied the 5 and 2 by 6, not by 7. It’s important to make sure that you multiply the factor you broke apart by the one you kept whole. So I should’ve written:
6x7=(6x2)+(6x5)
I’m sure y’all knew all that–but that’s, very roughly, how I’d teach it. I’d also show them what I meant with arrays, something like this:
XXXXXX
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=
XXXXXX
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only on a board, where I could show them and move things around and such.
