2 0 0 R A R O T O N G A N CHILDREN A G E D 6 - 1 0 Y E A R S
F.G.M. Biddulph,
Curriculum Development Officer,
Cook Islands.
Testing was carried out to determine the age at which Cook Islands
children are able to conserve substance, weight, length and area, as a basis
for curriculum development in primary mathematics and science.
The testing was conducted in four morning sessions of approximately 3 hours
each on 2nd, 3rd, 4th and 6th November 1977.
Four Cook Islands educators tested at each session. A fifth person (the report
writer) attended to the administrative side. Those who did the testing were:
Mrs Kauta Dean, Mr. Ngatoka Rongo, Mrs. Noovai Tyler, Mr. Kauraka
Kauraka, Mrs. Akaiti Ama, Mr. Kaoiti Marurai, Mr. Aaron Marsters and Mr.
Terepai Moetaua.
5 boys and 5 girls at each age level from 6-10 years were chosen at random
from each of the following schools on Rarotonga: Nikao, Arorangi, St.
Joseph's and Avarua.
A total of 50 children from each school was tested individually to give a sample
size of 40 children at each age level. Each of the 200 children performed each
of the four tasks so that 800 test performances in all were recorded.
For the most part, the 6 year olds were Grade 1 children, the 7 year olds were
Grade 2 children, and so on up to the 10 year olds who were mostly Grade 5
The four tests together with procedures for administering them are outlined

on the Conservation Tasks Sheets in the Appendix. All four are described in
Two of the tests were modified to make them more culturally relevant, using
procedures recommended by Ashton2.
(a) Dry coral sand was used instead of water to test for conservation of
substance since Rarotongan children have more experiences with sand
pouring than with water pouring. The children themselves did the pouring
to counteract for any magic belief.
(b) 'Lagoons', 'rocks', and 'fish' used in place of 'grass', 'cows', 'houses'
for the same reason.
Prior to the test sessions the group of testers met to:
(a) familiarize themselves with the tasks, and
(b) agree on a common translation of instructions into Cook Islands Maori.
Since Cook Islands Maori is the mother tongue of the majority of children,
test sessions were conducted in Maori. In a few cases it became evident that
the children spoke better English than Maori so instructions and questions
were given to these children in English.
Number and Percentage of Children Conserving
E B G Tot. % B G Tot. % B G Tot. % B G Tot. %
1 1 2 5
3 1 4 10
0 1 1 2.5
2 0 2 5
5 4 9 22.5
9 9 18 45
0 5 5 12.5
1 3 4 10
6 2 8 20
11 8 19 44.5
3 0 3 7.5
3 4 7 17.5
9 16 6: 22 55
15 10 25 62.5
6 7 13 32.5
6 3 9 22.5
8 9 17 42.5
14 17 31 77.5
8 8 16 40
3 5 8 20
36 22
52 45
17 21
15 15
Table 1 generally shows an increase in conservation ability with age in all task
areas. Thus, in the case" of conservation of substance, hardly any of the 6 year

olds could conserve, while at the 9-10 year level roughly half of the children
could do so. Conservation of weight shows the greatest gain with age — from
one-tenth able to conserve at age 6 years the figure increases to threequarters by
10 years. Similarly, by age 10 years 4 0 % of children can conserve length, and
20% can conserve area. The pattern is perhaps more evident in Figure 1.
A Chi Square table was employed to test for sex differences as shown in
Table 2.
Chi Square Results for Sex Differences
Substance Weight Length Area
(29) (48.5) (19) (15)
Boys 36 52 17
(29) (48.5) (19) (15)
Girls 22 45 21
58 97 38 30
(Expected frequencies in parentheses)
X2 = 3.406
af = 3
P = n.s.
Although the boys appear to have performed slightly better than the girls, at
least on the substance and weight tasks, the difference is not significant. It
could be due to chance factors. One must therefore conclude that no sex
differences exist in conservation ability as measured by the tasks described in
this report.
The only task area to show a steady or consistent increase in conservation
ability with age (as found in number conservation reported previously) is that
of weight. Apart from some variation around the 7-8 year level, ability in
conservation of length does follow a similar pattern. The same trend occurred
with conservation of area up to the 9 year level but then dropped back a few
percentage points at the 10 year level. The most marked variation occurred in
conservation of substance, where ability apparently drops off at the 8 year
level and again at the 10 year level (markedly). These variations are without

Percentage of Children Conserving
on Four Piagetian-type Tasks

explanation but could be due to limitations of sampling. If it had been
possible to double the number of children tested then a much more reliable
result could have been obtained, but it would not have been easy to test twice
as many children. Despite the number of people potentially available, it took
some effort to assemble four testers on any one day.
Although the reliability of the results is questionable, it can probably be
tentatively accepted that by age 10 years approximately:
75% of the children can conserve weight,
50% of the children can conserve substance,
40% of the children can conserve length,
25% of the children can conserve area.
Whether they could do so in other task situations relating to weight,
substance, length and area is unknown. That is, we do not really know
whether the children who conserved on the present tasks have a generalised
conservation ability in the areas tested. Also, we do not know whether
children who failed to conserve on the particular tasks used could in fact
conserve on other tasks.
If children are provided with a richer 'diet' of conceptual experiences at
school, then it is likely that a greater percentage of them could conserve in the
task situations described in this report. At the present time, however, and for
the next few years probably, primary mathematics and primary science
curriculum development will need to allow for the restricted (arrested even).
conservation ability of children in the primary schools.
The results of the conservation testing reported here séem to raise more
questions than they answer. It would appear necessary, for example, to:
(a) carry the testing through to the 12 year level,
(b) test at least 400 children (about 1/10 of the primary school children) in
order to be able to generalise to the population of Cook Islands primary
school children, and
(c) include a second task in each of the four conservation situations to pro-
vide a more valid result.
The most that can be said at this time is that in any one class in the primary
schools, teachers can expect to find children of widely differing cognitive
ability. To treat all children as if they had the same ability would be a mistake.
It appears that most primary children in the Cook Islands need a considerable
amount of concrete manipulative activity in the classroom; that is, they should

be using real objects and real situations to learn from, instead of listening to
words and writing words all the time. If teachers merely demonstrate with
apparatus, that too is useless. Each child must actively do the things himself if
the symbols and words are to have any meaning for him.
From the results so far, it would appear that many children, even at the age of
10 years (or about the Grade 5 level) still cannot conserve substance,
weight, length and area. Such children would be unable to use standard units
of measurement with any real understanding. The children who cannot
conserve length, for example, think that the same length can get bigger or
smaller (Increase or decrease) depending on the way it is arranged. In other
words, it is like a piece of elastic that can be stretched. Meaningful
measurement in, say, centimetres would probably be beyond the ability of
these children. But this does not mean that the children should not be given
measuring activities before they can conserve. On the contrary, they should
be given a whole range of activities (using non-standard units) and asked
many challenging questions to help them towards conservation.
1. Special thanks to the principals, teachers and children of Nikao, Arorangi,
St. Joseph's and Avarua schools w h o cheerfully accommodated us at
short notice.
2. To those educators who did the testing with sympathy and under-
standing, and especially to Mrs. Kauta Dean and Mr. Ngatoko Rongo
(who tested on each of the four days) and Mrs. Akaiti Ama (who
willingly consented to help us out on the final t w o days) a sincere
thank you.
1. Lovell, K. (1962), The Growth of Basic Mathematical and Scientific
Concepts in Children, London, University of London Press.
2. Ashton, P.T., 'Cross Cultural Piagetian Research: An Experimental
Perspective, Harvard Educational Review, 45 (4).