Conrad Wolfram: What is wrong with our math education (and how to fix it)
good.is
good.is
That said, tools like Mathmatica are here to stay, and the argument that we need to spend more time teaching the use of these tools as an aid to exploring and understanding fundamental concepts is probably correct.
I think the problem with your example, ams6110, is that Wolfram might retort that software developers don't need to have programed in assembly. Yes (says Wolfram), the absolute best developers in the world might be well-versed in the this, but that doesn't mean all developers should be so trained, in the way that we train everyone to do arithmatic.
To respond to this, I would say: no one would ever study Ramanujan theta functions without learning linear algebra, and no one should study linear algebra without learning arithmetic. Most other subjects must be compartmentalized, because it is impossibly difficult to derive biology from basic chemistry; some things must be accepted as given. But math is different. In math, you really can derive everything from the ground up, and doing so is immensely valuable.
However this is exactly how math is practiced.
Wouldn't it be better to start with higher order logic first, so students can see a value proposition then work our way down to the nitty gritty computation that no one needs to do unless they're advancing the field?
And I think you're wrong about starting with higher order logic. It's too easy to make plausible statements that are simply wrong. Learning the real nitty-gritty is essential to avoid sweeping errors.
Conrad Wolfram addresses this very point in the video (11:30). He says that the most valid point that hand-calculating helps understanding is that teaching processes themselves helps understanding, but that there's a better way to do that: programming. In other words, programming a math solution is better for teaching math understanding that hand solving it.
In the end, I think the idea he's trying to impart is that the core of math is not calculation at all, it just seems that way because they've been intertwined for so long. But now that we have computers to do the tedious calculations, we can work on defining and exploring what math really is: how different conceptual intuitions are related
Case and point, how many web developers do you know who could outline the TCP/IP protocols in great detail?
Second, give the schools more autonomy to choose curriculum and meet the needs of their students. Instead of standardizing the curriculum across the state and federal level--shoehorning every student, no matter their educational needs into one specific mold--give the schools more latitude to meet their students needs. Give the teachers some room to choose what they teach instead of having them teach straight to the standard of learning tests.
Finally, end teacher tenure and promote/fire based on merit. Good teachers who teach well should get raises and encouraged to stay teaching. Teachers who stink (I know I can think of several off the top of my head my classmates and I universally agreed stunk) should be let go and replaced with new teachers. Overtime, this builds a a stronger cadre of motivated individuals with an incentive to do well teaching instead of having protection from the all powerful teacher's union to
> end teacher tenure and promote/fire based on merit
These two points may not be compatible. How do you propose promoting based on merit other than the results of the standardized tests?
The problem is we are looking at this through an engineering lens. When looking for a quality teacher, other factors than results on a silly test should play a role. How do the students respond to the teacher? Is the teacher usually well prepared? Do they have a good reputation with the students for being fair? Are their lectures interesting? At some point, on the local level (individual school), I think parents and the administration have a good idea of who the good teachers are and who are lemons and I don't know if you could quantify this into a statistical system that is "impartial".
I'm not going to repeat my arguments. For some people he's right, for others he's very wrong.
This means I disagree with madmaze. Change the teachers, and the curriculum changes will follow. Change the curriculum with the same teachers, and you get New Math < http://en.wikipedia.org/wiki/New_Math >, which had some good ideas but was doomed.
Problem is, math and science degrees are a lot more expensive to employ.
The bigger problem is that you need to pay Math and Science degreed people more than other teachers because of scarcity and other high paying job opportunities. The current educational machine won't allow that.