Abacus, Schools, and Petitions

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bluefoxicy
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Abacus, Schools, and Petitions

Postby bluefoxicy » Wed Nov 02, 2011 2:50 pm UTC

Well may as well put this up front.

http://wh.gov/b1c

Petition to use the Soroban in elementary schools to teach basic Math. It needs 150 signatures to show up at all, and 25000 in a month to get any attention. I assume these are countermeasures to make sure one man can't change the world... well, one man who isn't Rupert Murdoch. I'm sure I could do this if I had a large platform to scream at the whole world from--they would listen if I owned Fox News.


Politics (and thinly veiled attempts to get an XKCD comic about the Soroban drawn) aside, I think there's a great argument for using the Soroban as a teaching tool in classes. More importantly, I think there's a great argument for importing knowledge from around the world.

The Soroban is the standard teaching tool for mathematics in Japan.

That's important point number one here: freaky foreign junk we obviously don't need because their superior math is obviously a function of our large class sizes holding us back, not their superior teaching methods.

The Soroban is used to teach elementary math, and also to teach anzan--mental calculation. Anzan culminates in third grade, where students watch a monitor flash numbers by at high speeds (up to around 3 numbers per second), 3-5 digits with floating decimal point, in the real number set (positive, negative, decimals). After 5-8 numbers, they quickly write down the sum of all numbers they've been shown. It's instant, rapid mental math, only doable with superior Japanese math skills.

I believe that a foundation in strong arithmetic supports a stronger grasp of Algebra. We know that a strong foundation in Algebra supports all higher maths--Geometry, Calculus, Statistics--as well as the mathematical sciences--Physics, Chemistry, and so on. Therefor I believe we need the best method of teaching Arithmetic in order to lay the basis for all math and sciences education and give students confidence in their math skills.

More importantly, however, I feel that our greatest path to success in schools is to go around the country and around the world determining what works best and to import that into the local school systems. Schools here have trouble from domestic issues distracting students--poor parenting, crime, teen pregnancy, the like--but those issues are completely separate from poorly functioning school systems and poorly designed curricula. We need to address both the social issues and the administrative issues--in short, we need to accept that both poor schools and poor societies create poor performance, and strive to improve both instead of blaming one or the other as suits us.

I feel that the best way to improve the schools is to find the absolute best systems in the world that are compatible with our current systems and society and to import their methods into our own systems. We can seek improvement once we've done that.

... I should edit this and put it all in active voice and clean up circular thought, but eh. It's not a term paper.

What are your thoughts?

Chen
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Re: Abacus, Schools, and Petitions

Postby Chen » Wed Nov 02, 2011 4:15 pm UTC

So how exactly does the device help in teaching? Is it simply something that aids in the initial memorization needed for multiplication tables?

aoeu
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Re: Abacus, Schools, and Petitions

Postby aoeu » Wed Nov 02, 2011 8:14 pm UTC

Top 10 countries for Pisa 2009 in Math:

  1. Shanghai, China
  2. Singapore
  3. Hong Kong, China
  4. South Korea
  5. Taiwan
  6. Finland
  7. Liechtenstein
  8. Switzerland
  9. Japan
  10. Canada

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eSOANEM
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Re: Abacus, Schools, and Petitions

Postby eSOANEM » Wed Nov 02, 2011 8:34 pm UTC

aoeu wrote:
  1. Shanghai, China


In what way is Shanghai a country? I get Hong Kong, it's a special administrative region so has a reasonable degree of independence, but Shanghai's part of mainland china.
my pronouns are they

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bluefoxicy
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Re: Abacus, Schools, and Petitions

Postby bluefoxicy » Wed Nov 02, 2011 8:38 pm UTC

Shanghai, China is interesting. Do they use the Suan Pan? (Similar device) It seems to be in decline ... as of 2004 it was stripped as a requirement for accounting. China is coming to favor the electronic calculator... I am unfamiliar with any arguments that the use of electronic calculators teaches and reenforces arithmetic skill.

Chen wrote:So how exactly does the device help in teaching? Is it simply something that aids in the initial memorization needed for multiplication tables?


Oh, the Soroban specifically? It's a visual/kinesthetic tool. It makes a student physically perform basic arithmetic, as well as kinesthetically engage in it. Thus learning is logical, visual, and kinesthetic.

As for memorization, the Soroban requires memorization of two lookup tables for addition and subtraction: Compliments on 5 {(4,1),(3,2)} and 10 {(9,1),(8,2),(7,3),(6,4),(5,5)}. It requires memorization of single digit multiplication and division tables for those operations, as they are reduced to addition and subtraction. The entire use of the Soroban involves using basic algorithms that apply these.

As for the specifics of "What" instead of "Why," Wikipedia purports the following:

People who become proficient in use of soroban almost automatically become adept at mental calculation, known as anzan (暗算?, "blind calculation") in Japanese. As a part of soroban instruction, intermediate students are asked to do calculation mentally by visualizing the soroban (or any other abacus) and working out the problem without trying to figure out the answer beforehand. This is one reason why, despite the advent of handheld calculators, some parents send their children to private tutors to learn the soroban.


I care less about the above technical discussion of what humans are good at and what they are bad at, and more really about the demonstrated advantages of a method or device. If you say to me that in theory a specific tool is faster, and give a large and valid body of scientific explanation for why, I will flatly not care when the whole of all demonstration of said tool requires ten times as much time for the same result. Obviously the tool does not work, because when put to use it does not follow the theory. In the same way, I am less concerned with justifying why the Soroban works than I am at citing that it does work for the specific purpose that I purport it to.


The Soroban uses a 4/1 layout, with 4 beads worth 1 and 1 bead worth 5 separated by a bar called the Reckoning Bar. The single bead is called the Heaven bead and the 4 lower beads are called the Earth bead.

If you have enough beads, use them. Two plus two is four. Seven is 5 and 2, which correspond to 1xHeaven and 2xEarth for 1 Heaven and 4 Earth beads. So to add 2 + 2 or 7 + 2 you simply set two Earth beads.

If not, you use complements on five or ten. Say 2 + 3. You have 2 Earth beads set and 0 Heaven beads, and you have 2 earth beads but want to add 3. Instead, the compliment of 3 on 5 is 2: 5 - 3 = 2. So set 5, subtract 2, get 5+0 = 5. For 3 + 3, it is the same: 0/3, subtract 2 and add 5, 1/1 which is 5+1=6.

The same is for, say, adding 7 to 9. You have 1/4 for 5+4=9, so you add 1 to the next bar to the left and then subtract 3, leaving 1/1 or 5+1=6, with the tens bead you get 16. 7 + 9 = 16 (I had to verify that after writing the explanation...).

It's a skill that takes time to learn... but then so is addition on paper. It's so mechanical that you don't really do the math, either; you wind up toggling all the numbers around in your head and spitting out an answer. Even if nobody makes you learn mental math, when you take away the soroban you still run through numbers in your head fast.

I want the standard to be assigning a page of 60 mixed multi-digit addition and subtraction problems to second graders and expecting them to finish it in 10 minutes. That's 10 seconds per problem, kind of slow. A first-kyu will blow that out of the water: once conscious thought is completely removed and the use of the soroban is completely mechanized with combined finger movements, the beads just move around in single passes down the line, reflexively and automatically. First-kyu certification in Japan also has a high speed mental math component, so you have to be able to do a large number of problems in minimal time (addition, subtraction, multiplication, and division; although roots are possible on the Soroban) in your head.

Because a Soroban-taught student is always using these tables, a large amount of the process of Arithmetic is completely bypassed. Because the student is always involved with a physical device, the full process is well-understood due to being logical, visual, and kinesthetic. Both of these factors are greatly significant.

A good reference (if you're inclined to learn the damn thing yourself) would probably be http://webhome.idirect.com/~totton/abac ... m#Soroban1 ... see for yourself what happens when you learn to use it. You can find a Soroban for $10-$15, usually plastic. I have no preferred suppliers. You can find problem sets at http://webhome.idirect.com/~totton/abacus/PDF.htm

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LaserGuy
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Re: Abacus, Schools, and Petitions

Postby LaserGuy » Thu Nov 03, 2011 8:37 pm UTC

bluefoxicy wrote:Shanghai, China is interesting. Do they use the Suan Pan? (Similar device) It seems to be in decline ... as of 2004 it was stripped as a requirement for accounting. China is coming to favor the electronic calculator... I am unfamiliar with any arguments that the use of electronic calculators teaches and reenforces arithmetic skill.


Electronic calculators generally improve mathematical ability compared to traditional methods. Article is regrettably behind a paywall. Here's the abstract.

The findings of 54 research studies were integrated through meta-analysis to determine the effects of calculators on student achievement and attitude levels. Effect sizes were generated through Glassian techniques of meta-analysis, and Hedges and Olkin's (1985) inferential statistical methods were used to test the significance of effect size data. Results revealed that students' operational skills and problem-solving skills improved when calculators were an integral part of testing and instruction. The results for both skill types were mixed when calculators were not part of assessment, but in all cases, calculator use did not hinder the development of mathematical skills. Students using calculators had better attitudes toward mathematics than their noncalculator counterparts. Further research is needed in the retention of mathematics skills after instruction and transfer of skills to other mathematics-related subjects.


I can't find any direct comparisons between the Soroban and the electronic calculator in terms of overall mathematics performance, though. For that matter, I can't find any research evaluating the effects of the Soroban on general mathematical proficiency, so saying this method is necessarily an improvement is somewhat premature.

Chen
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Re: Abacus, Schools, and Petitions

Postby Chen » Fri Nov 04, 2011 4:59 pm UTC

The various wiki pages seem to indicate it has a positive effect on learning to do fast mental math. Unfortunately I'm not so sure how important that is in terms of problem solving. One would imagine not terribly important since the bigger time issue is reading and understanding the problems.

Dark Avorian
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Re: Abacus, Schools, and Petitions

Postby Dark Avorian » Sat Nov 05, 2011 12:40 am UTC

Ummm...I think this is a case where you're really reading too much into too few data points and I can see a lot of confirmation bias. Just as a quick aside, it's been documented that the top 10% of US students in terms of family wealth can perform better than any other country ( of course, one still wonders how they would fare against the top 10% of every other country), and so far as I know the wealthy children of America use the abacus no more than any other students.
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FuzzyPanda
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Re: Abacus, Schools, and Petitions

Postby FuzzyPanda » Thu Jan 19, 2012 2:14 am UTC

Sorry to interrupt, but from the basic research I did, the soraban seems to remove the user from numbers almost as much as digital calculation. Users are encouraged to use a mental soraban without attempting to work out the answer beforehand. While it is definitely advantageous to be able to perform rapid mental arithmetic, I would propose that a stronger understanding of numbers can be gained without the use of a soroban.


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