Having grown up in public schools in the southern US, I don't understand why we focus so much on memorizing formulas but not the underlying concepts or how they apply to other things. The power of math is the ability to abstract other problems into math and then solve them with a standardized toolset. We spent the first decade of our schooling learning very basic mathematics (up to algebra), and I hadn't seen calculus until my second year of university.
It's no surprise to me that kids are having issues understanding the parts of a circle, why the formulas do what they do, or how to do the related math. I've been there. I think teaching basic physics and some of the more esoteric math earlier (number type sets, limits, boolean logic, simplified of course) would help with some of this. I always wondered how to do things infinitely or how to calculate things certain ways in algebra, and it always seemed like parts were missing. Calculus filled in so much of this for me, and I wish I had known it earlier. Physics and video games (wiremod) gave me reasons to learn some of the math.
Another thing I wish there had been more of is the history and practical implications of this stuff. I never cared about the quadratic formula before I learned about electric circuits or things falling in gravity. I didn't know at the time it went back to Babylon, India, and Greece.
Kids don't get taught how to think critically and use the tools at their disposal, and that's the largest problem with our education system. We learn how to ask someone for the proper tool to use and then do the work ourselves without thinking about it. It's probably an accurate representation of what work in much of America has come to nowadays, busy work, but it's a shame that we don't do something better for the next group coming along.
When schools try to teach a holistic sense of numeracy to connect with average students, with programs like Discovery, Tiger parents* revolt with stuff like http://wheresthemath.com/
* Using Tiger parent as a trope here, not specific to any ethnicity.
It's no surprise to me that kids are having issues understanding the parts of a circle, why the formulas do what they do, or how to do the related math. I've been there. I think teaching basic physics and some of the more esoteric math earlier (number type sets, limits, boolean logic, simplified of course) would help with some of this. I always wondered how to do things infinitely or how to calculate things certain ways in algebra, and it always seemed like parts were missing. Calculus filled in so much of this for me, and I wish I had known it earlier. Physics and video games (wiremod) gave me reasons to learn some of the math.
Another thing I wish there had been more of is the history and practical implications of this stuff. I never cared about the quadratic formula before I learned about electric circuits or things falling in gravity. I didn't know at the time it went back to Babylon, India, and Greece.
Kids don't get taught how to think critically and use the tools at their disposal, and that's the largest problem with our education system. We learn how to ask someone for the proper tool to use and then do the work ourselves without thinking about it. It's probably an accurate representation of what work in much of America has come to nowadays, busy work, but it's a shame that we don't do something better for the next group coming along.