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Author Topic: Teaching mental math  (Read 13937 times)
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« on: September 16, 2013, 11:24:29 AM »

I really want to teach my children to do mental math.  The recent discussions on the soroban have been so inspiring.  Such as these, among others.

Lacking a local abacus school, I've been on my own.  I used HEV academy's abacus curriculum (, and my children can now comfortably add and subtract on the soroban, but I don't know how to move forward for teaching anzan.  I think it has something to do with using your hand as an abacus at first?  ie, the thumb represents the 5-bead, and the four fingers represent the 1-beads?

<a href="" target="_blank"></a>
How much do children like this practice?  30-60 minutes a day is what I can do.  I need to be realistic in my expectations.   wub

I've also been impressed with Arthur Benjamin's work.  Ultimately I don't care which route we use to learn mental math, I just want to help my children eliminate the need for a calculator. 

<a href="" target="_blank"></a>

He has a book, and a couple different DVD courses out there.

Plus a book for teaching children:

There are also apps out there like this one:

Anyway, these are the resources I'm looking at.  I would love advice from people who have had success teaching mental math, be it anzan or otherwise.  I'm going to check out "Cheaper by the Dozen" again as I lost my copy and remember that he successfully taught mental math to his young children, during meals if I recall correctly.  My original plan was to move on to Saxon 5/4 soon, but now I'm thinking it would be better to devote my time to mental math first.  If their brain is a calculator, the coursework will be much easier for them.  smile


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« Reply #1 on: September 16, 2013, 02:31:03 PM »

but I don't know how to move forward for teaching anzan.  I think it has something to do with using your hand as an abacus at first?
No. Anzan is a mental picture of the soroban, and manipulating the mental version. Using the fingers makes it more visceral but the fingers aren't needed to actually do it. Like anything, you get better with practice and I'd think 30+ minutes per day will get you really good (though maybe not competition ready). Consistency will work in your favor.


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« Reply #2 on: September 16, 2013, 06:58:06 PM »

Have you checked out Jones Genius program? I really like the first program. It is not really mental math. But I have heard that the other programs are mental math, and math tricks heavy.... I have not seen those yet so someone else would need to verify.


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« Reply #3 on: September 17, 2013, 02:07:17 AM »

Thank you Tamsyn for asking this question. It's a question that's been on my mind after reading the other mental math posts that have cropped up lately on the forum. I too would love to know about books, websites, and other resources for those of us who do not have a Soroban/Anzan school in our area or who cannot afford some of the online schools mentioned on the Brillkids forum. I'm completely new at this and will be starting from scratch, but I'd love to teach my children how to do it and have it be as effective as some of the schools we've been reading about.

I did a little digging on the internet and so far have only found this. I don't know if it will help at all, but here's an interesting link and some mention of other books:

If anyone else more information, please, please, please share with us. There's got to be lots of other parent's wanting to do this as well!!!

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« Reply #4 on: September 17, 2013, 02:15:36 AM »

I browsed a little further and their sitemap seems delightful. Lots of info. It just makes me wonder if there are other free websites and online pdf books like they mention that would be helpful.

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« Reply #5 on: September 17, 2013, 02:21:46 AM »

One of the first and simplest exercises that Alex's Soroban teacher did with her/them was to have them work a problem on the abacus, tell them to take a 'picture' with their mind, and try to do the same problem in their mind. I know it sounds simplified, but she would actually talk them through it:
" clear your abacus. Plus three...minus three." Until the kids could actually 'see' the beads moving in their heads. We are asked to practice this with them as well, part of the time when doing the online homework.

The Soroban school is nearly 2 hours away, so we are doing a mix of online and going to class. Alex is also the youngest there by anywhere from 2-5 years, and it is difficult for her to sit for a 2 hour drive, and a 2 hour class, so this is a perfect option. In addition, we have a grad student who arrived from Japan 2 months ago coming to our house once per week to work with Alex, which is a big help to me...although we are struggling with the language barrier. We love the chance to expose Alex to the language though, so don't mind.

Godlovesyou- there have been lots of threads in BK about Soroban, but you might find this one useful as TmT has taken the time to compile all sorts of resources and options!


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« Reply #6 on: September 17, 2013, 02:33:44 AM »

The movement of the finger and the thumb are simply how the beads are moved on the physical abacus. She is repeating those same movements to help her 'move' the beads in her mind. Eventually the goal is to get to the point where they no longer need the helping finger motions.
The first day of class they had Alex chanting to remember which finger movements were used to move the beads...such as +1, Thumb up. -1, Finger down. +2, Thumb up. -2, Finger down.
Does that help? I can try to clarify a bit if it helps, but I am by no means an expert! Just learning with Alex:)
Parents are allowed to sit in on the class from the sidelines, and I aim to get the most for my money!


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« Reply #7 on: September 17, 2013, 03:03:59 AM »

I have been teaching the abacus to DS5 and he does math mentally in his mind already, so it is hard to know if he is visulaizing the beads in his mind to answer the question.   I realize that the smaller problems are best for him to learn to visualize but my instincts say he isn't visualizing the beads because of his math fact knowledge.  I guide him verbally through the visualization.   I had suspected that he would get stuck on the harder problems because it would be harder to visualize the numbers and use his math fact knowledge and he did.  Any tips on getting over this barrier?   I guess fingers moving an imaginary abacus???? Will math fact knowledge be just a temporary hurdle? I kind of see the benefit of teaching the abacus first now, but I really wanted number  sense first. 


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« Reply #8 on: September 17, 2013, 03:17:57 AM »


Thank you so much for the link. I can't wait to read through it all. It seems like lots of great material. I sooooooooo wish I could sit in on your class with you. If only someone would put out videos of classes like that. It's really a shame it's not as easily available in America as it is elsewhere.

By the way, I love reading your posts. I've actually taken the time in the past to click your profile and read though pages and pages of just your posts. All the math posts have really inspired me. Now, we try to spend as much time on math each day as we do on reading. With my 18 month old, the math seems a wee bit slower progressing than the reading, but we are keeping at it and usually get a couple hours each day of math activities. We started reading activities at 3 months and he can read amazingly well. He's even got the phonics down pat because of Reading Bear. He doesn't know his alphabet yet (except phonetically), but he can read any word we put in front of him (even very, very complex words). But unfortunately, I didn't find the math posts until he was about 1. So it seems much slower to me. Now, I'm just preparing ahead for later mental math learning and tons of other math topics I want to cover with him. Lots of mommy learning to get everything ready for baby learning. Oh, also on the topic of age, what age did you start Alex learning Soroban? Did you practice before you started the classes or just when you started? What age do you think is appropriate to start?

Many thanks again for the link. Keep on posting about math, it's always such a fun read to hear what you guys are doing.

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« Reply #9 on: September 17, 2013, 03:27:54 AM »

Will math fact knowledge be just a temporary hurdle? I kind of see the benefit of teaching the abacus first now, but I really wanted number  sense first.

My guess is yes. There's nothing wrong with having some math facts, and actually you need some simple ones for soroban (1+4, 2+3, etc) - the facts will fly out the window when the complexity goes up enough to tax the working memory. Part of that is number of subsequent digits added or subtracted, part is the speed. As they go up (more numbers stacked on more numbers) and go faster, the math facts simply can't keep pace. This shortcoming is a big reason for learning soroban in the first place. Our working memory is only so good, hence paper and pencil methods.

Work on speeding up the problems if you're worried about relying on math facts - or just stack number after number (+5, -4, -2, +3.... and on and on)


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« Reply #10 on: September 17, 2013, 04:04:58 AM »

PokerDad and Cokers,
PokerDad has answered the question just as our experience in class ha shown us. In fact, if you are only giving a problem like 3+2 to solve, I have no doubt the quickest way your child will arrive at the answer is via memorization! You have to give them faster and faster strings of numbers to almost 'bypass' that shortcut learned from memorization. Alex is really quite good at her math facts, is quick...but the strings of numbers involving addition and subtraction MUST be solved in a different manner on the abacus. She has just learned two different ways to do it. There are times where she will attempt to choose one over another and I have to remind her I want her to work a specific way.
For example, we are doing Singapore math as well, and she is trucking right along...but I need her to work her way through the problems in a standard fashion to make sure she has that down too. To develop a full understanding of the math.

And you DO have to have some math fact knowledge to do Soroban. The kids need to be strong in 'big friends' and 'little friends', all the ways of making 5 and 10, and they will use other math facts through 10 a lot.

      Awwww, you are too kind! Thanks for taking the time to tell me you enjoy my posts! I really need to post an update of what we are up to these days. And maybe some more math posts:)

We did do some initial Soroban work at home before we were able to find a place that would take her. We finally found someone when she was about 3.3. Most classes won't take kids until they are 5 or 6, in our experience. And it was quite an experience to go! Alex was BY FAR the youngest, and although she actually ROCKED the class by being able to answer before many of the kids? It was painfully obvious that she was a distraction to the other kids:(
It was just too much to expect that she would sit perfectly still, do her work without normal kid exuberance (and then some!)
And talk about asynchronous issues! She totally had a fit in the middle because she didn't get a purple pencil like her neighbor!!!
Ah, but I PUT her in an almost impossible situation. We had even driven up the night before and stayed in a hotel so she wouldn't have the drive AND class in the same, we are now doing the combination of online homework, email and Skype correspondence with the teacher, and an in-house tutor. At least until her maturity catches up a bit! I think she will travel 2x per month soon, and we will see. And interestingly enough, the more she practices Soroban, the greater her focus and concentration on other things. Same with her listening skills a she has learned to listen carefully when the problems are called out.


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« Reply #11 on: September 18, 2013, 01:10:34 PM »

Thank you everyone!  I did know that the ultimate goal is to manipulate an imaginary soroban, but I read somewhere how the soroban paralelled our hands and to take advantage of it, but I couldn't find that article again and it seems that this approach never comes into play at these schools.  Good to know.  Kerileanne, your experience has been most helpful.  Thank you and karma!   yes

I came across this site which has been very helpful in giving me a way to move forward.
Under the "Anzan" tab on the right, I found a printable that the kids can use to help them manipulate a soroban in their heads ( and a couple of free, simple software programs to create math problems for the kids to practice.  I'm still taking a stab in the dark as far as figuring out how quickly I should move forward and wondering how many 1-digit numbers they should be able to add before moving on to 2-digit numbers, and/or how much addition before subtraction.  So I'm going to look through the different curricula  available, but I have a better idea of what I'm shopping for now.

The hevacademy that we used was a great introduction to soroban, I think.  It has 33 lessons and teaches how to add, subtract, carry, borrow, internalize the "friends" in relation to 10 and 5 (I like "Big friends" and "little friends", and will start using that term) and use the correct fingering.  It was fairly inexpensive especially if the other things on the website are useful to you.  But it's a very basic introduction.  There are no strings of numbers, and no mixing of operations.  Each exercise focuses on one skill set alone.  I'm glad that I started here, but now we need to move on.  I tried adding 10 four-digit numbers on the abacus yesterday and I got it wrong the first time, so I obviously need more practice too.  I feel like I know where we are headed again, and that's exciting.  Thank you again everyone.  smile


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