Abacus use can boost math skills
kottke.org
kottke.org
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.
You don't fear ridicule much, you're eager to try, lots of iterations in a small time; often instant results.
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...
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!
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/ 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.
The major complaint from parents with this seems to be they can't understand it. But that's exactly the point: their kids are supposed to be getting a more rigorous education (in the sense of understanding vs. being able to find an answer).
Another key problem: in the US, a lot of our math educators (especially at the elementary level) really don't like math. At the end of the day, the teacher has to explain, assign and grade the curriculum. If they don't understand the core concepts, or don't like teaching them (for instance, they know how to do the carrying-digits multiplication, but never have played with breaking up numbers to add them), they can't teach those concepts effectively. And we put nowhere near the amount of time or money into training our existing teachers as Singapore does. Common Core is an attempt to provide common concepts and training, so we can focus on making teachers better at areas they struggle with. But you can't do that if there's no will or resources to improve.
Singapore Math has had years of refinement to get where it is. Common Core is just starting down that road.
And for the record, Singapore Math absolutely does teach "standard math algorithms". They just build up to them in pieces so that the algorithm will be dead obvious when they finally present it. There is a world of difference between this and confusing kids with 3 different algorithms, leaving them with no idea which is which or how to keep them straight.
But now we come to this...
The major complaint from parents with this seems to be they can't understand it. But that's exactly the point: their kids are supposed to be getting a more rigorous education (in the sense of understanding vs. being able to find an answer).
Excuse my language for a moment.
Do you have any fucking idea how condescending it is to receive this type of bullshit response to my complaint? I'd be willing to bet money that my background in and understanding of math is more extensive than yours, and CERTAINLY more so than the vast majority of proponents of Common Core that I see this from. Should you disagree, please provide evidence of your graduate degrees in math, placement in the top 100 on the Putnam, published research papers, or public tutorials explaining complex math concepts on par with http://www.elem.com/~btilly/kelly-criterion/ or http://elem.com/~btilly/effective-ab-testing/.
The problem is NOT that my son's ELEMENTARY SCHOOL TEACHER is giving him a MORE RIGOROUS math education than I received. It is that she FAILED TO TEACH him. Full. Stop. She FAILED to TEACH him.
Even so, on the standardized tests that we use to measure this fucking bullshit, HE WAS BETTER THAN 95% OF KIDS HIS AGE IN CALIFORNIA. This was true DESPITE his lacking basic skills like long multiplication!
In other words he is what Common Core proponents will cite AS A GODDAMNED SUCCESS!!! And yet I had to spend my fucking time and money to fix their failure. And not, I assure you, due to any lack of ability on his part. His scores relative to other California children are a testament to THAT fact.
Language warning off.
Please read my rant multiple times, and try to put yourself into my shoes. And hopefully you'll think twice before dismissing other people's feedback in such a condescending manner.
Furthermore there is nothing new about this pattern. I grew up knowing about the new math disaster, and now I'm watching it repeat.
Here is the basic outline of how these reforms go.
1. Reformers have wonderful ideas about how children can learn better, understand more, etc.
2. On a small scale, done by motivated and knowledgable people, it works well. (Easily true through some combination of true enthusiasm, https://en.wikipedia.org/wiki/Hawthorne_effect and random chance.)
3. Reformers try to get the good word out and get enthusiastic support from frustrated parents, interested educators, textbook manufacturers, and so on. Who have good ideas, refine the proposal, and begin the difficult work of getting support for the proposal and materials ready. (This was probably an accident the first few times, but it is unimaginable by now that the education industry isn't now actively aiming to be on the leading edge of these waves.)
4. The reforms hit the big time! Politicians line up, new standards are adopted, new curricula is rolled out, teachers are retrained, new textbooks. Billions of dollars gets spent here. (This step is very, very profitable for the education industry.)
5. There are glitches in the rollouts. Problems can be blamed on poor training of teachers, incomplete adoption of reforms, parents resistant to change, and so on. Reformers can dismiss all of this as not their fault, things are getting better and problems will be solved once everyone is on board. (At the time this can be dismissed as teething pains. But it is predictably inevitable given how much gets changed at once.)
6. Complaints get louder. Politicians are listening. Schools are fully on board with the reform, but parents push back. The vast majority of complaints continue to be dismissed by reformers as the result of improperly trained teachers, ignorant parents, and so on. Teachers publicly toe the party line, but many are privately unhappy. (This is about where Common Core is now.)
7. Unhappiness coalesces into support for NEW reforms. The reform has now become the OLD reform. Reformers remain convinced that they can fix the world, but they are now facing political headwinds and are losing ground. (Want to bet on whether this will happen soon.)
8. A new reform wins, hitting its step #4. The old reform is officially toast. However it will hang on for a long time in pockets and corners. And ideas from the old reform enter the educational gestalt as potentially parts of seeds for a new reform.
I knew about this cycle growing up. My mother was a teacher and had to deal with it for her whole life. She eventually quit when "whole language teaching" came in and she was going to be forced to give up phonics. (Never mind that her students reliably finished grade 1 reading at a grade 3 level. In our schools ideology trumps results.) I understand that you are hearing about this from educators who are part of the usual reform pattern. What you are hearing from those educators echos things that have been said in many prior movements, and will be said in many future ones.
Take, for instance, your statement that, "And it would be great if part of the support we gave to teachers was paying people like you to provide training to them, and helping those teachers who don't like teaching math learn what challenging and achievable standards actually are." That's not new. It is a common way to get people to try to become part of the reformers solution.
My answer to that is no. I know this pattern. I know how it turns out. The problem is generally not any individual reform. It is in how we DO reforms in this country. It reliably creates profits at the cost of serving our children poorly. That is evil by any definition that I care about, and I do not wish to support evil by becoming part of it.
From my outsider perspective, the comment you are replying to is entirely reasonable and not personal (“The major complaint from parents [..] seems to be” is not the same as “your complaint right here”), and then you flew off the handle and started cursing the commenter and your son’s teacher in all caps.
P.S. this “If we want to actually fix elementary math education, that would be simple.” is a pretty ridiculous statement, unless by “simple” you mean something like, «Create a new job for elementary school math teachers; hire well qualified candidates; give them rigorous teacher training; pay them much better, provide a longer career ladder, give them more autonomy, and show them dramatically more respect than currently; and reorganize the whole school day to give the new math teachers time for introspection, collaboration, and professional development. While we’re at it, fix and improve school facilities, and make sure every school/teacher has the resources they need.» In that case, sure, “simple”. (Note that the specific curriculum used has little to do with any of this.)
If it wasn't the stock way of ignoring complaints for Common Core, I'm sure that I would have responded differently.
I couldn't agree with you more on the homework front. However I don't think homework is intrinsically the problem, I think the problem is the fact that our current educational system is based around pedagogy, of which doing homework is only a part. I personally think the fact that Common Core is designed to be more Socratic.
The key problem is that Common Core is an ambitious set of ideas that requires everything to be done differently than it had been before. While there are a lot of good ideas in there, there are going to be inevitable mistakes and a shaking out period while the challenges get figured out and people learn best practices for how to make it work. In the meantime our children are guinea pigs with widely differing experiences. My son's experience being on the bad side.
However we have seen this picture before. Everything that I just said about Common Core could have been said 50 years ago about New Math. The result was Why Johnny Can't Add, and the "Back to Basics" movement. Want to bet on whether something like this happens again with Common Core?
And so I predict that our educational system won't figure out how to do Common Core right. Instead we'll have another reform movement, which will likewise have good intentions, good rhetoric, and in the end will likewise fail. As has been happening to us in math since the launch of Sputnik convinced us that the US is behind and needs to catch up.
If your awareness of reform efforts starts with Common Core, then there is a lot of history that you're missing. Every reform movement convinces people that it is working. And they will continue believing that it would have worked until long after it is dead.
Some child is probably reasoning: "I answered this question this way because 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.
For example, I know a lot of children complain about how they will never have to use they math they are learning when they grow up. I think it's a really valid complaint, and I know teachers recognize that issue as well because the write problems that deal with real-world situations.
The things is that a lot of the real-world situations that end up being used in questions are still pretty abstract for a child. Like, money, building fences, finding the area of yards, etc.
A lot of these problems could be translated to actual physical projects. For instance, put everyone in groups of four, and say "here is a little yard with toy animals in it, figure out how much string you need to go around the posts, then come up and cut off a single piece of string. The group that gets the closest wins."
That being said, I think that's kind of a Montessori solution, since you'd probably want kids to choose the activity that interests them the most. It's definitely too much to ask one teacher to lesson plan 3 or 4 little activities for each thing a given group of children need to learn every day, and then monitor those activities as they are happening.
Honestly, I think the majority of the education I've retained from my childhood is from things like Boy Scouts, Cub Scouts and other extracurricular activities like OM/DI.
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...
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/Salamis_Tablet
This led to this pretty interesting paper -
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
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.
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.
When I was growing up in the early seventies, my dad still occasionally used a suanpan to do calculations for his business.
As printing calculators got cheaper, it eventually got retired (I have it now, but don't use it) but he did teach me how to use it.
It does not take very long to get good/fast at using it, at least for stuff like adding up a pile of receipts.
Effectively you have something akin to a binary watch, where you move the top bead to indicate if the bottom 4 beads are 0 to 4 or 5 to 9.
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).
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.
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.
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.
Veritasium also mentioned this recently: 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.
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.
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.
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 where the guy makes a lot of difficult calculations.
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.
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.
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.
"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.
In some ways I owe my career to Warcraft 3
This I take as a given as a very positive parental attitude. Children have to much screen time, reduce if possible.
It's this myth -
>It's a comfort and familiarity with the computer that allows the user to easily adapt to new things.
That worries me.
Too much computer time is devastating to the brain and the person.
Less is way better than to much.
Of course the just right amount is best. But since 50% of parents are below average parents, I think encouraging less is better than more. Screen time is swamping children, it doesn't need to be encouraged, the myth of the first world kid not getting enough computers is like the myth of the first world kid not getting enough calories.
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.
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 [2] https://en.wikipedia.org/wiki/Comparison_of_Texas_Instrument...
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.
Then, notation in some cases is inconsistent and weird. https://www.youtube.com/watch?v=sULa9Lc4pck
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.