Abacus

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A Brief Historical Sketch on the Abacus

“An Ukiyoe woodblock print of the Edo Period (1603-1867) shows a youth calculating on a soroban” From “The Abacus Today”, Mathematics in School, 4(5), 1975:19”

As a historical point of view, human being has been evolved for some reasons. In these sense, all materials in our daily life are easily adapted by those who are good at applying to brand new technologies. In mathematics, there is no exception to follow undeniable rules. Before accepting these rules, we might have been able to calculate simple things - which are included adding, subtracting, multiplying and dividing in a certain level - in our head. If not, we are still working on a certain level of simple calculation. Even though we could easily have done it in our own head, we certainly could not have done it as right way. For some reason, we tried to get a right answer with doing less working in progress.

“Nothing could be further from the truth. The abacus is at once one of the oldest, most enduring, and efficient products of the human mind. The Abacus has served mankind well, aiding him in commerce and invention. It is likely that the abacus was developed independently at different times in different civilizations; The Peruvian Indians, for instance, used a form of abacus for rapid calculation even before the arrival of the white man. The results of computation were recorded by knots tied in a cord.” (Haga, 1964:398) According to the Mathematical Association, we could get a brief historical archive on Abacus as below. “The principles of Abacus arithmetic were first developed in the Middle East over 5000 years ago by the Sumerian civilization. This civilization was probably the first to develop the subject of mathematics and their sexagesimal number system which is based on 60 is still with us in the way that we measure angles and time” (The Mathematical Association, 1981:2-3)

“A collection of various types of abacus is displayed at the Museum of Monetary History in the Fuji Bank’s head office in Tokyo” From “The Abacus Today”, Mathematics in School, 4(5), 1975:19
Through this practice, we could simply get a right answer through our own cognitive system. “In its earliest form the Abacus was probably a sand table with pebbles being used as counters. From this form it evolved to its modern design with beads moving on rods. This version dates from the Greek and Roman civilizations. The Abacus in its various forms continued to be used in Western Europe until the Middle Ages.” (The Mathematical Association, 1981:2-3)
“A clerk in the Hongkong and Shanghai Bank, From “The Abacus Today”, Mathematics in School, 4(5), 1975:19
In this situation, we may also need to get a sort of genius tools to aid our insufficient analytical system. In this sense, these days we take it for granted that we can easily add, subtract, multiply and divide numbers. It was pretty hard to see people those who use the Abacus for some reason. Especially, we could not figure out any institution to become well-trained technicians those who have a spectacular performance given by whom. It seems like the most heyday on Abacus is around 1960~90 just right before being computerized. Why has the abacus being popular at that time? We are already getting sick of the answer of this: the efficiency in some level.

Even if the spread of abacus focuses upon Asian Cultures, it is totally not. According to Haga(1964:398) “At one time the abacus was used in American schools to teach addition and subtraction. It has much to recommend it; it is pretty much cheap, fast, efficient, and versatile.” Furthermore, “one school in California, the abacus was introduced in all second and third grade classes as part of a project to improve speed and accuracy in the handling of numbers.” (Haga, 1964:398)

As we could easily assume, technologies do not dwell on the Abacus to improve speed and accuracy in handling of numbers. It was just one of the tons of advanced calculations in analytical system.

How it works

Tell me about Abacus: How to use it?

It consists with seven beads on each row. “Two of the beads are above the bar (upper beads) and five are below the bar (lower beads). The upper beads are worth “5” and the lower beads are worth “1”. Each row represents a decimal place. The right-hand row shows 1s (1 to 9) the second row 10s (10 to 90) and so on. To show a number beads are placed against the bar. “(Maxwell, 1981:3) Unlikely the Chinese Abacus, “the Japanese Abacus has only 1 upper and 4 lowers beads.” (Maxwell, 1981:3)

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It is because these two beads which are located in the most top and bottom is not needed at all in terms of double meaning. Even if the abacus needs to practice to calculate numbers, it is carried out a series of calculation in terms of “addition and subtraction, Simple and long multiplication, and simple and long division, and finding square and cube roots.” (Maxwell, 1981:3) I am not going to show how to calculate every single calculation, but it is obvious to need to a sort of train for that. If you want to get a sense of calculations on the abacus see the article.

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Remediation

Technically Speaking on the Abacus

In an information era, we do not need to make a note and cultivate rules in a certain level, since we could get an aid from advanced technologies to focus upon an “Efficiency and Accuracy”. For the first time, it was such an evolutionary effect on abacus. If we are getting used to how to encode each number on abacus, we could easily get the result as soon as we could. After then, it is pretty much limited to calculate every single numbers. As we already recognized, it is kind of being part of unlimited things: calculate numbers. Even if the abacus has been used such an efficient calculator, it is not good enough to use it until today.

There is no reason if you are working on professional specialists related in numbers; you do not need to purchase a calculator at least.
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calculator on smartphones
Most mobile phone companies include such a great functions on their phone needless to say on smart phone users. If you are smart phone user, you could get tons of versions of calculator on application store. (See attached images on one of smart phones)

Digital vs. Analog: To Cybernerd

According to Susan Buckmorss “Benjamin took seriously the debris of mass culture as the source of philosophical truth”(5). “For Benjamin the various remains of nineteenth century culture –buildings, technologies and commodities, but also illustrations and literary texts – served as inscriptions that could lead us to understand in ways in which a culture perceived itself and conceptualized the “Deeper” ideological layers of its construction. As Tom Gunning puts it, “If Benjamin’s method is fully understood, technology can reveal the dream world of society as much as its pragmatic rationalization.” (Huhtamo, 1997:221)

As the formal researches on history, it does not dwell on history itself anymore. “In this sense, history belongs to the present as much as it belongs to the past. It cannot claim an objective status it can only become conscious of its ambiguous role as a mediator and a “meaning processor” operating between the present and the past. “(Huhtamo, 1997:221)

Historical "Arbitrary"

Between “Obvious” and “Arbitrary”: What is a biased on the Abacus?

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Sometimes we have been gone through unusual experiences when we need to being working on “the otherness” for some reason. In this sense, we are not deeply aware of why the Western writing runs not right to left but left to right just unlikely Islamic writing styles. We simply take for granted it as our way of living and just apprehend it as “the otherness: which is based upon a totally heterogeneous cultural system.” As we already recognized the former section; “how to use it, there is a certain rule which is absolutely biased upon right-handed men. Figure 2 below let us know the number 6,427.

Especially, it is obviously good at right-handed men. (See how to multiply on abacus as below)

“…to multiply one need to know ones multiplication tables and how to add on the Abacus. Simple multiplication is fairly straightforward. One puts the multiplier on the left-hand row to remind one what it is and puts the multiplicand on the right-hand side of the Abacus, leaving the right-hand row clear. Then multiply the right-hand digit of the multiplicand.Remove this digit and place the product on the right-hand row that you have left clear.Multiply the next digit of the multiplicand.”(Maxwell,1981:4)

And also in a certain sense, most Asian Culture which is oriented on Abacus did not much care about left-handed men. What if some little child has left-handed, it is considered as one of unusual behaviors to fix. In this sense, it is a kind of design convention resulting from the prevalent tendencies of the historical situation. In common belief in technology, we easily accept technology is a significant force in society. “Referred to as “technological determinism”, this belief affirms that changes in technology exert a greater influence on societies and their processes than any other force.” (Smith, 1994:2) In other words, some sort of “technological determinism” alters the way of thinking within human beings. That paradigm affects invention of abacus which is biased on right-handed men.

The Pedagogical action: The “Arbitrary” Effect

Based upon the idea of “Obvious”, Moores write which is a quite reasonable statement as below:

“By designating the cultural as arbitrary, Bourdieu reverses the normal perception of things, which is that the sacred objects of high culture are such because of some quality intrinsic to them. From this essentialist point of view they deserve their place and their veneration because of something about them that is ‘real’ – they really are beautiful in the way that knowledge is really true. This, in fact, Bourdieu argues, is an illusion. In truth, the field of culture is arbitrary in that its positions, and the objects that mark them, have no intrinsic justifications or qualities.” (Moore, 2004:447)

Moreover, Bourdieu and passeron(1977:5) asserts “All pedagogic action is, objectively, symbolic violence insofar as it is the imposition of a cultural arbitrary by an arbitrary power.” With the heyday on Abacus, we could assert all pedagogic action - related in making an expert which is good at calculating on abacus – contains entirely motivated and explainable traits unlikely “cultural arbitrary”

Number Representation

Meanings of Skill: Cognitive development Vs. Competition

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A Primary school child at a private lesson, From “The Abacus Today”, Mathematics in School, 4(5), 1975:19
Why are primary school students working on Abacus to acquire a skill? Could we say there is any intended purpose or not? How do we figure out the purpose of training children as “Calculation Expert”? After getting a certain degree of level, what it means for children as cognitive levels? How do we configure out the meaning of number on abacus? These are the questions address in this section.

What if you want to be an expert on abacus, you need to be well-trained. According to previous researches, “a general orientation toward the study of skills and their development is outlined, in which analyses of representation, transfer, and context are used to explore the consequences of developing a specific skill. This general approach is then applied to the study of abacus training and its implications for school achievement and cognitive development.” (Stigler, Chalip and Miller, 1986: 447) There is no exception on abacus as well. To develop these skills, there is no way to publicize the abacus as much as possible as sort of a governmental level. (see a picture as below)

“Indeed, in Japan, where abacus lessons are mandatory for third and fourth grades of the primary school, a skilled student can add and subtract faster than by press the buttons, the light wooden beads have been skillfully flicked to give the answer. To gain high skill in the use of the abacus, Japanese children attend private schools and take nationally organized examination” (The Mathematical Association, 1975:18) Even though, Elementary schools in Japan have a mandatory course just for abacus, it is not good enough for making such a good expert on abacus.

Some students who pursue additional training attend after school classes as a private lesson. As we could get a sense of competition, “Children who pursue this additional abacus training use their skill primarily for competition, both national and international.”(Stigler, Chalip and Miller: 1986:448)

According to Spitzer (1942:450-451), there are absolutely significant characteristics related in the representation of quantities on the abacus. 1. “The markers (beads) can be used to represent various concrete objects – to aid the children secure an understanding of these efficient abstract uses of number.” 2. “The value of a number depends on its position – “consider how much more easily position can be explained on abacus.” 3. “Closely associated with the ideas discussed in the preceding paragraphs is the abacus can be used to illustrate, namely, the idea of a place-holder or the function of zero.” 4. “The number system illustrated by the abacus is the idea of collection.” 5. “The use of the abacus is teaching is to illustrate the true nature of carrying and borrowing.”

Even if the Abacus itself has a quite significant to develop cognitive system, it is not good enough as times go by. As technologies let us know what the efficiency itself is.