

Conrad Wolfram: What is wrong with our math education (and how to fix it) - madmaze
http://www.good.is/post/math-isn-t-just-computation-so-why-is-that-all-we-teach/

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ams6110
Just as you don't really understand how a CPU works until you've programmed in
assembly, you don't really understand math if you haven't done hand-
computation, at least up to a point. If your approach to any math problem is
"plug it into Mathmatica" you will never be able to creatively apply basic
concepts to more complicated problems and you will never have any sense of
whether the answers it provides are "reasonable."

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.

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AndrewMoffat
> Just as you don't really understand how a CPU works until you've programmed
> in assembly, you don't really understand math if you haven't done hand-
> computation, at least up to a point.

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

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alextp
Agreed, but only up to a point. To program it is fundamental to have a strong
intuition as to what should happen, why, and how to get there. Doing that
without some amount of manual computation is temerary.

~~~
DanWaterworth
Actually, I disagree. Programming is about building and using abstractions. It
is not strictly necessary to understand how the abstractions are built.

Case and point, how many web developers do you know who could outline the
TCP/IP protocols in great detail?

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floppydisk
A good portion of this problem would be solved in the long(er) term if we
pursued a 3-track plan. First, cut back on the amount of bureaucracy running
the school systems. Whenever state cuts roll around, you never hear about
office administrator's getting cut. . .just teachers. Where I live, we have an
absurdly high ratio of administrator to teacher ratio and when cuts come
around the teachers go first. The more overhead we've got, the less we can
spend on teachers to retain the people who actually teach.

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

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archgoon
>Give the teachers some room to choose what they teach instead of having them
teach straight to the standard of learning tests

> 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?

~~~
floppydisk
As an engineer, I love statistical data or numbers I can crunch and use to
make a supposedly more objective comparison between things. I believe the
problem with standardized testing is we are trying to take that idea and then
apply it to something inherently non numerical--the acquisition of knowledge.
Contrast this with economics and I think there's a startling difference. In
Econ, we participate with numbers, something easily quantifiable. In education
we participate with our minds and we have no easy, objective, way to quantify
this into convenient numbers. For instance, standardized testing is inherently
biased against people who don't take tests well meaning the test will not
accurately represent their level of knowledge which could then have further
repercussions when they apply to college.

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".

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hsmyers
I believe that there are currently more significant problems than those
mentioned in the (very good) TED talk---how do we stop the continued trend of
denigration of teaching and the profession in general? The current populist
idea of blame all of the teachers for the nightmare that administration gone
insane is, is not going to lead us unto the future. It will lead us back to a
time of ignorance and idiocy.

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jessriedel
Populism favors common people and blaming the elite. The idea you describe
("blame all of the teachers for the nightmare that administration gone insane
is") is the opposite of this.

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ColinWright
This has been submitted many times in the past few months, with the same point
and counter-points rehashed endlessly. Do a search for Conrad Wolfram to see
what I mean.

I'm not going to repeat my arguments. For some people he's right, for others
he's very wrong.

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peterpeters
The real question is how to change the way the teachers teach.

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jessriedel
The singular way to do it would be to employ math teachers with math/science
degrees, not (just) teaching degrees. I had 3 teachers in high school with a
math/science PhDs (I went to a magnet school), and their teaching was heads
and shoulders above all the other teachers...save one, who I believe had a
Master's in physics.

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.

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protomyth
I agree with the need for actual degreed people in Math and Science teaching.
If an adult went to a training center and got a person with an education
degree and certificate instead of someone who put the years in for a technical
degree, you would want your money back.

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.

