But what about baker’s dozens? 
That’s what those Kumon assholes must have used as an excuse.
If Kumon was doing 13, 17, and 19 (but not 14, 15, 16, and 18), I imagine it was because of they had a goal of 1-20, and had found those three primes to be the biggest stumbling blocks.
Wow, these are really well done.
Yes of course. Brute force memorization is not the ONLY thing they teach. They teach math but brute force memorization is a very foundational element of teaching math in those countries at this age.
Do you think there is a antagonism towards memorization in common core and the way it is being applied?
I thought that was one of the antecedents to common core. That it contained the basic principles of common core. Perhaps there isn’t a study out there. Do you have one?
I’m not an expert in Common Core. My exposure is limited to my personal experience. Speaking to other parents, my personal experience does not seem unique.
Then perhaps it’s just the teachers in my school (consistently ranked one of the best elementary schools in the state). Perhaps they are dumbing everything down so everyone can get a trophy or maybe its just September and everything will make sense in June but the sneering attitude I encountered towards memorization of multiplication tables makes me doubt it.
If you can honestly tell me that common core is better than the old way and that it is not more challenging to teach than the old way, then I will drop it. If you say that we do not lose in actual teaching efficacy what we gain in hypothetical “deep learning” then I will wait and see how things look at the end of the year. But, I am having trouble getting to that conclusion on my own based on what I have seen.
They’re pretty amazing. There’s a lot of chance for kids to really chew on the deep concepts, but it’s also structured in a way that most kids can follow. A lot of constructivist math just hopes that kids will arrive at mathematical understanding, given the appropriate playground of problems to mess around in, but in my experience that only works for about half of my students. Engage NY? It works for most all my students (with exceptions for kids with severe learning disabilities, who may reach third grade unable to add 8+1, for example).
Damuri, of course teachers use methods that are designed for teaching people who are bad at math. They’re third graders. They’re not good at math yet. If they were, we wouldn’t need math classes in schools in the first place.
Old man shouts at clouds, film at 11.
Seriously - ‘wtf is this bullshit way of teaching that isn’t exactly the way I was taught which of course can only be the One True Way to teach anything ever’.
My kids go to school in Tokyo. The math classes are amazing. Zero ‘brute memorization’ btw. Almost all the exercises are real-world / word (picture) based.
I didn’t read the whole thread, just the first page.
Personally, I like common core. It teaches math the way I was taught to do math in college. I got my bachelors degree in physics in the early 90s followed by graduate degrees in engineering and applied mathematics. I remember when I started college I could not understand how the professors and some of the graduate students could do math so quickly in their heads. I felt really intimidated and thought all the science nerds I went to school with were much smarter and quicker than I was. It was unreal. Over time, I realized that it was how they did math and thought about math, not that they had more skill or intelligence. Over time I developed the same methodology; it was implicitly taught over the 8+ years of my college education. Now when I look at a problem like 9712 or 47^2 I can quickly and easily do it in my head because I know that 9712 = 1200-36 and 47^2 = 2500-30+9. There were other, similar, tricks with division, logarithms, exponents, and trigonometry that I use as a matter of course. And when you really master linear algebra, it is amazing what you can do with systems of equations…
Anyway, I digress. When my children came home several years ago and asked for help with their math homework (they are currently in grades 10 and 8), I was pleased and surprised to see that this was exactly the way they were being taught. Instead of teaching them to do long division or the long hand multiplication I learned in the 3rd grade, they were being taught to group numbers and to factor them (if not explicitly). They were being taught to think in orders of magnitude and to take short cuts like I learned in college. I don’t really know if this is common core, or the new math, or what, but I do know that the way my daughters are being taught math is far superior to the way I was taught.
Oh, and finally, the whole 3 * 7 = 7+7+7 and not 3+3+3+3+3+3+3 is an internet meme and just bullshit. I have never seen a teacher over the last whatever years that would have marked that wrong on my children’s homework.
That was “new math”, a math curriculum designed by mathematicians to give students a better basis for moving into mathematics and math-intense disciplines in science and engineering. Which is different from just learning enough core concepts to get by. (New Math was in reaction to the idea that students didn’t really need any math at all, because their teachers had managed to get by without understanding or using any.)
Common core is supposed to make students better citizens, on the basis that productive citizens need a basic understanding of core concepts. And it’s not trying to achieve anything so highfalutin as better mathematicians :). CC wasn’t so much a reaction to an idea, it was a reaction to confusion and ignorance.
Your math is off.
I’m gonna be ornery.
I get what you’re saying, but when I talk about someone being good at math, I mean more than that they have a lot of training in theorems and algorithms: I mean that they understand new ideas quickly and are capable of playing with numbers and drawing generalizations. A six-year-old who notices that whenever you add two even numbers you get another even number, and who can explain that that’s because even numbers are a bunch of pairs, and if you add some more pairs you’ll still have a bunch of pairs, is in one sense far better at math than a 20-year-old making a solid B- in their calculus class.
Common Core works best with kids who can think deeply. The goal is to get all kids there, but I haven’t always had that experience.
You haven’t, but I have. I’ve actually, very calmly, corrected that misapprehension in a co-worker who is in most respects a spectacular teacher.
I may be misunderstanding what you’re saying, but if I’m not, you’re wrong. Common Core is 100% trying to make kids better mathematicians. It’s not necessarily trying to turn them into professional mathematicians, so maybe that’s what you mean, but it’s absolutely trying to make them into human beings who can do math better.
That, or he made a typo.
Yup. I think I see what he was going for, maybe:
47^2=
47* 47=
(50-3)(50-3)=
2500-2(503)+9=
2500-300+9=
2209
So, he left out the final 0 in “300.”
It took me figuring the whole thing out using a method I wouldn’t normally use (I’d’ve done 2500-350-347) to see the typo, though; my first reading was just that his math was totally off.
Do your kids go to school in the Japanese public school system?
ninja’d
I would have done the same as you 2500-350-347.
That seems a lot easier than (50-3)*(50-3)
5050
-350
-350
-3-3
Wow, that is a sad thing; I am sorry you had that experience.
Yep, typo.
That’s an interesting way to do it, I had not thought of that before. Still, multiplying 3 times 47 is a pain (IMHO), I think I will stick with my expansion.
YMMV (obviously).
47^2 = (50-3)47 = 5047 - 347 = 50(50-3) - 347 = 50^2 - 350 - 3*47
This seems more convoluted than (a-b)^2 = a^2 + b^2 - 2ab.
But whatever works for you.
This was one of the main things that I always told my kids (to their teachers horror): not all the methods they were being taught were necessarily the best methods.
While that’s true, there are ways to say that that would really piss me off as a teacher. The methods we teach can fill several niches:
-They might be inefficient, but help children understand what’s going on with a particular operation. Drawing squares, lines, and dots to represent addition, or using a number line to represent subtraction aren’t intended to be the final methods that a student graduates high school using; however, when they’re first learning the operations, they represent different aspects of the operations. (Squares/lines/dots relate to base 10 blocks and help students move from a concrete understanding of place value to a semiabstract understanding; number lines are amazing for demonstrating the relationship between addition and subtraction).
-They might be inefficient, but allow a struggling child to get the right answer. If a kid can’t use the vertical algorithm to add 387+479, they might still add 300+400, and 80+70, and 7+9, then add 700+150+16 to get 866.
-They might be inefficient for some problems but efficient for others. Adding up to solve a subtraction problem is a real dumb approach for 738-401, but it’s a great approach for 403-296.
I rarely have parents who tell their kids to ignore what I teach them in class in favor of methods they teach at home. It’s much more common for parents to come to conferences with a gleam in their eye, telling me how they’re gonna teach their kids to borrow whether I like it or not. The latter parents are generally easy to win over, when I tell them how great it is to know how to borrow, but that I want their kid to have multiple ways to visualize and understand and solve math problems.
I never told my kids to ignore their teachers, you guys are the professional teachers, not I. On the contrary, I would tell them to do it exactly the way the teacher instructed. I would try to deduce what knowledge the teacher was trying to instill in them and explain it and include a guess on why the teacher was trying to teach it. I thought the number lines and square/lines/dots were brilliant! Sometimes (usually if they were struggling with it or had leaped ahead), I would share why I thought it was inefficient (if I thought it was) and share what I thought were better methods. Sometimes my kids would not understand my method or would struggle with it and I would try to teach them an alternative (like adding up to do subtraction). The vast majority of the time, my kids would just follow the instructions of the teacher happily with no problems. I never taught my children to favor one method over others (at least I hope I didn’t), I tried instead to teach them that there are a lot of ways to look at math and they should try to learn them all as I always found it amazing to find new methods.
Both my daughters love math and do well in it. They very rarely come to me for help anymore; neither of them seem to need it :(. Hopefully I did not scar them too badly with my overactive parental involvement. They both claim that math is their favorite subject, but I doubt that either of them will go into science or math as a career.