Abacus Teaching Material (1)

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JAYAVARAD GRAPHICS
Abacus Teaching Material
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• Teaching approaches
• There are several approaches to teaching the use
  of the abacus. Since one method might not work
  effectively for all students, teachers should be
  familiar with several methods. The most commonly
  used approaches are
• the partners or logic approach,
• the secrets approach,
• the counting method, and
• adaptations or combinations of these approaches.
• Each is briefly described below, with an example
  (347) worked out according to that approach.
• The logic method or partner method focuses on
  understanding the what and why of the steps
  in solving a problem on the abacus. It requires
  that the student know the partners or compliments
  of the numbers up to ten (523, 514).
  Verbalizing the steps and the reasons for each
  movement made on the abacus is an important
  feature of this approach. At first, the teacher
  must explain the steps and reasons as the student
  works through the problem. Then the student
  should
•  

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Model  1 Zhuzuan Methodlogy 8 2 16 Rs.30 Rs.480
Model 2 Zhuzuan Methodlogy 8 3 24 Rs.60 Rs.1440
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verbalize the process as he or she works the
problem. Over time, this conversation can be
shortened, and finally the process is
internalized. This approach would benefit
students who can follow the explanation and can
understand, and even enjoy, the logical concepts
involved. Example The problem is 34. What
number comes first? The answer is 3. So we set
the 3 on the abacus. Now we need to add 4. Do we
have 4 more ones to add? No. Since we dont have
enough ones to add, we can add the 5 bead (set
5). But 5 is too many we only wanted to add 4.
So well have to clear the extra bead or beads.
What is 4s partner in 5? The answer is 1. So
well clear one extra bead. Now what is our
answer? The answer is 7. Example The problem
is 34. What number comes first? The answer is 3.
Set 3. Can you set 4 directly? No. What is the
smallest amount that can be set that is greater
than 4? The answer is 5. Set the 5 bead. How many
more is 5 than 4? The answer is 1. Clear 1 bead.
What is the answer? The answer is 7. The
secrets method focuses on the process of moving
the abacus beads in a particular sequence,
following a specific set of rules for different
numbers and operations. It does not emphasize the
understanding of that process, rather the rote
memory of the bead movements. It would be
appropriate for students who would benefit from a
manipulative process they could rely on, without
having to fully understand the principles behind
each step of that process.
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Example The problem is 34. What number comes
first? The answer is 3. So set 3 (raise three
earth counters). Now we want to add 4. In order
to do that, we must set 5 (bring down a heaven
counter) and clear 1 (clear one earth counter).
What is our answer? The answer is 7. The
counting method has the student count each bead
as it is added or subtracted, moving from the
unit beads to the 5 beads (but counting only 1
for all beads). There are also specific rules
regarding certain numbers and operations, but
fewer than the full set of secrets. It does not
emphasize understanding the concepts behind the
bead movements. This approach could also be
appropriate for youngsters who would benefit from
a manipulative process they could rely on,
without having to understand each individual
step. Example The problem is 34. What
number comes first? The answer is 3. So we set 3.
Now we want to add 4. To do that, we push up
another unit bead (count 1), then another unit
bead (count 2), then push down the bead above the
counting bar (count 3), and clear all four beads
under the counting bar. Finally, push up one more
unit bead (count 4). What is the answer? The
answer is 7.
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There are several resources available which
demonstrate how to teach the use of the abacus
employing the above approaches. Abacus Made Easy
(Davidow, 1975) utilizes the logic approach. The
Japanese Abacus Its Use and Theory (Kojima,
1954) describes the secrets approach. Abacus
Basic Competency (Millaway, 1994) employs the
counting approach. Use of the Cranmer Abacus
(Livingston, 1997) explains both logic and
counting approaches. Teachers of blind children
have made a variety of modifications to all of
these approaches in order to meet the individual
learning styles of their students. For example,
students included in the regular classroom for
much of the time can work their addition and
subtraction problems from right to left to
coincide with the way the teacher works through
the problem with the class. An example of a
more specific modification relates to division,
and is sometimes referred to as the subtraction
method of division. The divisor is placed to the
far left on the abacus, then 2 columns are left
blank, followed by the dividend. The quotient is
the sum of partial answers obtained as the
student works through the problem, and is placed
to the far right.
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Another specific example of a modification of the
logic method involves multiplication of one, two
or three digit multipliers and one or two digit
multiplicands. For example, in the problem 93x25,
the first factor (93) is set in the billions
place, the second factor (25) in the millions
place, and the answer in the thousands and
hundreds places. Instead of working from the
outside in, the entire multiplicand is multiplied
by the first digit of the multiplier then the
entire multiplicand is multiplied by the second
digit of the multiplier.
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