Cammie's Anzan (mental math)

[nadia0801]

We're blessed to have enrolled in an abacus school (though it's 2-hrs of total travel for us). Yesterday was Cammie's 4th session but I felt she's ready to do anzan. The school has several levels (Foundation, Junior, Level 1 til 7). They introduce mental imaging on Level1 for ages 7-up. Cammie, being on the lowest level (foundation) is just starting one digit addition & subtraction but at home, I'm letting her choose to answer by "imagination" or use her abacus when doing her home-work.

Today, at almost 3 years & 5 months old, she answers six-string addition and subtraction. She's not that fast yet and only uses 1-digit numbers but I'm super happy that she can picture the abacus in her head! Thank you for all the inspiration we got from this forum, if it wasn't for all of your posts, we wouldn't have plunged into this wonderful world of abacus. She was not a big fan of math (me too) but with abacus, it's like playtime to her.

<a href="http://www.youtube.com/v/vD6MXc3219Q&rel=1" target="_blank">http://www.youtube.com/v/vD6MXc3219Q&rel=1</a>

[Elys]

That's amazing Nadia!!! What a gifted child you have !! Good job to both Mummy and Cammie!

[Soroban]

Hi Nadia,

Congratulations!

I had a quick questions: Do they use the term "remove" for subtraction in the class? or something else?

Thanks,
Tom

[nadia0801]

Thanks Elys and Tom!

@ Tom:

At school they use "less". At home, even before she started school, I say "minus" and "remove" when I dictate to her. Is there a standard?

Also, I remembered your post that mixing addition and subtraction is detrimental or might be confusing to students. Cammie's school teaches these operations at the same time. Should I be worried? Many thanks to your input!

[Tombliboo]

Oh my goodness she is amazing!! How fantastic! Well done to you both.

I cannot believe what I am seeing on this forum! I have only just started LM with my 8 month old. Would you be so kind to tell me how you got to this point with Cammie?

[PokerDad]

Thanks for sharing. It was fun to see her moving the beads in exaggerated movements

I won't speak for Tom (and am looking forward to reading his further input in this thread), but in my own limited experience with soroban, it can be easy to start confusing addition with subtraction across a few place values. In other words, I don't think mixing addition and subtraction in one problem will be an issue if there's no carry function happening. That was how I understood Tom's concern anyway.

[Mandabplus3]

How cool! I don't think it matters how easy the sums were or if it is adding or takeaway, it's clear from the video that she can visualize it all, and understands it enough to get the answer right. That's quite an achievement in one so young. Would you think to attribute her visualization skills to her right brain training ( mandala, tweedlewink...) or more to the fact that she just know ALOT and now learns quickly?
Poker dad am I to assume from your post that the method you use teaches addition first and then subtraction quite a bit later? I am confused by your comment although i understand the carrying across place values. I quite liked the math programs that basically taught the two simultaneously but as opposites. I could see a future in the notion as sums got more complex.
Once again I am just curious to learn 

[PokerDad]

Mandabplus3: I don't teach soroban. I was referring to my own experience practicing it, and someone my age, that already knows math, occasionally confused the addition and subtraction functions when practicing 3 or 4 digit arithmetic on the soroban when first starting out. When Tom, an actual soroban instructor, mentioned that he liked to teach one before the other, this made sense to me because of my experience. But what Cammie is doing is single digit and I think going forwards and backwards (adding and subtracting) will be just fine.

[Dr Miles R Jones]

Nadia,

Thanks for the fabulous video of Cammie.  There are case histories of rapid mental calculators who developed their abilities via extensive use of the abacus.  Cammie's ability to do strings of calculations is great!  Sounds like you are a great mom and teacher.

[Dr Miles R Jones]

Nadia,

Just wanted to weigh in on the question of teaching addition before subtraction.  This is somewhat standard procedure but not a good one.   Much more time and emphasis is usually put on addition and therefore children are typically much weaker in subtraction.  This is repeated when multiplication and division are introduced later.  Multiplication skill is strong because it is practiced more often.  Multiplication is often stronger than subtraction, and division is typically the weakest skill of all because it receives the least time on task.  This is all a result of the way it is taught, basically time on task.  It is no harder to subtract than add, no harder to divide than multiply.

I teach addition and subtraction at the same time.  This begins with numeration concepts like counting forward and backward.  We typically count forward a good bit which is the main mechanism of addition.  In my experience, counting backwards is rarely practiced which is the basic process in subtraction.  Is it any wonder?  I might suggest when you count forwards you always follow it by counting backwards.  A countdown, like in a rocket launch, is a great visual to go with practicing counting backwards. 

When you add, say 5 + 3 = 8 then make a habit of reversing it and say 8 - 3 = 5. If you know the addition you should also know the subtraction, they are related operations.  Equalize your practice of opposite operations so you don't leave holes in your child's foundation skills.  That is my advice.

Keep us posted on your use of the abacus.  Yours is a great contribution and I want to know how Cammie progresses.  Thanks so much for your input.

[Mandabplus3]

Poker dad now I understand. So do you think the confusion you experienced was a result of being a beginner on the abacus, the fact that you could already do the math or that you may be stronger in addition than subtraction? Or ? I don't use an abacus so I don't yet know how it translates to the beads but I was looking for the reason for if/when I decide to learn along side my son and middle daughter ( who actually likes math like me ) just so I have something to look out for as I plan to teach them addition and subtraction at the same time.
Dr Jones- well said. I am a living prodigy of that type of educational fault. My addition is strong, subtraction weak. My multiplication is strong my division is embarrassing      I liked the idea of giving them all equal weight and of teaching them as opposites. I don't know how this translates on an abacus though. Cammie seems to be handling it fine though.
Nadia what stance does the course Cammie attends take on the addition and subtraction thing? Also what are you planning to do with her until she is old enough to join in the anzan class? That is 3 and a half years of doing homework in her head and using the abacus while in class.  I assume she will progress a little faster than average will they allow her entry to the age 7 class early do you think?
It's encouraging to see your enthusiasm for abacus, it is just so unhurd of here in Australia. I was struggling to get my head around left to right addition....until my oldest was given some ( rather cryptic) for homework yesterday. It was SOOOOO much easier and quicker.

[PokerDad]

So do you think the confusion you experienced was a result of being a beginner on the abacus, the fact that you could already do the math or that you may be stronger in addition than subtraction?

Solely because I was new to abacus. Adding and subtracting with the abacus is different than the traditional math. Also, when I first started, no one told me how do problems on the soroban - I had to sit in my chair for a few minutes and figure out "how" to perform some of the carry functions. I haven't practiced in a while, so I'm sure I'd still have some problems on bigger digits (like 4 digit)... it can get confusing sometimes carrying across multiple place values. And on occasion, I found myself adding when I was supposed to subtract, or subtracting when I was supposed to add, LOL

FWIW, I think Dr. Jones' idea to teach math facts together is rock solid (assuming you're doing math facts). Geez, showing 5+3=8 and then 8-3=5 juxtaposed seems like common sense! (slaps head)... why didn't we learn this growing up?

[Mandabplus3]

Ahha I see. So I will be sure to get a program with step by step instruction, I can't see myself with the patience to figure it out myself! You must have been keen 
And yes some of our teachers need a slap in the head 

[aangeles]

Hi V!

It's great to see Cammie's progress in learning soroban! Keep up the great work! 

Regarding your question about confusing addition and subtraction - I am assuming Cammie is being taught and is doing "direct" addition/subtraction at this point - that is, without the use of number bonds or formula, right? Based on my experience with Ella and observations in their school, I think it is very unlikely that they would confuse  addition and subtraction at this point even if you teach them at the same time. In fact, I think it is essential to teach them addition and subtraction simultaneously during "direct" calculation in order for them to be able to get to the next stage, which is doing the 2 operations using number bonds and formula (what the teachers call FSE at their school). It is when they start learning to calculate using FSE that I can see the potential for confusion exactly as Tom explained. For example, at the next stage they will be taught that there are 3 ways of ADDING 8, and one of the ways is by using FSE - first you take away 2 by adding 3 and taking away 5 then you add 10. Then, when doing subtraction using FSE, they will learn that when SUBTRACTING 2, one of the ways is also by adding 3 and taking away 5 (and you DON'T add 10), and I think the confusion for some children arises when they can't remember when to add a 10-bead and when not to, especially when they are doing the calculations really fast because the finger movements are the same. I mean, I myself got confused just typing it out here, not to mention when I was trying to figure it out to teach Ella! The good news is, our children really are much more amazing than what we often give them credit for! When Ella was learning FSE, she was able to get all the concepts after just a single demonstration of how to add 6 and she was even able to extrapolate the methods to figure out by herself how to add 7, 8, and 9 even before her teacher started teaching 7,8, and 9! And, with one demonstration of how to subtract 1, she also figured out how to subtract 2, 3, 4, and all the rest. She is now doing three- and four-digit calculations at home without any sign of confusion.   

[Dr Miles R Jones]

I really like what Cammie is doing with strings of operations.  She seems to be imaging with her fingers to some degree, do you think?

I have always wanted to learn calculation with the abacus.  I bought one but really haven't dedicated myself to master it.

That's why your experience is so invaluable.

By the way, when you reverse operations PokerDad, you don't have to rewrite the problem just start at the bottom and go back up.

Glad that helped.  So many of the most useful techniques are really simple.

 One reason I like this forum is that there are so many good ideas I haven't thought of or used.

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