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As someone who has a pretty extensive math background, I can say that the conceptualization of what Common Core is trying to do is not often understood by most but I can appreciate its approach. One of the problems with the way math was taught in my elementary, junior high, and high school was that it taught rote memorization of approaches to mathematical problems rather than actually understanding why we were doing something.
Common Core teaches a conceptualization and true understanding of the depth of mathematics and its explanation of reality.
For example:
What we learned: Two negatives equal a positive (Fine. We get that. But why? Other than just memorizing that fact, do you really understand why? Maybe you do now that you're much older but did it make sense to you 'back then' other than it was just an easy thing to remember?)
What Common Core teaches: That there is an actual separation right or or left of two numbers such that trying to subtract a negative number literally moves you in the opposite direction on that number line.
That a lot of adults in this day and age don't get it or are frustrated with it is a testament to the fact that we learned rote memorization and don't truly understand the underlying concepts of the numbers and pure mathematics. Common Core, from a purified mathematical standpoint, is probably the better of the two - even though it's not exactly intuitive to us who were never taught pure mathematics.
As someone who has a pretty extensive math background, I can say that the conceptualization of what Common Core is trying to do is not often understood by most but I can appreciate its approach. One of the problems with the way math was taught in my elementary, junior high, and high school was that it taught rote memorization of approaches to mathematical problems rather than actually understanding why we were doing something.
Common Core teaches a conceptualization and true understanding of the depth of mathematics and its explanation of reality.
For example:
What we learned: Two negatives equal a positive (Fine. We get that. But why? Other than just memorizing that fact, do you really understand why? Maybe you do now that you're much older but did it make sense to you 'back then' other than it was just an easy thing to remember?)
What Common Core teaches: That there is an actual separation right or or left of two numbers such that trying to subtract a negative number literally moves you in the opposite direction on that number line.
That a lot of adults in this day and age don't get it or are frustrated with it is a testament to the fact that we learned rote memorization and don't truly understand the underlying concepts of the numbers and pure mathematics. Common Core, from a purified mathematical standpoint, is probably the better of the two - even though it's not exactly intuitive to us who were never taught pure mathematics.
Kids in K-12 are not taught pure Math. Most cannot explain "why". Most don't care why either.
They just want you to tell them what to do so they can get it done.
As someone who has a pretty extensive math background, I can say that the conceptualization of what Common Core is trying to do is not often understood by most but I can appreciate its approach. One of the problems with the way math was taught in my elementary, junior high, and high school was that it taught rote memorization of approaches to mathematical problems rather than actually understanding why we were doing something.
Common Core teaches a conceptualization and true understanding of the depth of mathematics and its explanation of reality.
For example:
What we learned: Two negatives equal a positive (Fine. We get that. But why? Other than just memorizing that fact, do you really understand why? Maybe you do now that you're much older but did it make sense to you 'back then' other than it was just an easy thing to remember?)
What Common Core teaches: That there is an actual separation right or or left of two numbers such that trying to subtract a negative number literally moves you in the opposite direction on that number line.
That a lot of adults in this day and age don't get it or are frustrated with it is a testament to the fact that we learned rote memorization and don't truly understand the underlying concepts of the numbers and pure mathematics. Common Core, from a purified mathematical standpoint, is probably the better of the two - even though it's not exactly intuitive to us who were never taught pure mathematics.
This is what a lot of edu-formers do not get. This is great, teaching the why. But they don't understand that one size does not fit all. They don't understand that half of the students are just not mentally geared to complete this new standard. This Common Core is going to benefit kids like mine. Reasonably intelligent, middle class white, concerned and involved parents and most importantly..a willingness to learn.
This is what a lot of edu-formers do not get. This is great, teaching the why. But they don't understand that one size does not fit all. They don't understand that half of the students are just not mentally geared to complete this new standard. This Common Core is going to benefit kids like mine. Reasonably intelligent, middle class white, concerned and involved parents and most importantly..a willingness to learn.
Apparently, not. Math has been taught that way in the US since at least the mid 1990s (University of Chicago-developed Everyday Math, etc.) and the result is that our TOP students rank below Asia's AVERAGE students.
Quote:
"Top U.S. students are falling behind even average students in Asia."
As someone who has a pretty extensive math background, I can say that the conceptualization of what Common Core is trying to do is not often understood by most but I can appreciate its approach. One of the problems with the way math was taught in my elementary, junior high, and high school was that it taught rote memorization of approaches to mathematical problems rather than actually understanding why we were doing something.
Common Core teaches a conceptualization and true understanding of the depth of mathematics and its explanation of reality.
For example:
What we learned: Two negatives equal a positive (Fine. We get that. But why? Other than just memorizing that fact, do you really understand why? Maybe you do now that you're much older but did it make sense to you 'back then' other than it was just an easy thing to remember?)
What Common Core teaches: That there is an actual separation right or or left of two numbers such that trying to subtract a negative number literally moves you in the opposite direction on that number line.
That a lot of adults in this day and age don't get it or are frustrated with it is a testament to the fact that we learned rote memorization and don't truly understand the underlying concepts of the numbers and pure mathematics. Common Core, from a purified mathematical standpoint, is probably the better of the two - even though it's not exactly intuitive to us who were never taught pure mathematics.
Uh, don't you mean that if you multiply two negative numbers you get a positive number? For instance (-4)*(-4) = 16 but adding the same numbers results in minus 8 while subtracting one from the other gives 0. I was taught how negative numbers worked also, and didn't need Common Core. I'm not exactly convinced that your idea of pure mathematics is any different than what has been taught prior to Common Core.
The idea is that you use the method that works best for the problem you're trying to solve. In my example, if I don't have a pen and a paper handy, it's easier to break down the numbers into smaller solvable chunks. In your example it's easier to just use a pen and paper.
The idea isn't that there is a 'best' method for everything. The idea is that you choose the method that works best for you and to understand how or why to use the tools you're given.
Sometimes to demonstrate an alternate method, you have to use a problem that is simple and better suited to other methods just to gain an understanding of how the alternate method works.
That is NOT what was broadcast about Common Core, and thus I think is the real issue. What you describe is the better way of handling it. But when I hear this lady talking and justifying that a wrong answer is acceptable, that's a problem in my eyes.
Quote:
Originally Posted by GCSTroop
One of the problems with the way math was taught in my elementary, junior high, and high school was that it taught rote memorization of approaches to mathematical problems rather than actually understanding why we were doing something.
Common Core teaches a conceptualization and true understanding of the depth of mathematics and its explanation of reality.
For example:
What we learned: Two negatives equal a positive (Fine. We get that. But why? Other than just memorizing that fact, do you really understand why? Maybe you do now that you're much older but did it make sense to you 'back then' other than it was just an easy thing to remember?)
Quote:
Originally Posted by O.C. Ogilvy
Uh, don't you mean that if you multiply two negative numbers you get a positive number?
Ogilvy is correct. But the thing is, it doesn't matter in the real world. Why are we so focused on helping kids understand something that won't help them in the workplace?
The reality is this. Rote memorization is designed to give you enough to solve simple problems, and that's enough. This psychological deep dive is pointless because, at the end of the day, it doesn't matter how I got to my right answer, only that the answer is correct. In the real world, unless it's an advanced topic, they don't care how you get to the right answer. They don't care if you break out a calculator, or use pen & paper, or use Google Calculator. Just get the right answer and move on, when talking about simple math. That's what I was taught, and it's critically helped me, even when I was stuck with math courses in college decades later.
There are WAY too many more difficult things that a kid is going to eventually need to learn to be wasting time diving into math like they're proposing.
That is NOT what was broadcast about Common Core, and thus I think is the real issue. What you describe is the better way of handling it. But when I hear this lady talking and justifying that a wrong answer is acceptable, that's a problem in my eyes.
Ogilvy is correct. But the thing is, it doesn't matter in the real world. Why are we so focused on helping kids understand something that won't help them in the workplace?
The reality is this. Rote memorization is designed to give you enough to solve simple problems, and that's enough. This psychological deep dive is pointless because, at the end of the day, it doesn't matter how I got to my right answer, only that the answer is correct. In the real world, unless it's an advanced topic, they don't care how you get to the right answer. They don't care if you break out a calculator, or use pen & paper, or use Google Calculator. Just get the right answer and move on, when talking about simple math. That's what I was taught, and it's critically helped me, even when I was stuck with math courses in college decades later.
There are WAY too many more difficult things that a kid is going to eventually need to learn to be wasting time diving into math like they're proposing.
Kids in K-12 are not taught pure Math. Most cannot explain "why". Most don't care why either.
They just want you to tell them what to do so they can get it done.
Which is exactly why American kids are falling farther and farther beyond their global peers. The get it done mentality leads to shortcuts and rote memorization instead of actual learning and understanding. Beyond the political grandstanding associated with Common Core, I cannot understand why any American would be against more difficult academic programs in the public schools.
Which is exactly why American kids are falling farther and farther beyond their global peers. The get it done mentality leads to shortcuts and rote memorization instead of actual learning and understanding. Beyond the political grandstanding associated with Common Core, I cannot understand why any American would be against more difficult academic programs in the public schools.
Fine. Let's see you articulate WHY 2+2=4, WHY 1/4=2/8 or WHY 4-5=-1
It helps you to solve difficult numbers problems . . .
I'd love to see the geometric proof that says the sum of all angles of a triangle is 179 degrees. That and 4*3 = 11 are similar wrong equations.
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