Abstract: Collected and organized the mathematical braille symbols used in Japan in the past and examined the process of establishment of the current system. Historical changes of Japanese mathematics Braille symbols from the Meiji era to the present are listed in chronological order. A provisional revised version for 2002 is also shown. Key words: mathematical braille symbols, visual impairment, education, historical transition
1. Introduction Mathematical braille symbols are indispensable for mathematical education of severely blind people. The history of Japanese braille is already over a hundred years since it was first established. Japanese mathematical braille symbols began with the Braille formula and were revised several times after that. The current system is based on "Braille Mathematical Symbol" issued by the Japan Braille Study Association in 1962 (Showa 37) year. This "Braille Mathematical Symbol" is a systematicization of past Mathematical Braille symbols in the Braille school textbook with Braille symbols and Braille notation, with the necessity of blind education obligation in 1948 (Showa 23). Although this system can cope with mathematics in elementary and secondary education courses, it can not cope with mathematics in the higher education stage. The revision and improvement is one of the most important tasks of blind education. Currently, research is underway to revise this system and further develop the symbolic system. The development of an optimum mathematical braille symbolic system in a special environment called Japanese braille requires sufficient experience and insight in Japanese braille and mathematics education. It is interesting to collect and organize the past symbols and clarify the process of establishing the current system, which is useful for future symbolic system development.
2. Transition of Mathematical Braille Symbol 2.1 From the Meiji to the present Japanese mathematics
Braille symbols are thought to have reached today through the following six stages:
① Emperor Meiji 1894 (Meiji 27) Braille table published in the celebration of the Emperor's 25
wedding anniversary.[2]
② "1901 (Meiji 40) Japan blind and dumb school idea" Japan Blind Digits and
Numerical Codes "[2]
③ 1921 "Japanese blind braille" issued by the Tokyo blind school in July 10)
④ "Braille mathematical symbolic commentary" issued by the Tokyo blind school in 1928
⑤ 1962 January 1961 "Braille Mathematical Symbol" issued by the Braille Study Group [3]
⑥ "Braille number issued by the Japan Braille Commission issued in 1988 Symbol explanation "[5]
The symbols used in the Meiji era (①, ② era) are mostly
(a) Braille symbols [1], (b) Symbols devised by J. Humblin Smith in 1895 [2], (c)
It is taken from the symbol [2] used in the British arithmetic book of 1895.
Table 1 shows the three kinds of symbols a, b, and c that became the origin of
Japanese mathematics Braille symbols.
In 2000, the Braille Braille Commuttee issued the "Braille Mathematical Symbol Explanation Interim Revised Version", which will be described later.
(1) Phase 1: Emperor Meiji 1894 (Meiji 27) At the beginning of the celebrations full of married celebration songs, Japanese braille and braille figures are listed. This symbol is shown in the rightmost column of Table 2. Symbols corresponding to each step from ② to ⑥ are shown in order from the right column of the table. The braille symbol in the leftmost column is the current symbol of ⑥. Since Kuramatsu Ishikawa established Japanese braille in Meiji 23, numbers and symbols have been used directly from Louis Braille. Ordinal numbers are those whose base is reduced by one level, and decimals are points of {6}. In the Braille era of Braille, the mathematical symbols were only No. 1 to No. 7 in Table 2. There was No. 8, but I do not know if it was used as a decimal point. It is not clear whether No. 9 to No. 14 were used as mathematical symbols simply by having Braille. In any case, this was the only thing that could be used as a mathematical symbol [1].
(2) Phase 2: 1907 (Meiji 40) August Tokyo Tokyo blind and dormitory school asked teachers Kuraji Ishikawa et al., And devised mathematical symbols with reference to symbols of Western countries. It is what is called "Japanese blind numeral and mathematical code". This symbol is shown in the second row from the right of Table 2. It can be seen that most of these are taken from the symbols shown in Table 1. The main items of the newly invented and added symbols are shown in the rightmost column of Table 3. The thing which changed completely was the minus (-) sign, because {2, 5} which was used as the minus sign to the newly devised wavy line (~) sign was to be used Seem. Also, instead of adopting the division (qdiv) symbol, the fraction line disappeared. The root symbol (qroot) became a completely different symbol. Since the parenthesis up to that point is confusing to be an equal sign (=), we do not imitate this, and it seems that small, medium, and brackets were stipulated by struggling with reference to the symbols in Table 1. The decimal point is {6} and remains in the first stage.
(3) Phase 3: Taylor in the UK completed a groundbreaking mathematical symbol in 1907 in July 1920 (Taisho 10), and when it was published in 1917, in 1918, as a uniform type in the United States It was adopted. This was immediately reported to Japan, and the Tokyo School for the Blind also proposed that Japan should adopt it. This proposal was passed at the first general meeting of the Empire Blind Education Association in July 1921 (Taisho 10), and Japanese mathematics It was decided as a Braille symbol. And by the Tokyo School for the Blind, it was published as "Japan Kokusaika Character". Immediately afterwards the uniform type did not spread all over the country, but the excellent point of this sign was understood well and it began to be used at the blind school throughout the country. Many symbols were revised at this stage, and a lot of symbols were newly decided. The revised symbols are shown in the third row from the right in Table 2 and the second row from the right in Table 3. The new symbol is shown in the rightmost column of Table 4. What is distinctive is that new fractional lines were decided, the decimal point was decided to {4, 6}, the radicals returned to the first stage, and the following symbols were changed . Equal signs, curly braces and square brackets, plus and minus, minus plus, qpi, wavy lines, etc. It is also significant that more than 20 symbols shown in Table 4 were newly devised. In particular, it is noteworthy that exponent symbols and subscripts first appeared. After that, decimals in Japan continue to be used {4, 6}.
(4) Phase 4: The university type adopted as the Japanese mathematical braille symbol in 1920 (Showa 3) year in 1910 was printed by the Tokyo School for the Blind and distributed to the whole country. Those decided in 1921 remain unchanged, but as some new important symbols are added, they are shown in the rightmost column of Table 5. A comma (,) and a factorial sign (!) Were newly decided. The second, third, and fourth power indices are newly decided.
(5) 5th stage The Japan Braille Study Association was established in January 1955 in 1962 to unify the mathematical Braille symbols of Japan, and at the 6th General Assembly of the Japanese Braille Study Association in July 1961 It was decided and "Braille mathematics sign" was issued in 1962. The big feature is that the decimal point was decided as {3}. In addition, the following symbols are new. >, <, (greater or equal), (less than or equal), (not equal), log, ~, (approx), :, !, () Such. Furthermore, as many symbols have been newly devised, the main items are shown in the rightmost column of Tables 6-1 to 6-3. The principle of the revision at this time was to use the combination of the points {4}, {5}, and {6} as a prefix. Until then the decimal point was {4, 6}, the Greek letter was {3}, the Greek capital letter was prefixed with a capital letter, but the lower case letters are {4 }, And the capital letter was {4, 6}. Also, {4, 6} was decided as a cancellation instruction sign. As a result, you will have to change the decimal point,
It is thought that the symbol (committed by Smith) {3} which was decided as a comma in the "number and numeric code" (2nd stage) was assigned to the decimal point. This decision was applied only to specialized textbooks and remained at {4, 6} in the general book [7]. The log symbol was also changed as it used {4, 5, 6}. As for the comma, the Tokyo blind school still remained at {2} determined by "Japanese training spot character". For parentheses, it seems that it was decided from the principle that the number other than the numeral and the character in the mathematical expression uses the 4 points of the lower two steps as much as possible. For the first time here, we have created a symbolic system that forms the basis of Japan's current system. After that the Japan Braille Committee was established in 1966 (1941). Due to problems such as the revision of the guidelines for high school studies in 1971, the appearance of visually impaired students majored in mathematics at university, the difficulties in describing logic, mapping, rows, etc., the Japanese Braille Study Group, The Japan Braille Committee added and revised several symbols and issued an increased version of "Braille Mathematical Symbol" in 1972 [4]. Symbols No. 119 to No. 127 in Table 6-3 are those that were additionally determined at this time.
(6) Step 6: Japan Braille Committee was established in 1981 (Showa 56) in 1966 (Showa 41). This association aimed at unification of Japanese braille as the only decision making institution of Braille symbols and notation in Japan, "Braille Mathematical Symbol Explanation" was issued by Braille Mathematical Symbol Expert Committee. The decimal point {3} is the same as Kana's "Wa" , and decided to decide {2} which had been applied to the comma until then to the decimal point at the 6th General Assembly of the day committee of 1973 (Showa 48) [6]. This was the same as those used at that time in France (from 1973) and the UK (from 1989). And all the commas were to turn into masses. The symbols No. 128 to No. 130 in Table 6-3 are newly added. {6} was determined as a concatenation at the end of the line of the formula. As can be seen from Tables 6-1 to 6-3, at this stage, based on the symbol of the Nikkan Ken at the 5th stage, no significant change has been made as a whole. 2.2 Provisional revised version for 2002 In September 2000, the Japanese Braille Commission issued "Interim revised edition on Braille mathematical symbols" [9].
The mathematical braille symbol notation described in this comment is to be applied from the use textbook of 2002, but most of the signs remain as determined in 1981. Only the newly added symbol and the revised symbol are shown in the rightmost column of Table 7. The current symbol is shown in the left column for comparison. New "formula indicator" and "fractional circle symbol" are introduced. The middle and bracket symbols are revised. Trigonometric abbreviation is abolished. This includes one that corresponds to ink-characters in a one-to-one manner, and that intends to preserve the "descending" symbol used for trigonometric function abbreviations for other uses I think that the.
3. Conclusion The enactment of Japanese Braille is the year 1890 (Meiji 23). The mathematical braille symbols have been revised many times over the next 100 years. It turns out that the table has undergone many transitions until the decimal point reaches the point of the current symbol, {2}, in particular. It is also interesting that the bridge {6} at the end of the line of the formula was officially decided for the first time by the same day committee, not before 1981 (Showa 56). Brackets have been revised several times, and it is said that middle and brackets will be revised from 2002 (Heisei 14). The condition essential for Braille symbols is that users are easy to use. The Japanese braille committee says it will continue drastic examination of the revision of Japanese mathematics Braille symbols. I want to carefully watch future trends.
1) PIERRE HENRI: La vie et l'oeuvre de Louis Braille, inventeur de l'Alphabet des aveugles (1809-1852), Paris : Presses Universitaires de France, 1952, 128 p., VIII pl. h.t.
2) Ogawara Keigo: Braille development history, Baifukan, 1937
3) Japan Braille Study Committee: Braille Mathematical Symbol, 1962
4) Japan Braille Study Committee, Japan Braille Commission: Braille Mathematical Symbol Revised Edition, 1972
5) Japan Braille Commission : Braille Mathematical Symbol Explanation, 1981
6) Japan Blind Welfare Study Group: Visual Impairment, No. 99, 1989
7) Japan Blind Welfare Study Group: Visual Impairment, No.1, 1989
8) Japan Braille Committee: Braille Mathematics -- Science Japan's Braille, No. 24, 1999
9) Japan Braille Committee: Braille Mathematical Symbol Explanatory Provisional Revision, 2000