The Role of Learning the Japanese Kuku Multiplication Chant in Simple Arithmetic Operations

doi:10.4236/ce.2011.23037

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Creative Education

2011. Vol.2, No.3, 276-278

The Role of Learning the Japanese Kuku Multiplication Chant in

Simple Arithmetic Operations

Hiroyasu Ito, Namiko Kubo-Kawai, Nobuo Masataka

Primate Research Institute, Kyoto University, Inuyama, Japan.

Email: [email protected]

Received April 5th, 2011; revised May 7th, 2011; accepted May 16th, 2011.

In Japanese primary schools, children are required to learn the kuku (“nine nines”) method of multiplication

during the formal course of mathematics. When learning, they are taught to recite it as though reciting a Chinese

poem or chanting. In the present study, we undertook an experiment designed to examine the role of learing the

Japanese kuku multiplication chant in arithmetic operations by requiring the participants to solve the three types

of simple arithmetic problems. In each problem presentation, an equation of simple addition (e.g., 3 (three)

added to 4 (four) makes 7 (seven)), of simple multiplication (e.g., 3 (three) multiplied by 4 (four) is 12 (twelve)),

or of kuku (e.g., 3 (three) 4 (four) 12 (twelve)) was auditorily presented with either the addend or augend in the

addition, or the multiplicand or multiplier in the multiplication or kuku always being acoustically masked by

peep sounds so that the participants did not hear the numbers masked. Comparison of the latency to their answer

across the three types of problems revealed that as a consequence of learning kuku, a learner could produce the

answers for the arithmetic multiplication problems as well as the answers for the kuku problems relatively more

easily as compared to the arithmetic addition problems. Implications of the results are argued with reference to

the cognitive load theory, a theory of learning and education which underwent substantial development and ex-

pansion during last two decades.

Keywords: Kuku, Mathematics, Arithmetic Operation, Number Sense, Cognitive Load Theory

Introduction

Numbers might be considered a ver y recent cultu ral invention

in the evolution of the human species. Indeed, number words and

digits arise from the specifically human and evolutionarily re-

cent ability to cr eate and mental ly manipul ate co mp lex s ymbols.

However, the sense of numbers is older. A sensitivity to nu-

merical properties of the world is present even in nonhuman

species (Dehaene, 1997; Dehaene, Dupoux, & Mehler, 1990;

Gallsitel & Gelman, 1992). For instance, lionesses with their

prides on the Serengeti Plains, Tanzania, decide to attack back

only when the number of defenders is superior to the number of

intruders. When deciding to drive the intruders off or not, they

evaluate the number of intruders just by hearing the roars pro-

duced (McComb, Packer, & Pusey, 1994). Altogether, previous

evidence consistently indicates that this mental magnitude rep-

resentation supports the more complex symbolic numerical

capabilities developed by humans alone.

Although such basic preverbal “number sense” provides a

foundation for formal mathematics by performing arithmetic

operations on approximate number representations, the devel-

opmental process of the capability of formal mathematical per-

formance would be environmentally modulated across the

variations of linguistic cultures in the world. Nevertheless, ex-

perimental evidence revealing such variations is still limited

except for that with deaf people who acquired sign languages as

their first languages (Bull, Marshark, & Baltto-Vallee, 2005;

Frosted, 1996; Heiling, 1995; Nunes & Moreno, 2002). In order

to pursue thi s issue , in the pr esent stu dy, we invest igated the rol e

of learning the Japanese kuku multiplication chant in arithmetic

operations in the formal mathematics.

In Japanese primary schools, children are required to memo-

rize the kuku (“nine nines”) method of multiplication during the

formal course of mathematics. When learn ing, they are taught to

recite it as though reciting a Chin ese poem or chanting. The digit

names are often modified to maintain the rhythm, analogous to

the phenomenon to recitation of a rhythmic poetry. As the

learning pro ceeds, all chi ldren, unless mentally ret arded, become

capable of reciting it from memor y, and the stored knowledge, as

verbal quantitative information, might serve as a foundation for

the formal mathematics they will learn later. Assuming such

possibility would one to reason the learning of the kuku to be

particularly helpful to children with dyscalculia, which may

affect as much as 5% of the total population (Sousa, 2008). In

fact, the history of kuku can be traced back more than 1,000

years (Lancy, 1983), during which, it might have been tradi-

tionally transmitted as a powerful convention of creative educa-

tion to support people ex periencing specific learni ng difficulti es.

Nonetheless, such potential creativity of the kuku still remains

novel in Western countries. In order to reveal that experimen-

tally, the present investigation was conceived.

As a first step to explore the possibility noted above, we un-

dertook an experiment designed to examine the role of learning

the kuku in arithmetic operations by requiring the adult partici-

pants to solve simple arithmetic problems. As our intent is to

investigate the role of learning the kuku in subsequent formal

mathematics development, it is certainly ideal to select primary

school students as the participants. It is also necessary to trace

the performance of these primary school students in formal

mathematics as a later stage. As a preliminary stage of such

future research, the present study was conducted. The findings

H. ITO ET AL. 277

revealed are argued with reference to the cognitive load theory

(CLT) because it is the most prevalent theory that explains how

the human cognitive architecture, in particular our memory

system, impacts learners’ performance (Sweller, 1988; Paas,

Renkl, & Sweller, 2003). According to CLT, there are three

types of loads, namely intrinsic cognitive load, extraneous cog-

nitive load, and germane cognitive load, each of which has

different implications for learning. In this article, we attempted

to discuss the findings in terms of such conceptu al framework of

CLT.

Methodology

In each problem presentation, in the present study, an equa-

tion of simple addition (e.g., 3 (three) added to 4 (four) makes 7

(seven)), of simple multiplication (e.g., 3 (three) multiplied by

4 (four) is 12 (twelve)), or of kuku (e.g., 3 (three) 4 (fours) 12

(twelve)) was auditorily presented with either the addend or

augend in the addition, or the multiplicand or multiplier in the

multiplication or kuku always being acoustically masked by

peep sounds so that the participants did not hear the numbers

masked. We asked them to answer the numbers which were

masked by the sounds as quickly as possible, and we compared

the latency to their answer across these three types of problems.

We hypothesized that as a consequence of learning kuku, the

learner would find answers for the arithmetic multiplication

problems relatively easily as compared to the arithmetic addi-

tion problems.

The participants were 20 adult (10 men and 10 women) in

their twenties (mean age: 22.10 years, SD: 1.02) who had ac-

quired Japanese as their first language. They had all been edu-

cated in the Japanese formal education system since the begin-

ning of the entrance into kindergarden at least until the comple-

tion of graduation from senior high school. All were healthy

and typically-developed. They had learned kuku in primary

school and had memorized it.

During the experiment, each participant was seated in an at-

tenuation chamber and wore a headphone. Each problem was

presented auditorily through the headphone using notebook

computer. Total of 20 equations of arithmetic addition, using

single digits (referred to as “addition problems” below), 20

equations of arithmetic multiplication, using single digits

(“multiplication problems”), and 20 phrases of kuku (“kuku

problems”) were presented to each participant. In 10 of the 20

addition problems, the addend was acoustically masked by

peepsounds whereas the augend was masked in the remaining

10. In each 10 of the 20 multiplication or of the 20 kuku prob-

lems, the multiplicand was masked while the multiplier was

masked in the remaining 10. The order of a total of 60 presenta-

tions was randomized. Inter-problem intervals were 5 sec. The

participants were asked to answer each problem as rapidly as

possible by pressing the number key located on a table near by

the participant corresponding to the answer. The behavioral

measure was the interval between the end of the presentation

and the onset of the pressing of the button (RT; reaction time).

Results

Results of our examination of the effects of learning kuku on

arithmetic operations are summarized in Figure 1. When an

addition problem was presented, mean (SD) RT was 6.44 (0.28)

s when the augend was masked and 6.50 (0.27) s when the ad-

dend was masked. When a multiplication problem was pre-

sented, mean (SD) RT was 6.17 (0.36) s when the multiplicand

was masked and 6.10 (0.37) s when multiplier was masked.

When the kuku problem was presented, mean RT (SD) was

6.14 (0.32) s when the multiplicand was masked and 5.96 (0.39)

s when the multiplier was masked. A two-factor within-subject

analysis of variance revealed significant main effects for type

of problems (F(2,38) = 61.19, p < .001) and for the position of

the masking sound (F(1,19) = 5.82, p < .05). There was also a

significant interaction between the factors (F(2,38) = 10.56, p

< .001). Multiple comparison analyses revealed that RT when

the addition problems were presented was significantly longer

than that when multiplication problems were presented (p < .01)

and that when kuku problems were presented (p < .001). When

the multiplicand was masked, RT was significantly longer that

that when the multiplier was masked in both the multiplication

problems (p < .01) and in the kuku problems (p < .001).

However, in the addition problems, RT did not differ between

when the augend was masked or when the addend was masked

(p > .10). Before you begin to format your paper, first write and

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Discussion

The RT required to answer each type of the presented arith-

metic problems would mostly be determined dependent upon

the degree to which a working memory load is involved in the

task (Baddeley, 2000). When solving problems, the task more

or less puts requiring on temporarily holding and manipulating

task-relevant information as a consequence of previous learning

experiences (Dehaene et al., 2003). Once the information is

stored, control process within working memory occurs by ena-

bling the coordination, transformation, and integration of stored

information (Masataka et al., 2007). According to this reason-

ing, the fact itself would not be astonishing that the RT for

solving the kuku problems was much shorter than that for solv-

ing the addition problems. This is a typical example of learning

Figure 1.

Results of the examination of the effects of learning kuku on arithmetic

operations.

H. ITO ET AL.

278

process outlined by CLT (Sweller, 1988; Paas, Renkl, &

Sweller, 2003), in which each relevant element of high-element

interactivity material that enables learning can be learned indi-

vidually, but they cannot be understood until all of the elements

and their interactions are processed simultaneously. Such ele-

ment interactivity is the drive of the first category of cognitive

load in CLT, which is referred to as intrinsic cognitive load

because demands on working memory capacity imposed by

element interactivity are intrinsic to the material being learned.

Different materials differ in their levels of element interactivity

and therefore intrinsic cognitive load, and they cannot be al-

tered by instructional manipulations.

In fact, working memory, in which all conscious cognitive

processing occurs, is capable of handling only a very limited

number of novel interacting elements. While this number is far

below the number of interacting elements that occurs in most

areas of human intellectual activity, long-term memory pro-

vides humans with the ability to vastly expand this processing

ability. This memory store can contain vast numbers of sche-

mas that are cognitive constructs which incorporates multiple

elements of information into a single element with a specific

function. In this regard, the fact should be noticeable that the

RT for solving the multiplication problems recorded in the

present study was approximately equivalent to that for solving

the kuku problems rather than to that for solving the addition

problems. This strongly indicates that the participants utilized

their knowledge of kuku to obtain the answers for the multipli-

cation problems. No doubt, this knowledge is stored in long-

term memory.

CLT explains that schemas can be brought from long-term

memory to working memory. While working memory might,

for example, only deal one element that can be handled easily

among a large number of interacting elements, their incorpora-

tion in a schema reduces the load of working memory. It is by

this process that human cognitive architecture handles complex

material that appears to exceed the capacity of working mem-

ory and that learning the Japanese kuku multiplication chant

becomes an effective aid to performing arithmetic operations.

Acknowledgements

The present study was supported by a grant-in-aid from the

Ministry of Education, Science, Sports and Culture, Japanese

Government (#20243034) as well as by Global COE Research

Program (A06 to Kyoto University). We are grateful to Eliza-

beth Nakajima for her reading an earlier version of this manu-

script and correcting its English.

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