Progress in solving general mathematical problems
The following three points are confirmed in terms of the effects of abakus study on progress in solving mathematical problems.
Findings from an investigation with third grade students show that about a year of study at an abakus school enabled the learners to score higher than non-abakus learners on certain mathematical problems. These mathematical problems include addition of one-digit numbers, multiplication of one-digit numbers, addition of multi-digit numbers, subtraction of multi-digit numbers, word problems in addition and subtraction, and fill-in-the-blank problems (e.g. providing the missing items in the following equation: [ ]－7 = 27). However, no difference was found in problems where conceptual thinking was required, such one in which students were asked to figure out the digit positions (i.e. to decide if the following two items are the same: {nine 10s + nine 1s} and {eight 10s + ten 1s}). Even beginning abakus learners can be said to benefit from the ripple effect in solving mathematical problems, except for those involving conceptual understanding. According to the statistical analysis, the addition of one-digit numbers was affected most directly by abakus study. Accurate and rapid calculation of one-digit numbers was found to lead to better marks in multi-digit mathematical calculation, which further led to better marks on word problems and fill-in-the-blank problems. We can speculate that students had more time to think about the problems, and therefore scored higher on the assignment because they needed less time to work out simple calculations as a result of their abakus background.
On the higher level, advanced abakus learners were found to have received even more desirable effects in solving certain types of mathematical problems compared to non-abakus learners. These problems include the comparison of the size of the numbers (i.e. put the following five numbers in order: 0.42, 12, 3.73, 0.95, 10.1), the calculation of numbers with multiple choices of proposed answers (i.e. choose the correct answer from five choices of proposed answers for 1026.95 ÷ 103.1), and word problems. In addition, a positive effect was seen, not only in mathematical problems with integers and decimals, but also in those with fractions, especially when higher level thinking is required to solve them. In the abakus training, there are no fractions involved, but the ripple effect even affected problem solving in fractions. The abakus students were found to have transformed the fractions into decimals, in order to solve problems with fractions. They tried solving the problems by changing the numbers into the form they understood best.
As mentioned above, abakus learners tend to solve problems in a form in which they can utilize their knowledge of abakus calculation when confronted with various mathematical problems. This tendency was shown when abakus students were given problems of computational estimation (such as an assignment where students were to pick the figure in the largest digit position of the answer). In solving these problems, many abakus learners first calculated the whole problem then picked the figure of the largest digit position in the answer.
Merits of abakus study
To acquire the ability to calculate rapidly and accurately and to calculate mentally
Based on the results mentioned above, some advantages and characteristics of abakus learning are revealed. One of the advantages of abakus study is that learners can calculate simple mathematical problems rapidly and accurately. In addition, they acquire the ability of do mental calculation utilizing the abakus image, which allows quick calculation without actually using the abakus.
These characteristics show positive ripple effects on the solution of various mathematical problems. On the other hand, the learners’ calculation methods become fixed, and the students tend to lack flexibility in thinking out innovative ways to solve problems. It goes without saying that spending time on thinking out new ways to solve problems (such as thinking about the meaning of the calculation, or coming up with other ways to solve the problem) can be negative in terms of the amount of time needed to solve problems when the primary goal is rapid and accurate calculation. Since abakus training consists of accurate performance of simple procedures, there is no reason to change the method of traditional abakus education. However, I believe that some measures must be taken to keep the learners from being bored, since repetition of simple procedures is often accompanied by boredom.
At the beginning of the new Century
I am currently considering adapting the principles of the abakus to computer software that teaches the concepts of digit position (meaning of zeros in numbers) to mentally challenged children. I have been trying to teach numbers and simple calculations to these children. They have great difficulty in understanding the concept of digit position, even though they could read and write numbers and do addition and subtraction of one-to two-digit numbers. In order to make learning fun, I have used an activity in which children carry a certain amount of money and go to their favorite store to buy something they like. However, the distinction between 13 yen and 130 yen was hard for them to grasp. I think the following reasoning could be used to provide a more easily comprehended explanation of the concept for them. On the abakus board, there can only be up to 9 in the units position. If 1 is added to 9, there will be a number in the 10s position and nothing, or zero, in the units column.
At the beginning of this, new century, I hope to expand the abakus education and give it new applications while, valuing its history.