Common Core math problem with easy solution
- Thread starter Monello
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kom526
They call me ... Sarcasmo
My (K-Teacher) wife and I were just talking about this scenario just this weekend. She took a 6 week certification maintenance class this summer that was all common core mathematics. It was ridiculous. I actually had her try and teach me how to solve a CC problem and it suuucked. Granted, I was taught the rote method and my brain wanted to use that method, but I finally grasped the concept. The concept is terrible and convoluted, but I managed to 'get it'. I do not agree with CC but it is the new 'Standard'.
somdfunguy
not impressed
I'm in Virginia, one of the few states that hasn't adopted it. I'm hoping it stays that way.
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intertidal
New Member
The teachers hear all the complaints and get all the blame - which should, by right, go to the politicians who gave out big contracts to their friends for selling Common Core, just the latest fad sold so some consultants could get rich. Not only is it stupid, but we all paid for it with taxes (and worse, your wife with her time).
kom526
They call me ... Sarcasmo
I said something to that effect to her. "There were a bunch of guys at NASA that put men on the moon using rote mathematics." (And circular slide rules) To piggyback on Intertidal's comment, she did state that this is her 4th set of curriculum standards in 21 years.
#corporateeducation
LibertyBeacon
Unto dust we shall return
Apparently the person who wrote that piece of paper has been perverted by Common Core English. I think "old fashioned" is the word he was seeking.
intertidal
New Member
I said something to that effect to her. "There were a bunch of guys at NASA that put men on the moon using rote mathematics." (And circular slide rules) To piggyback on Intertidal's comment, she did state that this is her 4th set of curriculum standards in 21 years.
I could not do what your (and my) wife do every day. They are the only ones who care about the kids and learning - and they get all the abuse from every side.
The other part of the story of selling these fads is the lucrative selling of "assessments" - usually by sole source, to assess the foolish fads. You see it all the time at the BPW in Annapolis. I have to congratulate the slimy politicians - they have won by convincing the idiots among us that its all the fault of those rich teachers and their generous (in MD?) pensions while they spend taxpayer money to enrich their corporate buddies peddling this garbage.
intertidal
New Member
Yes. Perhaps she was tired after writing it, along with many other problems, over 200 times at night while also juggling the needs of her own family.
Larry Gude
Strung Out
What the flying hell???
Where does this come from? I am curious how this works out in class because that appears to take a LOT more thought than the 'old fashion'.
LibertyBeacon
Unto dust we shall return
I'm sure that's it. Writing a few words on a piece of paper is decidedly exhausting.
Radiant1
Soul Probe
I was horrible at math in school. I taught myself what amounts to the common core and can do math easier and faster in my head now. I think the concept will pay off it's just that trying to learn the method in the early stages on paper sucks (not to mention looks ridiculous to us old fashiioned folks). Who knows, in the future we may have a generation of kids who can whip off numbers out of their head in mere seconds, and wouldn't that be nice?
Isn't that the American way?
..... she did state that this is her 4th set of curriculum standards in 21 years.
indeed you have 'invent' a new method every few yrs, otherwise you cannot sell new text books
mAlice
professional daydreamer
Can you?
Tilted
..
I've never looked into how common core teaches math. So I'm saying from the jump that I'm not sure what its general strategy is and thus whether that strategy makes sense.
That said, the question posted in the OP - and the thought process it seems to be testing and which it seems to be based on - makes sense. We use a base 10 numerical system. Whether people realize it or not, the calculations they do rely on that base 10 nature of our numerical system. The way that problem is asking the child to find the answer is, more or less, the way we all come up with that answer or similar, but more complex, answers.
Yes, for really easy calculations like that one the answer is more like common sense. What's 8 + 5? Well, 13 of course. For that problem, it would be easier to just say the answer is 13. But why is that the answer? How do we just know that 8 + 5 equals 13? Our brains got there somehow. Well, it's through understanding the base 10 nature of our numerical system and having memorized certain basic arithematic calculations. That's really the only way we can calculate such things. We remember that 7 + 3 equals 10 and that 6 + 4 equals 10 and that 6 - 2 equals 4, and we understand (to different degrees) that our system is base 10; and based on those simple points of knowledge we're able to figure out what 118 + 206 is. That one we don't (typically) just remember, we have to calculate it (though perhaps still subconsciously and essentially instantly).
It seems to me that the methodology on display in the test from the OP (if that's what common core does, I'm not sure it is) is just trying to have children learn by being more consciously aware of the process they're using - the same process that others are using, though subconsciously and without understanding that that's the process they're using. And of course when teaching such things we start by using very simple problems - so, our common sense tells us those problems are easy and then we jump to the notion that it's silly thinking about such simple calculations that way (i.e. by considering and manipulating them based on the base 10 nature of our numerical system). It may seem silly for such easy problems, but that's how you learn and recognize what's really going on. And, again, that's more or less how all of us do calculations. We have to, else there's no way to get to the answers save having memorized all of them.
When I see the number 984, I see the number 984. But when I've some need to do a calculation based on it - addition or subtraction or even multiplication or division - I don't see it as 984; I see it as a thousand that's missing 16, and I see that missing 16 as a 10 with an extra 6. When I see 2,118 my mind understands it as 2 thousands with an extra 100, an extra 10 and an extra 8. So when I need to add those 2 numbers together (or add 20 similar numbers together), I sum them up based on their base 10 components and thus can do it very fast. The same thing when I'm, e.g., multiplying them - 984 x 19 is 20 x 1000 minus 20 times 10 minus 20 times 6 minus 1 times 984. My brain remembers all those individual base 10 calculations so it can complete the process within a couple seconds and mostly automatically. I'm guessing, though again not sure, that's the kind of efficiency that teaching this thought process is trying to create. And understanding the base 10 nature of our numerical system (and taking advantage of it) doesn't just increase our speed, it also increases accuracy as initial errors tend to stand out.
Anyway, the point is that what that question is asking the child to do is not some crazy weird thing. It's what everyone does (though often subconsciously) when they perform calculations, at least more complex ones. They're just walking kids through that process and getting them to be more aware of it rather than taking it for granted. I think, if kids understand it better at a younger age, they're more likely to be more mathematically competent as they grow older. As it is, it seems to me that our population in general is woefully mathematically incompetent. And, perhaps even worse, people seem scared of math - it's like they recognize that they don't get it and it makes them feel stupid. Surely it's better if we equip children with the tools - e.g. a better understanding of what's really going on in their heads when they try to do calculations - to not be so insecure when it comes to math. We can't get around math, it's the language through which the universe interacts with itself and with us. We ought to be better at it than we are.
Again, I'm not sure if common core is the answer - I don't know what it's all about. But the thought process asked for in the OP seems reasonable to me. It's because I understand the simple realities behind simple calculations (which common sense alone would allow me and others to do even without being consciously aware of the underlying process) that I'm able to do more complex ones quickly and in my head.
That said, the question posted in the OP - and the thought process it seems to be testing and which it seems to be based on - makes sense. We use a base 10 numerical system. Whether people realize it or not, the calculations they do rely on that base 10 nature of our numerical system. The way that problem is asking the child to find the answer is, more or less, the way we all come up with that answer or similar, but more complex, answers.
Yes, for really easy calculations like that one the answer is more like common sense. What's 8 + 5? Well, 13 of course. For that problem, it would be easier to just say the answer is 13. But why is that the answer? How do we just know that 8 + 5 equals 13? Our brains got there somehow. Well, it's through understanding the base 10 nature of our numerical system and having memorized certain basic arithematic calculations. That's really the only way we can calculate such things. We remember that 7 + 3 equals 10 and that 6 + 4 equals 10 and that 6 - 2 equals 4, and we understand (to different degrees) that our system is base 10; and based on those simple points of knowledge we're able to figure out what 118 + 206 is. That one we don't (typically) just remember, we have to calculate it (though perhaps still subconsciously and essentially instantly).
It seems to me that the methodology on display in the test from the OP (if that's what common core does, I'm not sure it is) is just trying to have children learn by being more consciously aware of the process they're using - the same process that others are using, though subconsciously and without understanding that that's the process they're using. And of course when teaching such things we start by using very simple problems - so, our common sense tells us those problems are easy and then we jump to the notion that it's silly thinking about such simple calculations that way (i.e. by considering and manipulating them based on the base 10 nature of our numerical system). It may seem silly for such easy problems, but that's how you learn and recognize what's really going on. And, again, that's more or less how all of us do calculations. We have to, else there's no way to get to the answers save having memorized all of them.
When I see the number 984, I see the number 984. But when I've some need to do a calculation based on it - addition or subtraction or even multiplication or division - I don't see it as 984; I see it as a thousand that's missing 16, and I see that missing 16 as a 10 with an extra 6. When I see 2,118 my mind understands it as 2 thousands with an extra 100, an extra 10 and an extra 8. So when I need to add those 2 numbers together (or add 20 similar numbers together), I sum them up based on their base 10 components and thus can do it very fast. The same thing when I'm, e.g., multiplying them - 984 x 19 is 20 x 1000 minus 20 times 10 minus 20 times 6 minus 1 times 984. My brain remembers all those individual base 10 calculations so it can complete the process within a couple seconds and mostly automatically. I'm guessing, though again not sure, that's the kind of efficiency that teaching this thought process is trying to create. And understanding the base 10 nature of our numerical system (and taking advantage of it) doesn't just increase our speed, it also increases accuracy as initial errors tend to stand out.
Anyway, the point is that what that question is asking the child to do is not some crazy weird thing. It's what everyone does (though often subconsciously) when they perform calculations, at least more complex ones. They're just walking kids through that process and getting them to be more aware of it rather than taking it for granted. I think, if kids understand it better at a younger age, they're more likely to be more mathematically competent as they grow older. As it is, it seems to me that our population in general is woefully mathematically incompetent. And, perhaps even worse, people seem scared of math - it's like they recognize that they don't get it and it makes them feel stupid. Surely it's better if we equip children with the tools - e.g. a better understanding of what's really going on in their heads when they try to do calculations - to not be so insecure when it comes to math. We can't get around math, it's the language through which the universe interacts with itself and with us. We ought to be better at it than we are.
Again, I'm not sure if common core is the answer - I don't know what it's all about. But the thought process asked for in the OP seems reasonable to me. It's because I understand the simple realities behind simple calculations (which common sense alone would allow me and others to do even without being consciously aware of the underlying process) that I'm able to do more complex ones quickly and in my head.
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This makes my head explode and makes absolutely no sense to me. I remember back in 1975/6 timeframe that the next great math thing was to drop our American way of doing math and convert to all metrics instead. Fortunately, that fell to the wayside rather quickly.
Amused_despair
New Member
stubbornly refusing to adopt the Metric System isn't actually a bragging point for us. Maybe we woub't slam our spacecraft into the surface of Mars if we totally adopted the Metric system?
Radiant1
Soul Probe
Haha, NO! BUT, I can do it a hell of a lot faster than I used to, which makes my life a bit easier. Maybe I could whip the numbers out faster had I learned it from the get go, who knows. :shrug: