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[quote=Anonymous][quote]I think this is why Americans are so bad at math and come up with things like 2.0. There is a general disinterest in anything that is difficult. Everything should be easy. Everyone should get an A or B. If you need to work hard in school then something must be wrong with the school. 
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I am the Computer Engineer that posted above and I could not agree with you more!  Seriously, someone could hold a gun to my head and say agree more, and I'd be like &quot;impossible, I can't&quot;.  I will disagree with one (minor) point, many of the foreign students did not do as well because while they could do the math, they could not apply the concepts.  Some how under the old bad system we managed have the knowledge to be superior to every other country in the world with our designs and innovations.  The mantra of everyone in the world is better than us was common back then to, but I just don't think it is true.

[quote]Fluency isn't about just memorizing random facts which I think many people get caught up in. Fluency is about performing more and more difficult calculations with speed so that those relationships are part of your working memory. This allows you to pull these quickly when you encounter more complex math problems. If you lack fluency, you'll struggle to keep up in more advanced classes and work based problems.
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In my college you ALWAYS had to describe how you derived the equation, there is nothing new about that.  The rote work is what provides fluency out of working memory just like the previous poster wrote.

When my HGC math-gifted child asks for help on how to write an explanation for why she knows 3/5 is less than 2/3 and I explain you find the common denominator of 15 which makes the problem 9/15 &lt; 10/15.

She tells me that she hasn't been taught how to find the common denominator and they are supposed draw a diagram of boxes and shade and write a sentence about the boxes.  I am perplexed.  She says some of the kids in class know how to find the common denominator but she has never been taught how to.  She is far enough along in her curriculum that drawing boxes is a time waste, she needs to just be doing the math.

I fully understand the reason for a graphic drawing to show the difference, but she also needs to know how to find the common denominator and do simple fraction math.  It is a dumbing down of math so that everyone can draw a box, because not everyone can do the math or understand the concept of a common denominator.

[quote]I agree, that at some point, you have to be able to do math quickly in your head.
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Higher level math is not really done in your head, back in the old days you had points deducted on exams for skipping steps. Do you know square roots and cube roots by heart? Yes because you use them so often, but it's mainly pencil to paper and show your work.

[quote]Its the requirement that the explanation be given in words and sentence form that is the problem. If the students were allowed to represent their understanding by reverse engineering the problem, showing diagrams, equations or other visual approaches that more elegantly and accurately convey understanding then that would be fantastic. 
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I worked in a hardcore development environment, every office had a white board and we used MEANINGFUL diagrams for high level concepts constantly and this is also how we were taught in college.  If we long hand wrote out sentences for higher level conceptual designs (other than specifications) when working collaboratively no work could have been accomplished.

I also worked as a TA and honestly some people just don't get math, no matter how many diagrams and explanation I provided, but they had other strengths and often transferred into another programs which were a better fit.

The problem with C2.0 is that they go over the same thing over and over again.  Box diagram after box diagram, writing sentence after sentence.

I asked my child last night what the difference was between the HGC and her previous regular question.  She said kids would just ask questions that were obvious over and over again, when she just wanted to get to work and done.  I feel sorry for the higher achieving kids (which there are plenty of!) that are stuck in regular classes, that is why every elementary school should have advanced math classrooms, instead of lumping everyone together to the point of making the brighter kids hate math because they are doing busy work drawing boxes, dots, and graphs well beyond when they have grasped the concept.[/quote]

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