without the physical constraints like no of beads & positions of the beads. Beads value are represented by icons:
Mushroom
1
Smiley
5
Apple
10
Strawberry
50
Robin
100
Superman
500
I use a whiteboard ( in this case the Microsoft whiteboard ) to perform the Arithmetic - any whiteboard is good. The purpose is to make the Arithmetic fun with visual aids. Users are free to use their own pictures, however this system deploy many pictures and is memory intensive - this is a downside of the system. The advantages of this system include page sharing and collaboration.
The icons theoretically can be placed anyway in the frame - they are not even constrained to be on the same column. This though is true, in practice is foolhardy. On a regular Abacus the values of the beads are dependent on which of the columns and which of the two banks they are in. In this system the icons already represent values which are declared in advance of usage and hence are independent of columns or placement.
Addition
These pictures do not do justice to this visual abacus. I was only trying to show the thinking processes.The idea is to show your charge that the additional 9 beads could form 1 ten with one of
the existing 3 beads leading to the addition of an apple and the removal of a mushroom. The smiley and five mushrooms morph into an apple. The apple with 2 mushrooms = 10 + 2 or 12.
the existing 3 beads leading to the addition of an apple and the removal of a mushroom. The smiley and five mushrooms morph into an apple. The apple with 2 mushrooms = 10 + 2 or 12.
The actual process can be seen here
More examples on Addition
The 2 smileys morph into an apple and 1 apple & 3 mushrooms = 13
Like the first example the smiley together with 5 mushrooms morph into
one more apple. 2 apples and 1 mushroom = 21
one more apple. 2 apples and 1 mushroom = 21
Once again 1 smiley + 5 mushrooms morph into 1 apple forming 5 apples.
The five apples are exchanged for 1 strawberry ( 5 x 10 = 50 )
leaving 1 strawberry 1 smiley & 1 mushroom = 50 + 5 + 1 = 56
The five apples are exchanged for 1 strawberry ( 5 x 10 = 50 )
leaving 1 strawberry 1 smiley & 1 mushroom = 50 + 5 + 1 = 56
Finally attempting difficulty *** for a young elementary schooler
If you refer to the start, 1 robin = 100.
The 1 smiley and 5 mushrooms form 1 apple.
As can be observed , rather obvious, we have :
3 robins , 1 strawberry & 3 apples = 300 + 50 + 30 = 380
The 1 smiley and 5 mushrooms form 1 apple.
As can be observed , rather obvious, we have :
3 robins , 1 strawberry & 3 apples = 300 + 50 + 30 = 380
Subtraction
Visual Abacus Subtraction
Multiplication
Video showing 9 x 8
Division
There were certain assumptions taken with this example
Your charge is able to handle 5 x 2 & 4 x 2. And, of course
if your charge knows the 2-table well then, this example is moot.
The idea expressed here is to take off as big a chunk from the dividend
as your charge can handle.
Your charge is able to handle 5 x 2 & 4 x 2. And, of course
if your charge knows the 2-table well then, this example is moot.
The idea expressed here is to take off as big a chunk from the dividend
as your charge can handle.
Long Division 343 ÷ 8
Note: This visual abacus can be presented in many forms. It really doesn’t have to be digital.
You can use playing cards , different coloured plasticine, coloured- cardboard-cut-outs, wood-crafts,figurines ,whatever your kid likes and that’s the catch - play on his/her interests. Just have your presentation conform to your kid’s taste and you may have hours with him/her learning Arithmetic and having fun together. However, Abacus has a downside when applied to small ones - when we add 7 & 8 the usual way the kid is made to count to 7 and then onwards through 8 until he/she reaches 15. We the adults learn our basic Addition this way. With Abacus the 7 is masked - with a 5 and 2 - and the addition is further masked by a 5 from the 8 forming a 10 immediately so your kid doesn’t do the counting the normal way. And,making it worse the remaining 3 & 2 form a five, also almost immediately. These problems compounded together can cause him/her grief and may actually be a hindrance. I have no statistics either way but thought to make a note of my observation for your deliberation.
One other thing - Mental Abacus in my humble opinion is a waste of time and effort.I have experimented with memory methods which mental abacus is akin to. To have memory method working well and speedily enough one have to have a well-developed right brain. With this method you have to have the ability to see, feel and even be able to touch the beads mentally. This is the idea behind memory method. That’s the reason why the failure rate is very high. There is also a serious flaw with memory method - if you are able to ingrain the result of your calculation in your brain well enough to retain it then you will have a hard time trying to erase the area of your memory where the result is stored when called upon to do the next calculation - its not like you have an erasure to do the job. Theoretically, the resolution to this problem is to develop a memory palace/castle so you can store your calculations in different rooms - this is easy on paper but….. Then there is this potential problem of you according too much effort and energy developing your right brain to the point that your left brain will suffer. So, by this argument you are already deciding the future of your charge. How many people who have good left and right brain actually succeed in real life. Look to China for example, they have the people with best memory and speed in calculation but how many of those have actually gone on to have a good career. Good memory and speed in calculation do not put bread on your table. High logical ability, I have seen, forges many inventions. Expressed in another form, it is the difference between a specialist and a generalist. Highly developed right brain or left brain people are the scientists, engineers ,artists, musicians etc whereas a somewhat developed left and right brain person would by logic be able to perform both sides of the spectrum of abilities but is not good enough to be there on the podium - sure they get applause, but its just that. This is actually a choice you may have to make and, are you sure you want to make this choice for your kid, so early in his/her life ? Another grouse of mine is this - why clutter up your precious long-term-memory with unnecessary things when we are walking around with smart phones. Soon enough your charge would be needing those long-term-memory to do well in school, so don't waste them on non-necessities. The opportunity cost may be too high.
You can use playing cards , different coloured plasticine, coloured- cardboard-cut-outs, wood-crafts,figurines ,whatever your kid likes and that’s the catch - play on his/her interests. Just have your presentation conform to your kid’s taste and you may have hours with him/her learning Arithmetic and having fun together. However, Abacus has a downside when applied to small ones - when we add 7 & 8 the usual way the kid is made to count to 7 and then onwards through 8 until he/she reaches 15. We the adults learn our basic Addition this way. With Abacus the 7 is masked - with a 5 and 2 - and the addition is further masked by a 5 from the 8 forming a 10 immediately so your kid doesn’t do the counting the normal way. And,making it worse the remaining 3 & 2 form a five, also almost immediately. These problems compounded together can cause him/her grief and may actually be a hindrance. I have no statistics either way but thought to make a note of my observation for your deliberation.
One other thing - Mental Abacus in my humble opinion is a waste of time and effort.I have experimented with memory methods which mental abacus is akin to. To have memory method working well and speedily enough one have to have a well-developed right brain. With this method you have to have the ability to see, feel and even be able to touch the beads mentally. This is the idea behind memory method. That’s the reason why the failure rate is very high. There is also a serious flaw with memory method - if you are able to ingrain the result of your calculation in your brain well enough to retain it then you will have a hard time trying to erase the area of your memory where the result is stored when called upon to do the next calculation - its not like you have an erasure to do the job. Theoretically, the resolution to this problem is to develop a memory palace/castle so you can store your calculations in different rooms - this is easy on paper but….. Then there is this potential problem of you according too much effort and energy developing your right brain to the point that your left brain will suffer. So, by this argument you are already deciding the future of your charge. How many people who have good left and right brain actually succeed in real life. Look to China for example, they have the people with best memory and speed in calculation but how many of those have actually gone on to have a good career. Good memory and speed in calculation do not put bread on your table. High logical ability, I have seen, forges many inventions. Expressed in another form, it is the difference between a specialist and a generalist. Highly developed right brain or left brain people are the scientists, engineers ,artists, musicians etc whereas a somewhat developed left and right brain person would by logic be able to perform both sides of the spectrum of abilities but is not good enough to be there on the podium - sure they get applause, but its just that. This is actually a choice you may have to make and, are you sure you want to make this choice for your kid, so early in his/her life ? Another grouse of mine is this - why clutter up your precious long-term-memory with unnecessary things when we are walking around with smart phones. Soon enough your charge would be needing those long-term-memory to do well in school, so don't waste them on non-necessities. The opportunity cost may be too high.
No comments:
Post a Comment