Re: Math Education: An Inconvenient Truth

Timing out some of the methods shown in the video I am responding to. http://www.wheresthemath.com/

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[brittymathgeek]

China is great because:

1)the so called horrible method you are using is called the distributive property and is taught extensively to early elementary students in China; traditional US students get taught this in 6/7th grade

2)students in china are taught multiple ways to solve a problem; traditional US is taught 1

3)China is conceptually learning focused; the US learning has been procedure based (memorize the algorithm) Seems like your "best" methods are the problem.

(Liping Ma...google her)

[websnarf]

@brittymathgeek : 1) No, the horrible method is called "Terc investigations". The distributive property applies to the standard method just as it does to the Terc method. The difference is that the std method gives you a fixed algorithm.

2) reference?

3) How many Nobel prizes does China have compared to USA? Now compare population sizes. The US's problem is not that there is no learning being imparted. Its *who* gets taught by *whom*.

Liping Ma does not support the Terc method.

[cuantumk]

I do the cluster method but that's only in my head really, it's pretty inconvenient and superfluous in paper in my opinion. I prefer they keep teaching the standard methods, they're definitely clear cut and would help students later on, when they need to take higher level math in high school. But that's just my opinion...

[websnarf]

@MacLaurin83 : If you are really faster, then prove it. I don't see how its possible, you write many times more things, and group into more ultimate operations. This video has been up for years, and nobody has dared respond to it with an actual video showing anything different.

Series: You don't *KNOW* that you have convergence, unless you use a method like long division.

[MacLaurin83]

@websnarf As are my abilities. Yet Im faster with the terc method. Your training is not doing math. It consists in physically being able to draw certain lines faster, not having to spend that split second deciding whether to use an equivalence arrow or not, etc. For the series: In this case we have absolute convergence, so we can rearrange w/o changing the value. We do not prove convergence ofc, but if thats the point we could still use any algorithm. Theres nothing special with long.

[websnarf]

@MacLaurin83 : My abilities are way beyond the technicalities of any of the methods. So my personal training is a complete non-factor in this test. Like most people, I use a calculator (one that I built myself, but that's another story). You actually cannot prove that an infinite expression is a particular value because you can manipulate it. The long division construction is one way of proving that the result is convergent whenever |x|<1, which manipulation doesn't do.

[websnarf]

@MacLaurin83 : Arithmetic is not intuitive -- it must be taught. Please look up the Piraha, or any other hunter-gather group for an examples. Arithmetic only becomes self-reinforcing once algebra is taught. This isn't a matter of proof, all the methods work -- that's not the point. The point is what it takes to give children a mastery of arithmetic which is required *before* you proceed to algebra.

[websnarf]

@MacLaurin83 : The standard algorithm can be easily checked by literally anyone, including the person who first did it, by simply rerunning the algorithm. The extra numbers and where they are placed are unique and have to be there for the multiplication to be computed correctly. The terc method is not an algorithm at all, but just a continuous arbitrary regrouping of the multiplication into different equivalences. There are many ways to do the same multiplication using terc.

[MacLaurin83]

@websnarf I dont think the speed test is a measure of your understanding, but I DO think its a measure of your "training." If you always use one method, then ofc it will be faster. I do the terc method pretty fast let me tell you. And as for polynomial division you could ofcourse use any algorithm for division, not just long. It would have to be pretty hefty polynomials for me to use it. And you could just prove (1-x)(1+x+...)=1 by expanding, which feels simpler to me and does not use division

[MacLaurin83]

@websnarf What do you mean by "its not being checked against anything?" I cannot see that the other algorithms are checked against anything in particular. Neither are they self correcting. And why should the understanding of arithmetics be allowed only when doing algebra? Arithmetics is not being taught to kids as a special case of a field or wathever, but is (generally) based on intuition. You could ofc prove all methods, but then why not USE the proof AS our method?