10 ms·

Abacus use can boost math skills

128 points by Osiris30 10y ago

hedgew 10y ago
>“Based on everything we know about early math education and its long-term effects, I’ll make the prediction that children who thrive with abacus will have higher math scores later in life, perhaps even on the SAT” Also not so suprisingly, children who thrive in early math education will tend to have higher math scores later in life. That's about all we seem to know about early math education anyways.
JamilD 10y ago
I find play to be the most effective way of learning. When I was learning, for example, the backpropagation algorithm, no amount of lectures could've helped me understand better than just drawing a network, thinking "what happens when I change the weights here?", and toying with the equations. It gives you an intimate familiarity and understanding that you can't get anywhere else.
- agumonkey 10y ago
  Play disengage a very bad emotional state often found in classes. You don't fear ridicule much, you're eager to try, lots of iterations in a small time; often instant results.
  - Declanomous 10y ago
    This is what I like about common core. I think a lot of hate for it comes from the fear of being wrong in school that a lot of people have growing up. The common core homework people post online with captions like "how is my child supposed to know the answer to this?" The point is they aren't, they are supposed to come up with a guess and explain their reasoning.
    - l3m0ndr0p 10y ago
      Common core is a blight on children and needs to be eradicated for the USA schools. This systems has destroyed my child's self esteem and ability to grasp simple/moderate math problems. The schools were blaming my child, yet they didn't even consider that methods of teaching are wrong and should be modified to suit an individual. The one-size fits all doesn't work & never will. Fuck common core and the people who are making money off of it.
    - yjftsjthsd-h 10y ago
      Yes, but they're being graded, at which point it isn't really play.
      - Pulcinella 10y ago
        That really depends on the school and grade level. The homework I assign is usually graded for completion, not accuracy. You still have to do it, but there is less pressure on getting the right answer instead of learning.
    - 0xdeadbeefbabe 10y ago
      Some of the hate for it comes from it being a mandate for everyone. I don't believe you can force people to be playful about their homework in the right way. Some child is probably reasoning: "I answered this question this way because I want to be done with my stupid homework."
      - Pulcinella 10y ago
        "...I want to be done with my stupid homework." In a way, this is a huge difficulty with learning in general. Practice can feel repetitive and boring, especially if you don't care for the skill you are practicing. As a teacher I'm not sure what to do about this. I teach science and the "fun" parts are frequently tied to things students don't like (e.g. Algebraic calculations needed for simple data analysis like calculating averages or rearranging a formula to solve for momentum). The students are curious about science, but hate the math parts because they struggle with the algebra. Doing algebra isn't the point, it's just a tool you need to do the science. The goal is to be good enough at the algebra that it doesn't require any real brain power so that the students can focus on the science, what their resaults really mean, understanding the system, etc. If you have a poor grasp of algebra then you are going to have a bad time. I'm not sure what to do for these students except have them practice and I'm not sure how to always make practice enjoyable. I'm not talking about homework here, necessarily, and I don't think homework is appropriate for all grade levels in all situations.
partycoder 10y ago
In my opinion the best abacus you can get is the 5 beads per rod one (soroban). The 7 bead one pictured in the article header is slower to work with (classic suanpan). The 10 bead one used in the west for kids may be good to have an intuition about quantities, but for practical use it is the worst. You can get a soroban, learn the basic algorithms, then use an soroban drilling app to gain speed. With practice, you can exploit muscle memory and stop using a physical abacus. The abacus provides a workable mental model for numeric operations. In contrast, calculators are opaque machines. They take inputs and provide an answer but do not expose their inner workings in a way that can be assimilated and learned by the user.
- bogle 10y ago
  I have a couple of soroban at home. One has lovely, bright, colourful beads to attract the children. They are attracted, they try to use them as roller-skates. Which soroban drilling app have you used?
  - partycoder 10y ago
    This Android one is free and very responsive. https://play.google.com/store/apps/details?id=br.net.btco.soroban&hl=en https://play.google.com/store/apps/details?id=br.net.btco.so... There are Youtube videos explaining the algorithms. A basic exercise is just counting, and then do a countdown. And then try to do it as quickly as possible. Then do it in intervals of 2 rather than 1, then 3, and so on.
- cnlevy 10y ago
  Flash Anzan is impressive for a westerner : https://www.theguardian.com/science/alexs-adventures-in-numberland/2012/oct/29/mathematics https://www.theguardian.com/science/alexs-adventures-in-numb...
  - deleted 10y ago
    [deleted]
- digi_owl 10y ago
ideonexus 10y ago
I see these kinds of benefits in over-learning keyboards as well. The few classes I've taught to children and teenagers, you can see a dramatic difference between the students who are familiar with keyboards and those whose parents--I speculate--don't allow them screen time. This extends into adulthood. The people I work with who have that well-practiced familiarity with keyboards and keyboard shortcuts--using them as if extensions of themselves--easily adapt to any new software interface. The adults who hunt around the screen with a mouse have a great deal of difficulty with change and are almost helpless when confronted with a new interface--even if the menu items are all in the same places as the last software. It's a comfort and familiarity with the computer that allows the user to easily adapt to new things. It totally makes sense to me that working with an abacus would have similar benefits for making students comfortable with math.
- dragonwriter 10y ago
  > you can see a dramatic difference between the students who are familiar with keyboards and those whose parents--I speculate--don't allow them screen time. "Screen time" and keyboard use are very different things; while most opportunities for keyboard use also involve screen time, quite a lot of modern screen time doesn't involve keyboard use. I would bet that those unfamiliar with keyboards are a much larger group than those whose parents don't allow them screen time, the former group being a superset of the latter.
- koroch 10y ago
  It's all gone down hill after we stopped using the command line. Back in my day ...
  - rubber_duck 10y ago
    Hand crafting punch cards for that OG physical experience.
    - yjftsjthsd-h 10y ago
      Keyboards are higher bandwidth than punch cards, mice, or touch screens; currently they appear to be the best option.
hammerandtongs 10y ago
So from the hour I wasted yesterday poking around the web after reading this article - http://webhome.idirect.com/~totton/abacus/PDF.htm http://webhome.idirect.com/~totton/abacus/PDF.htm Seems like the best free resource. This book seems like the standard english text on soroban - https://smile.amazon.com/Japanese-Abacus-Its-Use-Theory/dp/0804802785/ https://smile.amazon.com/Japanese-Abacus-Its-Use-Theory/dp/0... The first few chapters are great. This book from the sixties mentions that abacus are actually a middle-eastern invention and came east with trade. Abacus in fixed frames are a later invention for speed but earlier versions would have more resembled a backgammon table using pebbles. https://en.wikipedia.org/wiki/Abacus https://en.wikipedia.org/wiki/Abacus https://en.wikipedia.org/wiki/Salamis_Tablet https://en.wikipedia.org/wiki/Salamis_Tablet This led to this pretty interesting paper - https://arxiv.org/pdf/1206.4349.pdf https://arxiv.org/pdf/1206.4349.pdf It seems like there is a pretty large gap in our understanding of how people actually did calculation? Cheers
n00b101 10y ago
The American elementary and high school education system would do young students a huge favour by abandoning the use of electronic calculators. I have no doubt that the abacus is a superb pedagogical tool but simple pencil and paper calculation would be a huge improvement over the calculator culture in early mathematical education. I majored in Applied Mathematics in university and did not use a calculator in a single class or exam - it was explicitly forbidden to use them. But I was also educated in the American elementary and high school curriculum. I am thoroughly convinced that the use of calculators in the American system does a huge disservice to students. The calculator culture begins at an astonishingly young age, in elementary school, when kids are first introduced to the Texas Instruments TI-108 calculator [1]. This bright blue and red, solar-powered gadget is very exciting for children in a classroom, but it is poison. At the very age that students should be drilling mental math, they are instead given this huge crutch. It's like never taking the training wheels off a child's bicycle, robbing them of the opportunity to actually learn to ride a bicycle. The same story is repeated in middle school (with the same TI-108). And then you reach high school. You would think that at least now the the training wheels would come off. But instead, you are "upgraded" from bicycle with training wheels to an adult-sized tricycle. I am, of course, speaking of the Texas Instruments "graphing calculator" [2]. This abomination is a full-fledged programmable computer with CAS software. You are encouraged (even required) to use this machine all the way through Advanced Placement Calculus. If you are not distracted in class playing video games on your "graphing calculator," then you may use it to automatically solve algebraic and trigonometric equations and evaluate derivatives and integrals. Why bother memorizing identities when you can just program them into a computer? If you have been programming from an early age, then you may be in the worst place possible because you are predisposed to wasting your time trying to program your way out of math homework instead of focusing on learning math. When students complain about why they have to learn Calculus, your American math teachers tell you that nobody "in the real world" actually solves integrals by hand and it's all done on computers, but you have to learn it anyway for obscure pedagogical reasons. An aspiring future Comp Sci student is likely to take this as a clear signal that it's all a waste of time, and soon high school will be over and you'll never need to worry about this antiquated Calculus thing again - your computer will do it all for you. There are other ways in which American mathematics education is extremely flawed, but the calculator culture is the worst offence by far. I suspect that the bureaucrats who decide on such things rationalize this by calibrating the curriculum to what they see as the "lowest common denominator" student who will never need to learn anything beyond basic algebra and arithmetic. The goal of the system is to train this student to be a productive, low-wage worker, with just enough mathematical training to be able to mindlessly punch numbers into a cash register or simple spreadsheet on the rare occasion that the need for numerical computation may arise in their "careers." I have a three year old and I have no idea what I could do to save him from this insane system, short of moving to a different continent. [1] https://en.wikipedia.org/wiki/TI-108 https://en.wikipedia.org/wiki/TI-108 [2] https://en.wikipedia.org/wiki/Comparison_of_Texas_Instruments_graphing_calculators https://en.wikipedia.org/wiki/Comparison_of_Texas_Instrument...
jimmies 10y ago
It seems like the things that are more painful to learn and use make your brain work harder, and thus make you learn better. Or, maybe it is the case that people who know to use the hard stuff are interested in the subject enough to learn how to do it the hard way. You wouldn't be surprised that those who use Assembly to program tend to have better programming skills compared to those who only can program in Visual Basic, would you? Veritasium also mentioned this recently: https://www.youtube.com/watch?v=UBVV8pch1dM https://www.youtube.com/watch?v=UBVV8pch1dM The more interesting question to ask to me is (1) whether it is the abacus that makes children learn better, or it is just that children who choose to use the abacus learn better (2) whether teaching abacus use at the beginning has the same effect as teaching abacus use later on after the students already know how to use the calculator. If children who choose to use the abacus learn better, then it wouldn't surprise me, but it means that teaching abacus wouldn't help. If that is false and (2) is true, then we know we better off teach abacus (or assembly) -- it doesn't matter when. But if (2) is false, it means that we have a huge trade-off to consider. Because either we teach the hard stuff at the beginning and discourage a lot of students, or we don't and have worse learning outcomes.
- abecedarius 10y ago
  The post links to a randomized controlled trial. (I only read the abstract.)
- MengerSponge 10y ago
  Your Assembly/Visual Basic question is going to be badly biased. The barrier to entry with VB is lower, so you'll see more low-skill programmers. This reduces the average competence of the entire cohort, but doesn't tell you anything about the high-skill users. Now if you could show that learning assembly led to better programming skills, you'd be talking about something similar. I suspect that a comparison of introductory programming via assembly vs a modern high-level language would find lower overall proficiency in the assembly group, although a few students would do fine. Personally, I suspect that there isn't anything particularly unique about using an abacus, compared to other manipulation techniques. These are probably all superior to calculators, which are generally awful.
ForHackernews 10y ago
There's a cute story in Surely You're Joking, Mr. Feynman where a man with an abacus challenges him to an arithmetic contest: http://www.ee.ryerson.ca/~elf/abacus/feynman.html http://www.ee.ryerson.ca/~elf/abacus/feynman.html
- scarmig 10y ago
  He's a bit too pleased with himself at the end there: they simply are using different algorithms, and those naturally have different performance properties for different inputs. Feynman is relying on a prepopulated lookup table and some heuristics, while the abacus guy is relying on whichever algorithm is best suited for calculating cube roots on an abacus. Though, I admit, I'd probably be pleased as a peach too.
  - yosefk 10y ago
    Feynman uses a much larger set of algorithms though, and can come up with new ones. The guy with the abacus seems like he didn't know why his algorithms worked, he just executed them.
- _yosefk 10y ago
  And in this story he claims that abacus use is mechanical and rids you of having to "know" numbers or approximate methods or understanding anything about the computation and why answers come out as they do. You're just executing steps and the more complex the computation, the more steps you do with no understanding whatsoever. So the opposite thesis from TFA.
  - sn9 10y ago
    It's not really an opposing thesis. The moral of the story is that his opponent became married to the use of the abacus and convinced of its superiority and that led to an overreliance on it and inflexible thinking. The thesis of the TFA is that the abacus can be a great tool for teaching arithmetic and number sense. It doesn't argue that it's the only thing you'll ever need and you should use other tools.
retox 10y ago
Probably off-topic but I checked Isaac Asimov's "Realm of Numbers" from my library on the recommendation of HN and it's great. One of the earlier chapters outlines how the abacus and its concept of 'the unmoved row' could have helped forment the idea of zero. Very interesting text, no idea if the ideas are considered incorrect these days but still entertained and educated. 10/10 read.
myth_drannon 10y ago
Related to abacus use. Sam Harris podcast "Complexity & Stupidity" https://www.samharris.org/blog/item/complexity-stupidity https://www.samharris.org/blog/item/complexity-stupidity mentions abacus skills. The skill "spreads" to other areas of the brain they call it "complementary cognitive artifacts" Quotes : Harris: What else would you put on this list of complementary cognitive artifacts? Krakauer: The other example that I’m very enamored of is the abacus. The abacus is a device for doing arithmetic in the world with our hands and eyes. But expert abacus users no longer have to use the physical abacus. They actually create a virtual abacus in the visual cortex. And that’s particularly interesting, because a novice abacus user like me or you thinks about them either verbally or in terms of our frontal cortex. But as you get better and better, the place in the brain where the abacus is represented shifts, from language-like areas to visual, spatial areas in the brain. It really is a beautiful example of an object in the world restructuring the brain to perform a task efficiently—in other words, by my definition, intelligently.
neves 10y ago
Do you have references about how to use an abacus? I just know how the obvious uses: counting, summing and subtracting. There is a famous story about Richard Feynman and the abacus: http://www.ee.ryerson.ca:8080/~elf/abacus/feynman.html http://www.ee.ryerson.ca:8080/~elf/abacus/feynman.html where the guy makes a lot of difficult calculations.
- partycoder 10y ago
  I love that book. The "Fixing radios by thinking" part is a great insight on how Feynman developed such powerful intuition around physics at an early age. In contrast, modern electronics are not as transparent and intuitive as their vacuum tube counterparts. I wonder what would have happened if Feynman had to fix radios with transistors or integrated circuits.
- neves 10y ago
  I've just found a great one: http://webhome.idirect.com/~totton/abacus/PDF.htm http://webhome.idirect.com/~totton/abacus/PDF.htm
meow_mix 10y ago
Maria Montessori had a lot to say on the importance incorporating tactile elements in early education. This is why Montessori schools generally incorporate tools like the abacus (at least mine did). Not surprised we're re-learning some of her findings today
- nkrisc 10y ago
  The Montessori school I went to didn't have an abacus for us to use, but to your point, the physical representations of 10^1 (a row of 10 beads), 10^2 (a 10x10 square of beads), and 10^3 (a 10x10x10 cube of beads) using beads helped me understand exponents much more quickly. Unfortunately we did not have a 10x10x10x10 tesseract of beads.
  - roywiggins 10y ago
    I'm a huge fan of the Montessori binomial cube: http://www.montessoriworld.org/sensory/sbinoml.html http://www.montessoriworld.org/sensory/sbinoml.html
    - nkrisc 10y ago
      Of course! We had those too. I had totally forgotten about that.
- agumonkey 10y ago
  Jaron Lanier did experiments in VR with switched limbs, so your brain tries to make sense of a new "geometry". I also felt regularly that all kinds of inputs are very stimulating for the brain and bolden the memory. For instance writing down with pen and paper requires more brain activity than a keyboard. Computers seem faster for note taking but the ease actually removes the colateral inputs that stimulate/challenge your brain and thus helps learning (you also have to reflect about what to trim and how to organize your notes, thus creating so semantic map of the topic).
jweir 10y ago
vim
robbiewxyz 10y ago
I absolutely see this. Just today I've been helping teach a friend's child to do multiple-digit multiplication on paper. In that kind of thing, understanding place values (the ones-tens-hundreds columns) is so important. It's amazed me how many high school students even don't quite get the idea of place values and what base 10 means. The abacus requires a good understanding of that concept from the start. So, while the "skill spreading" might also contribute, with the abacus, it's a basic and essential concept to really understand for all higher-level math.
forkandwait 10y ago
Can anyone recommend an actual abacus to buy?
- Animats 10y ago
  To add and subtract, I'd suggest a soroban, the Japanese 4 and 1 bead per row abacus in hand-held size. Those were in wide use until a few decades ago, and can be operated quickly. They're still available on Amazon and Alibaba. Get one where the beads are cone-shaped, not round; those are easier to manipulate. Don't bother with a "reset button"; you can do that with one finger in a second, rattling down the columns. It's not a very useful skill, but it's not hard to learn. I wouldn't inflict it on kids. The 5 and 2 bead form is more of a school thing. I probably still have one, packed away with the slide rule. My HP-11C is on my desk.
racl101 10y ago
It's a great way to understand our base 10 number system. That definitely gets lost when using calculators and computers. As well, I have to believe it would help a child understand any other number system such as binary, octal and hexadecimal.

128 points by Osiris30 10y ago

>“Based on everything we know about early math education and its long-term effects, I’ll make the prediction that children who thrive with abacus will have higher math scores later in life, perhaps even on the SAT” Also not so suprisingly, children who thrive in early math education will tend to have higher math scores later in life. That's about all we seem to know about early math education anyways.

JamilD 10y ago

I find play to be the most effective way of learning. When I was learning, for example, the backpropagation algorithm, no amount of lectures could've helped me understand better than just drawing a network, thinking "what happens when I change the weights here?", and toying with the equations. It gives you an intimate familiarity and understanding that you can't get anywhere else.

agumonkey 10y ago
Play disengage a very bad emotional state often found in classes. You don't fear ridicule much, you're eager to try, lots of iterations in a small time; often instant results.
- Declanomous 10y ago
  This is what I like about common core. I think a lot of hate for it comes from the fear of being wrong in school that a lot of people have growing up. The common core homework people post online with captions like "how is my child supposed to know the answer to this?" The point is they aren't, they are supposed to come up with a guess and explain their reasoning.
  - l3m0ndr0p 10y ago
    Common core is a blight on children and needs to be eradicated for the USA schools. This systems has destroyed my child's self esteem and ability to grasp simple/moderate math problems. The schools were blaming my child, yet they didn't even consider that methods of teaching are wrong and should be modified to suit an individual. The one-size fits all doesn't work & never will. Fuck common core and the people who are making money off of it.
  - yjftsjthsd-h 10y ago
    Yes, but they're being graded, at which point it isn't really play.
    - Pulcinella 10y ago
      That really depends on the school and grade level. The homework I assign is usually graded for completion, not accuracy. You still have to do it, but there is less pressure on getting the right answer instead of learning.
  - 0xdeadbeefbabe 10y ago
    Some of the hate for it comes from it being a mandate for everyone. I don't believe you can force people to be playful about their homework in the right way. Some child is probably reasoning: "I answered this question this way because I want to be done with my stupid homework."
    - Pulcinella 10y ago
      "...I want to be done with my stupid homework." In a way, this is a huge difficulty with learning in general. Practice can feel repetitive and boring, especially if you don't care for the skill you are practicing. As a teacher I'm not sure what to do about this. I teach science and the "fun" parts are frequently tied to things students don't like (e.g. Algebraic calculations needed for simple data analysis like calculating averages or rearranging a formula to solve for momentum). The students are curious about science, but hate the math parts because they struggle with the algebra. Doing algebra isn't the point, it's just a tool you need to do the science. The goal is to be good enough at the algebra that it doesn't require any real brain power so that the students can focus on the science, what their resaults really mean, understanding the system, etc. If you have a poor grasp of algebra then you are going to have a bad time. I'm not sure what to do for these students except have them practice and I'm not sure how to always make practice enjoyable. I'm not talking about homework here, necessarily, and I don't think homework is appropriate for all grade levels in all situations.

partycoder 10y ago

In my opinion the best abacus you can get is the 5 beads per rod one (soroban). The 7 bead one pictured in the article header is slower to work with (classic suanpan). The 10 bead one used in the west for kids may be good to have an intuition about quantities, but for practical use it is the worst. You can get a soroban, learn the basic algorithms, then use an soroban drilling app to gain speed. With practice, you can exploit muscle memory and stop using a physical abacus. The abacus provides a workable mental model for numeric operations. In contrast, calculators are opaque machines. They take inputs and provide an answer but do not expose their inner workings in a way that can be assimilated and learned by the user.

bogle 10y ago
I have a couple of soroban at home. One has lovely, bright, colourful beads to attract the children. They are attracted, they try to use them as roller-skates. Which soroban drilling app have you used?
- partycoder 10y ago
  This Android one is free and very responsive. https://play.google.com/store/apps/details?id=br.net.btco.soroban&hl=en https://play.google.com/store/apps/details?id=br.net.btco.so... There are Youtube videos explaining the algorithms. A basic exercise is just counting, and then do a countdown. And then try to do it as quickly as possible. Then do it in intervals of 2 rather than 1, then 3, and so on.
cnlevy 10y ago
Flash Anzan is impressive for a westerner : https://www.theguardian.com/science/alexs-adventures-in-numberland/2012/oct/29/mathematics https://www.theguardian.com/science/alexs-adventures-in-numb...
- deleted 10y ago
  [deleted]
digi_owl 10y ago

ideonexus 10y ago

I see these kinds of benefits in over-learning keyboards as well. The few classes I've taught to children and teenagers, you can see a dramatic difference between the students who are familiar with keyboards and those whose parents--I speculate--don't allow them screen time. This extends into adulthood. The people I work with who have that well-practiced familiarity with keyboards and keyboard shortcuts--using them as if extensions of themselves--easily adapt to any new software interface. The adults who hunt around the screen with a mouse have a great deal of difficulty with change and are almost helpless when confronted with a new interface--even if the menu items are all in the same places as the last software. It's a comfort and familiarity with the computer that allows the user to easily adapt to new things. It totally makes sense to me that working with an abacus would have similar benefits for making students comfortable with math.

dragonwriter 10y ago
> you can see a dramatic difference between the students who are familiar with keyboards and those whose parents--I speculate--don't allow them screen time. "Screen time" and keyboard use are very different things; while most opportunities for keyboard use also involve screen time, quite a lot of modern screen time doesn't involve keyboard use. I would bet that those unfamiliar with keyboards are a much larger group than those whose parents don't allow them screen time, the former group being a superset of the latter.
koroch 10y ago
It's all gone down hill after we stopped using the command line. Back in my day ...
- rubber_duck 10y ago
  Hand crafting punch cards for that OG physical experience.
  - yjftsjthsd-h 10y ago
    Keyboards are higher bandwidth than punch cards, mice, or touch screens; currently they appear to be the best option.

hammerandtongs 10y ago

So from the hour I wasted yesterday poking around the web after reading this article - http://webhome.idirect.com/~totton/abacus/PDF.htm http://webhome.idirect.com/~totton/abacus/PDF.htm Seems like the best free resource. This book seems like the standard english text on soroban - https://smile.amazon.com/Japanese-Abacus-Its-Use-Theory/dp/0804802785/ https://smile.amazon.com/Japanese-Abacus-Its-Use-Theory/dp/0... The first few chapters are great. This book from the sixties mentions that abacus are actually a middle-eastern invention and came east with trade. Abacus in fixed frames are a later invention for speed but earlier versions would have more resembled a backgammon table using pebbles. https://en.wikipedia.org/wiki/Abacus https://en.wikipedia.org/wiki/Abacus https://en.wikipedia.org/wiki/Salamis_Tablet https://en.wikipedia.org/wiki/Salamis_Tablet This led to this pretty interesting paper - https://arxiv.org/pdf/1206.4349.pdf https://arxiv.org/pdf/1206.4349.pdf It seems like there is a pretty large gap in our understanding of how people actually did calculation? Cheers

n00b101 10y ago

The American elementary and high school education system would do young students a huge favour by abandoning the use of electronic calculators. I have no doubt that the abacus is a superb pedagogical tool but simple pencil and paper calculation would be a huge improvement over the calculator culture in early mathematical education. I majored in Applied Mathematics in university and did not use a calculator in a single class or exam - it was explicitly forbidden to use them. But I was also educated in the American elementary and high school curriculum. I am thoroughly convinced that the use of calculators in the American system does a huge disservice to students. The calculator culture begins at an astonishingly young age, in elementary school, when kids are first introduced to the Texas Instruments TI-108 calculator [1]. This bright blue and red, solar-powered gadget is very exciting for children in a classroom, but it is poison. At the very age that students should be drilling mental math, they are instead given this huge crutch. It's like never taking the training wheels off a child's bicycle, robbing them of the opportunity to actually learn to ride a bicycle. The same story is repeated in middle school (with the same TI-108). And then you reach high school. You would think that at least now the the training wheels would come off. But instead, you are "upgraded" from bicycle with training wheels to an adult-sized tricycle. I am, of course, speaking of the Texas Instruments "graphing calculator" [2]. This abomination is a full-fledged programmable computer with CAS software. You are encouraged (even required) to use this machine all the way through Advanced Placement Calculus. If you are not distracted in class playing video games on your "graphing calculator," then you may use it to automatically solve algebraic and trigonometric equations and evaluate derivatives and integrals. Why bother memorizing identities when you can just program them into a computer? If you have been programming from an early age, then you may be in the worst place possible because you are predisposed to wasting your time trying to program your way out of math homework instead of focusing on learning math. When students complain about why they have to learn Calculus, your American math teachers tell you that nobody "in the real world" actually solves integrals by hand and it's all done on computers, but you have to learn it anyway for obscure pedagogical reasons. An aspiring future Comp Sci student is likely to take this as a clear signal that it's all a waste of time, and soon high school will be over and you'll never need to worry about this antiquated Calculus thing again - your computer will do it all for you. There are other ways in which American mathematics education is extremely flawed, but the calculator culture is the worst offence by far. I suspect that the bureaucrats who decide on such things rationalize this by calibrating the curriculum to what they see as the "lowest common denominator" student who will never need to learn anything beyond basic algebra and arithmetic. The goal of the system is to train this student to be a productive, low-wage worker, with just enough mathematical training to be able to mindlessly punch numbers into a cash register or simple spreadsheet on the rare occasion that the need for numerical computation may arise in their "careers." I have a three year old and I have no idea what I could do to save him from this insane system, short of moving to a different continent. [1] https://en.wikipedia.org/wiki/TI-108 https://en.wikipedia.org/wiki/TI-108 [2] https://en.wikipedia.org/wiki/Comparison_of_Texas_Instruments_graphing_calculators https://en.wikipedia.org/wiki/Comparison_of_Texas_Instrument...

jimmies 10y ago

It seems like the things that are more painful to learn and use make your brain work harder, and thus make you learn better. Or, maybe it is the case that people who know to use the hard stuff are interested in the subject enough to learn how to do it the hard way. You wouldn't be surprised that those who use Assembly to program tend to have better programming skills compared to those who only can program in Visual Basic, would you? Veritasium also mentioned this recently: https://www.youtube.com/watch?v=UBVV8pch1dM https://www.youtube.com/watch?v=UBVV8pch1dM The more interesting question to ask to me is (1) whether it is the abacus that makes children learn better, or it is just that children who choose to use the abacus learn better (2) whether teaching abacus use at the beginning has the same effect as teaching abacus use later on after the students already know how to use the calculator. If children who choose to use the abacus learn better, then it wouldn't surprise me, but it means that teaching abacus wouldn't help. If that is false and (2) is true, then we know we better off teach abacus (or assembly) -- it doesn't matter when. But if (2) is false, it means that we have a huge trade-off to consider. Because either we teach the hard stuff at the beginning and discourage a lot of students, or we don't and have worse learning outcomes.

abecedarius 10y ago
The post links to a randomized controlled trial. (I only read the abstract.)
MengerSponge 10y ago
Your Assembly/Visual Basic question is going to be badly biased. The barrier to entry with VB is lower, so you'll see more low-skill programmers. This reduces the average competence of the entire cohort, but doesn't tell you anything about the high-skill users. Now if you could show that learning assembly led to better programming skills, you'd be talking about something similar. I suspect that a comparison of introductory programming via assembly vs a modern high-level language would find lower overall proficiency in the assembly group, although a few students would do fine. Personally, I suspect that there isn't anything particularly unique about using an abacus, compared to other manipulation techniques. These are probably all superior to calculators, which are generally awful.

ForHackernews 10y ago

There's a cute story in Surely You're Joking, Mr. Feynman where a man with an abacus challenges him to an arithmetic contest: http://www.ee.ryerson.ca/~elf/abacus/feynman.html http://www.ee.ryerson.ca/~elf/abacus/feynman.html

scarmig 10y ago
He's a bit too pleased with himself at the end there: they simply are using different algorithms, and those naturally have different performance properties for different inputs. Feynman is relying on a prepopulated lookup table and some heuristics, while the abacus guy is relying on whichever algorithm is best suited for calculating cube roots on an abacus. Though, I admit, I'd probably be pleased as a peach too.
- yosefk 10y ago
  Feynman uses a much larger set of algorithms though, and can come up with new ones. The guy with the abacus seems like he didn't know why his algorithms worked, he just executed them.
_yosefk 10y ago
And in this story he claims that abacus use is mechanical and rids you of having to "know" numbers or approximate methods or understanding anything about the computation and why answers come out as they do. You're just executing steps and the more complex the computation, the more steps you do with no understanding whatsoever. So the opposite thesis from TFA.
- sn9 10y ago
  It's not really an opposing thesis. The moral of the story is that his opponent became married to the use of the abacus and convinced of its superiority and that led to an overreliance on it and inflexible thinking. The thesis of the TFA is that the abacus can be a great tool for teaching arithmetic and number sense. It doesn't argue that it's the only thing you'll ever need and you should use other tools.

retox 10y ago

Probably off-topic but I checked Isaac Asimov's "Realm of Numbers" from my library on the recommendation of HN and it's great. One of the earlier chapters outlines how the abacus and its concept of 'the unmoved row' could have helped forment the idea of zero. Very interesting text, no idea if the ideas are considered incorrect these days but still entertained and educated. 10/10 read.

myth_drannon 10y ago

Related to abacus use. Sam Harris podcast "Complexity & Stupidity" https://www.samharris.org/blog/item/complexity-stupidity https://www.samharris.org/blog/item/complexity-stupidity mentions abacus skills. The skill "spreads" to other areas of the brain they call it "complementary cognitive artifacts" Quotes : Harris: What else would you put on this list of complementary cognitive artifacts? Krakauer: The other example that I’m very enamored of is the abacus. The abacus is a device for doing arithmetic in the world with our hands and eyes. But expert abacus users no longer have to use the physical abacus. They actually create a virtual abacus in the visual cortex. And that’s particularly interesting, because a novice abacus user like me or you thinks about them either verbally or in terms of our frontal cortex. But as you get better and better, the place in the brain where the abacus is represented shifts, from language-like areas to visual, spatial areas in the brain. It really is a beautiful example of an object in the world restructuring the brain to perform a task efficiently—in other words, by my definition, intelligently.

neves 10y ago

Do you have references about how to use an abacus? I just know how the obvious uses: counting, summing and subtracting. There is a famous story about Richard Feynman and the abacus: http://www.ee.ryerson.ca:8080/~elf/abacus/feynman.html http://www.ee.ryerson.ca:8080/~elf/abacus/feynman.html where the guy makes a lot of difficult calculations.

partycoder 10y ago
I love that book. The "Fixing radios by thinking" part is a great insight on how Feynman developed such powerful intuition around physics at an early age. In contrast, modern electronics are not as transparent and intuitive as their vacuum tube counterparts. I wonder what would have happened if Feynman had to fix radios with transistors or integrated circuits.
neves 10y ago
I've just found a great one: http://webhome.idirect.com/~totton/abacus/PDF.htm http://webhome.idirect.com/~totton/abacus/PDF.htm

meow_mix 10y ago

Maria Montessori had a lot to say on the importance incorporating tactile elements in early education. This is why Montessori schools generally incorporate tools like the abacus (at least mine did). Not surprised we're re-learning some of her findings today

nkrisc 10y ago
The Montessori school I went to didn't have an abacus for us to use, but to your point, the physical representations of 10^1 (a row of 10 beads), 10^2 (a 10x10 square of beads), and 10^3 (a 10x10x10 cube of beads) using beads helped me understand exponents much more quickly. Unfortunately we did not have a 10x10x10x10 tesseract of beads.
- roywiggins 10y ago
  I'm a huge fan of the Montessori binomial cube: http://www.montessoriworld.org/sensory/sbinoml.html http://www.montessoriworld.org/sensory/sbinoml.html
  - nkrisc 10y ago
    Of course! We had those too. I had totally forgotten about that.
agumonkey 10y ago
Jaron Lanier did experiments in VR with switched limbs, so your brain tries to make sense of a new "geometry". I also felt regularly that all kinds of inputs are very stimulating for the brain and bolden the memory. For instance writing down with pen and paper requires more brain activity than a keyboard. Computers seem faster for note taking but the ease actually removes the colateral inputs that stimulate/challenge your brain and thus helps learning (you also have to reflect about what to trim and how to organize your notes, thus creating so semantic map of the topic).

jweir 10y ago

vim

robbiewxyz 10y ago

I absolutely see this. Just today I've been helping teach a friend's child to do multiple-digit multiplication on paper. In that kind of thing, understanding place values (the ones-tens-hundreds columns) is so important. It's amazed me how many high school students even don't quite get the idea of place values and what base 10 means. The abacus requires a good understanding of that concept from the start. So, while the "skill spreading" might also contribute, with the abacus, it's a basic and essential concept to really understand for all higher-level math.

forkandwait 10y ago

Can anyone recommend an actual abacus to buy?

Animats 10y ago
To add and subtract, I'd suggest a soroban, the Japanese 4 and 1 bead per row abacus in hand-held size. Those were in wide use until a few decades ago, and can be operated quickly. They're still available on Amazon and Alibaba. Get one where the beads are cone-shaped, not round; those are easier to manipulate. Don't bother with a "reset button"; you can do that with one finger in a second, rattling down the columns. It's not a very useful skill, but it's not hard to learn. I wouldn't inflict it on kids. The 5 and 2 bead form is more of a school thing. I probably still have one, packed away with the slide rule. My HP-11C is on my desk.

racl101 10y ago

It's a great way to understand our base 10 number system. That definitely gets lost when using calculators and computers. As well, I have to believe it would help a child understand any other number system such as binary, octal and hexadecimal.