
Abacus use can boost math skills - Osiris30
http://kottke.org/17/03/abacus-use-can-boost-math-skills-and-other-lessons-on-learning
======
JamilD
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
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
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.

~~~
btilly
What I don't like about common core is that it is leaving my son and his
classmates hopelessly confused and without basic calculation skills.

If we want to actually fix elementary math education, that would be simple.
Singapore has developed a math curriculum that puts them top in the world in
testing. Every research study that has used their system has found that it
works far better than we do. But we have an entire educational establishment
whose profits depend on our having periodic crises that let them rewrite all
of the textbooks and charge top dollar retraining all of our teachers.
Switching to something that works wouldn't make them money, so they will
undermine the political process to guarantee that it doesn't happen.

As for homework, that's a giant can of worms. There is plenty of research on
homework. It shows that homework is net neutral on actual learning, but a
strong negative on creating stress. Digging in, it turns out that it can help
or hurt, but whether it helps or hurts depends on whether there is someone at
home who makes sure that the child does correct practice rather than incorrect
practice. Therefore assigning homework's main impact (after home stress) is to
widen the educational gap between children of different socioeconomic
statuses.

The problem with common core homework is that the children don't know how to
do it, the parents can't figure out what the teacher wants, and the end result
is utter confusion. I've seen this first hand. I have a masters in math, but
I'd look at my son's 4th grade homework and say, "I can think of several
things that the teacher _might_ want, but I have no idea which one she does."
The end result was utter confusion in my son. Confusion that resulted in his
lacking basic skills until we hired a tutor to fix that.

Anyways Common Core is a complete and utter disaster. We aren't too far from
parents' resentment rising up and causing a new reform movement that will
predictably get hijacked by the same interests who guaranteed that Common Core
would fail. Which is nothing new. It has happened every 5-10 years for longer
than I've been alive...

~~~
uniclaude
> _As for homework, that 's a giant can of worms. There is plenty of research
> on homework. It shows that homework is net neutral on actual learning, but a
> strong negative on creating stress. Digging in, it turns out that it can
> help or hurt, but whether it helps or hurts depends on whether there is
> someone at home who makes sure that the child does correct practice rather
> than incorrect practice. Therefore assigning homework's main impact (after
> home stress) is to widen the educational gap between children of different
> socioeconomic statuses._

That sounds very interesting, and really matches what I've seen so far. Do you
have a link to some of this research? I'd like to share this with some friends
but would like to share more than a link to a single hn comment!

~~~
btilly
That comment sums up what I learned from [http://www.alfiekohn.org/homework-
myth/](http://www.alfiekohn.org/homework-myth/).

Every so often I run across more recent research on the same topic. It always
comes to the same conclusion.

But parents generally feel better about their kids having poor results if they
see evidence that their kids are at least putting out lots of effort. Homework
serves as evidence, so it is hard to get rid of it.

In the meantime I'm lucky that 3/4 of my children get to go to
[https://www.vandammeacademy.com/](https://www.vandammeacademy.com/) which
believes in doing what is proven to work. Therefore they have a no homework
policy, adopt proven methods like Singapore math, and so on. Which is why 3/4
of my children are getting a truly superior education with far, far less work.

Just to give a relevant anecdote about how strongly parents can feel about it,
I know a fellow parent there who turned down a $400k/year job at Google
because it would have meant that he had to move to Silicon Valley. He is
convinced that he has found the best K-8 school in the country and won't take
that away from his children.

He's far from the only parent at the school who feels that way.

------
hammerandtongs
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/0...](https://smile.amazon.com/Japanese-Abacus-Its-Use-
Theory/dp/0804802785/)

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

------
partycoder
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
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
This Android one is free and very responsive.

[https://play.google.com/store/apps/details?id=br.net.btco.so...](https://play.google.com/store/apps/details?id=br.net.btco.soroban&hl=en)

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.

------
meow_mix
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
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
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
Of course! We had those too. I had totally forgotten about that.

------
myth_drannon
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.

------
ForHackernews
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)

~~~
_yosefk
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
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.

------
jimmies
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.

~~~
MengerSponge
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.

------
hedgew
>“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.

------
retox
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.

------
neves
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.

~~~
neves
I've just found a great one:
[http://webhome.idirect.com/~totton/abacus/PDF.htm](http://webhome.idirect.com/~totton/abacus/PDF.htm)

------
robbiewxyz
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.

------
ideonexus
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.

~~~
koroch
It's all gone down hill after we stopped using the command line. Back in my
day ...

~~~
ashark
I did plenty of mavis beacon and such and hated it (though it drilled the
basics into me, at least) and used the DOS command line a bit, but what made
me _fast_ and _accurate_ was busy real-time chatrooms and IM. Basically Yahoo
Chat and ICQ, especially the former. If you wanted to chime in you had to be
very quick. If I'd never found something that _forced_ me to be fast if I
wanted to participate, I might well still be a crappy, slowish typist.

~~~
pythonaut_16
Online games were also great for this! You have to type quickly so that you
can keep up with actually playing the game, and you can't stare at the
keyboard because you need to keep an eye on what's actually going.

In some ways I owe my career to Warcraft 3

------
racl101
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.

------
n00b101
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_Instrument...](https://en.wikipedia.org/wiki/Comparison_of_Texas_Instruments_graphing_calculators)

~~~
jlos
Calculators are tools and just need to be used in an appropriate context.
Engineering programs in Canada allow no calculators for math classes
(Calculus, Linear Algebra, etc) but they are an absolute necessity for for
Engineering classes (e.g. dynamics). It's a very nice balance because the math
classes hone your abilities to think and reason mathematically unaided by the
engineering classes hone your ability to apply those skills without getting
bogged down in details about calculations.

~~~
n00b101
I don't disagree that computers/electronic calculators are appropriate tools
for engineering, science and business classes, even at the secondary or
primary school levels. Those are contexts where numerical computation with
"messy" numbers are necessary. Insisting on manual calculation in such a
context would be tedious and of no pedagogical value. I was only talking about
math classes, where exam questions can be made up with "clean" numbers so that
there is never any need for using a calculator.

Although, given that we are in 2017, I really don't think that the traditional
pocket calculator is a good tool in any educational context. In any context
where using a pocket calculator makes sense, a full-fledged computer makes
much more sense (except perhaps elementary school science classes). If you are
numerically solving equations in an engineering class (e.g. dynamics), then
you should really be using something like MATLAB or Python (or Julia!).
Similarly, if you are analyzing a financial statement in an accounting class,
it would make far more sense to use a spreadsheet rather than an HP 12C
calculator. Using a computer would be much more convenient and have far
greater pedagogical value for "real-world" training in such contexts.

I think the only reason that pocket calculators are prevalent in higher
education contexts (such as your dynamics course) is that it is more difficult
to cheat on an exam using a calculator (e.g. smuggling in notes) than it is
with a full-fledged computer. But that is really a computer security issue and
there ways to solve that problem which don't involve a throwback to
antiquated, 1960s desktop computing technology.

------
forkandwait
Can anyone recommend an actual abacus to buy?

~~~
Animats
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.

------
jweir
vim

