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 (3+4=7) 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 (5=2+3, 5=1+4). 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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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 3+4. 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 don’t 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 we’ll have to clear the extra bead or beads. What is 4’s partner in 5? The answer is 1. So we’ll clear one extra bead. Now what is our answer? The answer is 7.”

Example: “The problem is 3+4. 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.

Example: “The problem is 3+4. 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.