Common core made an effort to teach kids to think about numbers this way and people flipped the fuck out because that wasn’t how they were taught. Still mad about that.
The problem with common core math was not that they taught these techniques. It’s that they taught exclusively these techniques. These techniques are born from the meta manipulation of the numbers which comes when you have an understanding of the logic of arithmetic and see the patterns and how they can be manipulated. You need to understand why you can you “borrow” 1 from the 7 or the 9 to the other number and get the same answer, for example. It makes arithmetic easier for those who do it, yes, but only because we understand why you are doing it that way.
When you just teach the meta manipulation, the technique, without the reason, you are teaching a process that has no foundation. The smarter kids may learn to understand the foundational logic from that, but many will only memorize the rules they are taught without that understanding of why and then struggle to build more knowledge without that foundation later.
Math is a subject where each successive lesson is built on the previous lessons. Without being solid on your understanding, it is a house of cards waiting to fall.
When I was tutoring, i had a few elementary-school aged kids. They’d have homework where they had to do the problems three or so different ways, using each of the methods that they were taught (one of which was always the way I was taught when I was their age). I actually feel like I learned a lot from them, as there were some interesting tricks that I didn’t know before helping with the homework. I think that’s a really good way to approach it, because a kid may struggle with some of the methods but generally was able to “get it” with one of them, and which method was “the best” was entirely dependent on the kid. For me, being able to see which methods clicked and which ones didn’t helped me be more effective as a tutor, too, since it showed me a bit more about how their individual little brains were working.
But I agree, if you’re not also at least trying to explain why the different methods get you the same answer, it can lead to problems down the line. Some of them saw the “why” for themselves after enough time working at it, and some needed a bit more external guidance (which, considering they were coming to me for tuturoing, I guess they weren’t getting at school). My argument would be that no one really taught me “why” when I was in school learning The One Way to do math either. I still had to figure out little tricks that worked for me on my own, since my brain is kinda weird. It may not have taken me so long to believe that i’m actually pretty damn good at math if I’d done those kids’ homework when I was their age, as i would have had more tools in the toolbox to draw from.
To add to this, people come up with math tricks all the time but you then have to check it against the manual method, and often multiple times with different numbers, before you can connect the manual process to the trick for later use.
In my opinion I don’t think you can teach just the trick side of it, if thats what common core is.
The difference would just be how you think of the process. I sometimes shuffle around the numbers to make math easier, but the shortcut for adding 9s just feels different. Instead of 9+7 = 10 + 6, it’s more like 9+7 = 17-1. It feels less like solving it with math and more like using a cool trick, since you didn’t really use addition to solve the addition problem.
Sort of, same numbers different logic. Its like mixing up the order of operations. You could learn both tricks but it seems redundant if they do the same thing. Like having two of the same hammer.
And it scales with multiplication too. 9*7 is (7-1) and whatever adds to9, so 63. This breaks down for larger numbers, but works really well up to 9*10. I don’t know what “common core” teaches for that, but you can’t change the 9 to a 10 for multiplication (well, you could, but you’d need to subtract 7 from the answer).
Treating 9s special makes math a lot easier. Doing the “adjust numbers until they’re multiples of 10” works for more, but it’s also more mental effort. 9s show up a lot, so learning tricks to deal with them specifically is nice. I just memorized the rest instead of doing “common core” math to adjust things all the time.
That said, I do the rounding thing for large numbers. If I’m working with lots of digits, I’ll round to some clean multiple of 10 that divides by 3 (or whatever operation I need to do) nicely. For example, my kid and I were doing some mental math in the car converting fractional miles to feet (in this case 2/3 miles to feet). I used yards in a mile (1760) because it’s close to a nice multiple of three (1800), and did the math quickly in my head (1800 - 40 yards -> 6002 yards - 40 yards to ft * 2/3 -> 1200 yards - 120 ft2/3 -> 3600 ft - 80 ft -> 3520 ft). I calculated both parts of the rounding differently to make them divisible cleanly by 3. I don’t know what common core math teaches, but I certainly didn’t learn this in school, I just came up with it by combining a few tricks I learned largely on my own (i.e. if the digits add to 3, it’s divisible by 3) through years of trying to get faster at math drills. If I wasn’t driving, I would have done long division in my head, but I needed to be able to pause at stop signs to check for traffic and whatnot, and just remembering two numbers w/ units is much easier than remembering the current state of long division.
You are literally responding to a comment about how our education system is now teaching kids to understand the basic fundamentals of mathematics instead of just rote learning methods.
Common core made an effort to teach kids to think about numbers this way and people flipped the fuck out because that wasn’t how they were taught. Still mad about that.
The problem with common core math was not that they taught these techniques. It’s that they taught exclusively these techniques. These techniques are born from the meta manipulation of the numbers which comes when you have an understanding of the logic of arithmetic and see the patterns and how they can be manipulated. You need to understand why you can you “borrow” 1 from the 7 or the 9 to the other number and get the same answer, for example. It makes arithmetic easier for those who do it, yes, but only because we understand why you are doing it that way.
When you just teach the meta manipulation, the technique, without the reason, you are teaching a process that has no foundation. The smarter kids may learn to understand the foundational logic from that, but many will only memorize the rules they are taught without that understanding of why and then struggle to build more knowledge without that foundation later.
Math is a subject where each successive lesson is built on the previous lessons. Without being solid on your understanding, it is a house of cards waiting to fall.
When I was tutoring, i had a few elementary-school aged kids. They’d have homework where they had to do the problems three or so different ways, using each of the methods that they were taught (one of which was always the way I was taught when I was their age). I actually feel like I learned a lot from them, as there were some interesting tricks that I didn’t know before helping with the homework. I think that’s a really good way to approach it, because a kid may struggle with some of the methods but generally was able to “get it” with one of them, and which method was “the best” was entirely dependent on the kid. For me, being able to see which methods clicked and which ones didn’t helped me be more effective as a tutor, too, since it showed me a bit more about how their individual little brains were working.
But I agree, if you’re not also at least trying to explain why the different methods get you the same answer, it can lead to problems down the line. Some of them saw the “why” for themselves after enough time working at it, and some needed a bit more external guidance (which, considering they were coming to me for tuturoing, I guess they weren’t getting at school). My argument would be that no one really taught me “why” when I was in school learning The One Way to do math either. I still had to figure out little tricks that worked for me on my own, since my brain is kinda weird. It may not have taken me so long to believe that i’m actually pretty damn good at math if I’d done those kids’ homework when I was their age, as i would have had more tools in the toolbox to draw from.
To add to this, people come up with math tricks all the time but you then have to check it against the manual method, and often multiple times with different numbers, before you can connect the manual process to the trick for later use.
In my opinion I don’t think you can teach just the trick side of it, if thats what common core is.
There’s
peoplealiens who would add 9+7 instead of 10+6 or 8+8 in their heads?I do, because 9 plus anything is just a 1 in front of the other digit minus 1.
Weirdly enough, I just thought about using the methods here for the first time in my life earlier today. Weird.
This is also how it works in my head, but isn’t it the same as the other guy was saying, 10+6?
The difference would just be how you think of the process. I sometimes shuffle around the numbers to make math easier, but the shortcut for adding 9s just feels different. Instead of 9+7 = 10 + 6, it’s more like 9+7 = 17-1. It feels less like solving it with math and more like using a cool trick, since you didn’t really use addition to solve the addition problem.
Sort of, same numbers different logic. Its like mixing up the order of operations. You could learn both tricks but it seems redundant if they do the same thing. Like having two of the same hammer.
And it scales with multiplication too.
9*7is(7-1) and whatever adds to 9, so 63. This breaks down for larger numbers, but works really well up to9*10. I don’t know what “common core” teaches for that, but you can’t change the 9 to a 10 for multiplication (well, you could, but you’d need to subtract 7 from the answer).Treating 9s special makes math a lot easier. Doing the “adjust numbers until they’re multiples of 10” works for more, but it’s also more mental effort. 9s show up a lot, so learning tricks to deal with them specifically is nice. I just memorized the rest instead of doing “common core” math to adjust things all the time.
That said, I do the rounding thing for large numbers. If I’m working with lots of digits, I’ll round to some clean multiple of 10 that divides by 3 (or whatever operation I need to do) nicely. For example, my kid and I were doing some mental math in the car converting fractional miles to feet (in this case 2/3 miles to feet). I used yards in a mile (1760) because it’s close to a nice multiple of three (1800), and did the math quickly in my head (1800 - 40 yards -> 6002 yards - 40 yards to ft * 2/3 -> 1200 yards - 120 ft2/3 -> 3600 ft - 80 ft -> 3520 ft). I calculated both parts of the rounding differently to make them divisible cleanly by 3. I don’t know what common core math teaches, but I certainly didn’t learn this in school, I just came up with it by combining a few tricks I learned largely on my own (i.e. if the digits add to 3, it’s divisible by 3) through years of trying to get faster at math drills. If I wasn’t driving, I would have done long division in my head, but I needed to be able to pause at stop signs to check for traffic and whatnot, and just remembering two numbers w/ units is much easier than remembering the current state of long division.
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You are literally responding to a comment about how our education system is now teaching kids to understand the basic fundamentals of mathematics instead of just rote learning methods.
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