Conrad Wolfram: What is wrong with our math education (and how to fix it)

http://www.good.is/post/math-isn-t-just-computation-so-why-is-that-all-we-teach/

by madmaze • 15 years ago

23 18 15 years ago

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

madmaze• 15 years ago

more precisely how do we change the curriculum? and how do we ensure that all schools have enough access to computers to use them as a teaching and learning tool

jessriedel3• 15 years ago

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.

protomyth• 15 years ago

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.

hsmyers• 15 years ago

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.

jessriedel3• 15 years ago

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.

ams6110• 15 years ago

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.

jessriedel3• 15 years ago

To expand on you're point: math (and some math-like subjects) are flat out different than driving a car.

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.

AndrewMoffat• 15 years ago

> 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

Aloisius• 15 years ago

Speaking as someone who's primary problem with math in school was poor handwriting, I would have much preferred to learn via programming.

alextp• 15 years ago

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.

true_religion• 15 years ago

You may be correct but no one starts out programming in assembly then working their way up to higher order languages.

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?

ColinWright2• 15 years ago

I started programming with circuits, and then machine code.

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.

floppydisk2• 15 years ago

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

archgoon• 15 years ago

>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?

floppydisk2• 15 years ago

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".

ColinWright2• 15 years ago

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.

Conrad Wolfram: What is wrong with our math education (and how to fix it)

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