The techniques used for teaching that have been described thus far in this chapter are all fact mnemonic techniques. They are used on a one-to-one
basis to remember facts and, typically, one mnemonic association is made for each item to be remembered. As mentioned at the beginning of this chapter, however, there is another type of mnemonic called process mnemonics. These are used to help remember rules, principles, and procedures.
A Japanese educator, Masachika Nakane, was probably the first to develop and use forms of process mnemonics for instructional purposes (see Higbee, 1987; Higbee & Kunihira, 1985a). Prior to his death in 1984 at the age of 95, he spent some 70 years developing and using what he called
yodai mnemonics to teach students at the Ryoyo Institute in Kyoto where he worked as a teacher and principal. He used the term yodai, which means "the essence of structure," because the primary aim of these mnemonics is to summarise the organisation and the process of problem solving. Nakane claimed, for example, to have condensed the essence of trigonometry into a few rhymes that can be read within 60 seconds (Nakane, 1981: cited in Higbee & Kunihira, 1985a, who also reported that these rhymes cannot be meaningfully translated into English).
Higbee and Kunihira (1985a) noted that yodai is used in several Japanese schools (including the Ryoyo Institute) to teach a range of subjects including arithmetic, algebra, geometry, trigonometry, calculus, inorganic and organic chemistry, physics, biology, spelling and grammar, and the English language. Phrases, sentences, rhymes, and even songs are used i n the yodai system to help in learning and remembering the orderly steps involved in solving problems. Some even include verbal commands for gestures and/or activities requiring the use of blackboard, or paper and coloured pens. The Ryoyo Institute where Nakane worked is a demonstration and experimental school which has students from kindergarten through to high school. Higbee and Kunihira pointed out that the use of yodai mnemonics basically goes contrary to common approaches in Japanese and Western education (where comprehension precedes doing) in that, typically, yodai use involves doing before
understanding. They pointed out, however, that most mnemonics are similar in this sense, and that there is evidence to show that doing can effectively lead to learning. For example, this method is used in the Suzuki School of Music in Japan with successful outcomes, and Kunihira and Asher (1965) showed that a foreign language can be taught without mediation of the first language - and therefore initially without understanding.
Some specific examples would probably help explain better what yodai mnemonics are all about and how they work. Higbee (1987) and Higbee and Kunihira (1985a) provided several examples of yodai use, but most were in mathematics - perhaps because the others were too difficult to translate and explain in a coherent form in English. They pointed out that yodai mnemonics use familiar metaphors expressed in familiar words to teach mathematical operations in a simple and uncomplicated way to children. For example, because Japanese children apparently like playing with bugs, fractions have been represented by bugs. Thus a fraction - described as a bug to the children - has a head (the numerator) and a wing (the denominator). Terms like fraction, numerator, a n d
denomina tor are dispensed with. To add fractions, children are taught a
rule to "count the heads when the wings are the same." To multiply, they have to "put the heads together and put the wings together." The multiplication sign
(x)
signifies the crossed horns or feelers of the bugs, and cues the children to carry out the instruction just mentioned. In dividing, they have to turn one bug upside down and then multiply. Neither Higbee, nor Higbee and Kunihira, said anything about how they subtract fractions, but presumably the procedure/ rule would be much the same as in addition - except children would probably have to take 'heads' away.Wrestling is involved when multiplying binomials of the form
(a+b)(c+d). In this case, each term in parenthesis represents a wrestler of either the east team or the west team. Each member of the east team has
to meet and wrestle with each member of the west team, thus (a+b)( c+d) =
ac + ad + bc + bd. Passengers and luggage on a train are used to describe multiplication of binomials of the form (a+b)2 or (a+b)(a-b). Even the Japanese folk story of a boy named Momotaro gets utilised - when multiplying a monomial by a polynomial of the form a(b+c+d). The boy (a) is on a journey and he meets a dog (b), a pheasant (c), and a monkey (d), and takes each of them with him. Thus a(b+c+d) can be solved as ab + ac + ad. Parenthesis can also be described as baskets, and + and - signs can be represented by male and female respectively. Thus (a-b) could be a male bug and a female bug inside a basket (Higbee, 1987; Higbee and Kunihira, 1985a).
Perhaps the most impressive example of yodai use described by Higbee (1987) was in solving quadratic equations of the form ax2 + bx + c = O. At the Ryoyo Institute, Higbee observed and videotaped kindergarten children, who are about 5 years of age, solving such equations.
To solve for x in such an equation, the formula given below needs to be used.
The children at the Ryoyo Institute remember this formula and how to use it through a yodai mnemonic called the "flute song." The song goes as follows: fu-e-no ("flute's"), hi-bi-ki ("sound"), wa (topic marker which means "as for the previous"), mi-mi ("ear"), hi (which means to hold the previous sound when singing), yo-a-shi ("good"). In English, the song means " As for the flute's sound, it is good to the ear."
The syllables of the song correspond to components of the formula. Thus a child singing the flute song with others in the class could write on the board the solution for x:
= - bi mi mi - yo a su
fu e
Higbee (1987) pointed out that every component of the formula derives from the song except for su which replaces shi. Each syllable not only has a meaning in the song but in the formula as well. For example, the denominator contains the word flute (fu-e): but "fu" is also the first syllable of a Japanese word for 2 (futatsu), and "e" sounds like the letter a
as usually pronounced in Japan.
Higbee (1987) and Higbee and Kunihira (1985a) also briefly described uses of yodai mnemonics in organic chemistry. They pointed out that various
molecules from the chemical elements C (carbon), H (hydrogen), and 0
(oxygen) are portrayed as family members including mother, father, brother, sister, grandmother, grandfather, aunt, uncle, and so on. Yodai mnemonics are used to identify various compounds, and to combine them and figure out the results. Children also draw "kites" when working out the configurations of ring compounds like benzene.
Apart from anecdotal reports that a high percentage of Nakane's graduates from the Ryoyo Institute have successfully entered various professions such as medicine and engineering, and that many of them have attributed their interest in science and mathematics to how they were taught at the school, there is also some empirical research evidence showing that yodai mnemonics can be very effective teaching tools. Takizawa, Hatori, Kunihira, and Machida (1980: cited in Higbee & Kunihira, 1985a) found that children instructed using the bug mnemonics were able to compute with fractions as well as children who were in the grade above them and who had an advantage of a year of regular instruction. In another report, they found yodai mnemonics highly effective in improving the ability of high school students to solve complex computational problems (Hatori, Takizawa, Kunihira, & Machida, 1980: cited in Higbee & Kunihira, 1985a). Yodai mnemonics
were also shown to be more effective than traditional instruction methods in helping Japanese junior high school students learn how to construct trigonometric ratios and functions and to compute with them (Kunihira & Machida, 1981: cited in Higbee & Kunihira, 1985a). And Machida and Carlson (1984) found that yodai mnemonics were more effective than traditional methods of instruction in teaching Japanese students how to construct useful equations to solve algebra sentence problems using monomials and polynomials.