Piaget`s Conservation Tasks: The Logical and Developmental

JOURSAL
OF
EXPERIMENTAL
CHILD
PSfCIiOLOGY
Piaget’s
Conservation
Developmental
Priority
8,
234-249
(l%%)
Tasks: The Logical
and
of Identity
Conservation’
FRAP;K H. HOOPER
Tl;esf.
I’irginia
Tlniversity
The present
research
has investigated
Elkind’s
conceptual
distinction
between
identity
conservation
and equivalence
conservation.
Although
Piaget’s
description
and analysis
of conservation
acquisition
rests primarily
on considerations
of identity
conservation,
his assessment
format
has been
exclusively
equivalence
conservation.
The prrsent
argument
contends
that
equivalence
conservation
subsumra
identity
conserration
ability,
but also
includes
a necessary
logical
deduction
sequence
for adequate
equivalence
conservation
performance.
Accordingly,
identity
conservation
should
he an
earlier
developmental
acquisition
than equivalence
conservation.
Appropriate
settings
were devised
for identity
and equivalence
conservation assessment
which equated
the two conservatjion
tasks in terms of perceptual
cues and memory
requiremmts.
The tasks were administered.
in
a nonrepeated
measures
design,
to equal numbers
of males and females
at the kindergarten,
first, and second grade levels. A nonparametric
multiple
contingency
analysis
revealed
tha,t the main
effects of conservation
task
type,
age levels, and the sex dichotomy
were significant.
It, was concluded
that identity
conservation
definitely
precedes
equivalence
conservation
as
a developmental
achievement.
Accordingly,
Piaget’s
view of identity
and
equivalence
conservation
as simultaneous
or concommitant.
drvclopments
is erroneous.
Identity
conservation
cannot
be adequately
assessed in the
conventional
paired-stimulus
format,
and care should
be taken
in considering identity
processes
or explanatory
concepts
as a complete
description
of equivalence
conservation
achievement.
The Piagetian conservat,ion task format has been the subject of
detailed analysis with regard to its logical requirements (Elkind, 1967).
Elkind’s analysis distinguishes between identity conservation (the conservation of a given stimulus attribute, e.g., substance, weight, or volume,
across a reversible transformation and with regard t’o a single stimulus
‘This
study
is based on a dissertation
submitted
by the author
to Wayne
State
University
as partial
fulfillment
of the requirements
for the Doctor
of Philosophy
degree. The author
is grateful
to Dr. Irving
E. Siegel of the Merrill-Palmer
Institute
and Drs. Eli Salts and Charles
Solley
of Wayne
State University
for their helpful
advice
in the preparation
of this manuscript.
The author
also wishes
to thank
the administrators,
teachers,
and pupils
of the Mt. Clemens,
Michigan,
Community
School
District
for their courtesy
and assistance
in t.he present
research.
234
PIAGET’S
CONSERVATION
TASKS
235
item alone) and equivalence conservation
(the invariance of a quantitative relationship across a reversible transformation
of one of the elements
of that relationship).
This conceptual distinction
and the suggested
developmental
progression
from identity to equivalence conservation
achievement is the major focus of the present research.
The major aspects of the conventional conservation task may be outlined as follows:
Given: Two stimulus items A and B ; e.g., containers
with equal amounts of small seeds and three separate points or intervals
in the conservation
setting. Time 1: A = B (A and B are judged as
containing equal amounts of seeds) ; Time 2; B + C (The contents of
B are transferred
or transformed
to a container of a different shape, C) ;
Time S: A ? C (The S is questioned as to the relationship,
equality, or
difference of amount, between the standard stimulus A and the comparison stimulus C) .
If the S, when questioned at Time 3, responds that A = C, the E
infers that B and C were in fact judged equal in amount. In contrast,
the response A #B
results in the E’s inference that B # C, hence a
nonconservation judgment is assessed.
Note that in the convent.ional conservation set’ting outlined above
(designated equivalence conservation by Elkind) , the S is never actually
required to judge overtly the relationship of stitnuli B and C. Yet, the
realization that’ the property at issue, i.e., the substance-amount, weight
or volume of the stimulus array does not alter following the transformation of B to C, is patently essential to a correct solution of the criteria1
task. Obviously, a S who does not judge B = C is not likely to “conserve” the relationship of A = B; therefore, A = C as outlined above.
Identity conservation is defined as the realization that the single
stimulus transformation B into C does not alter a fundamental property
of the quantity in question. Piaget’s explanation and description of the
processeswhereby the child gradually passes from a &age of nonconservation to an intuitive and transitional stage and finally achieves the
third stage of completely logically justified conservation performance is
based directly on consideration of this identity case. Thus, the three
major post-facto rationales which are logically adequate and consistent
for Piaget, e.g., addition-subtraction schemas--“nothing has been added
or taken away”; reversibility--“if
you poured the seeds bac.k to the
first container, they would have the same amount”; and compensationproportionality or the compensation of relations--“that
glass of seeds
is shorter but narrower too,‘? refers to the relationship of B to C as
cited above. The later explanation category, the compensation of relations, plays a primary role in Piaget’s conceptualization of conservation
acquisition. While identity conservation is the focus of Piaget’s theoret-
236
FRANK
H.
HOOPER
ical explanation and forms the hasis for his description
of the stages
his assessment format is
of conservation
and quantifying
coordination,
primarily
the paired-stimulu :: equivalence &ting.
Although the post-frccfo explanations or justifications cited above may
well be veridical reflections of t)he processesleatling to identity conservation, they do not subsume or describe the total solution to the convent#ional equivalence conservation problem. In the equivalence case, the
child’s successful completion of the problem demantls two components:
(1) A recognition of t,he B = C invariance, and
(2) the logical deduction
of A = B, B = C; therefore. A = C, or the maintenance of a quantit,at#ive relationship across the irrelevant t)ransformation of one element
in this relationship. It is this quantitative relationship which is the
essenceof the equivalence paradigm, and the only logical means to its
solut’ion. If the S (adult or child’) is presented with only .I, and C, and
asked to make a judgment, concerning t,heir relative amounts, under- ot
overestimation of one of t#he stimuli generally occurs (Elkind, 1967).
The S is faced wit,h an illusion situation and a logical solution to the
judgment, questions is not, possible without the previous information
regarding an equality relationship.
Since equivalence conservation requires the additional deduction
sequence, it should be a later cognitive achievement than identity
conservation. It also follows that identity conservation should be a
necessary hut not’ a sufficient prerequisite condition for adequate equiralenrc conscrvat~ion performance. In contrast, Piaget, apparently assumes
“that, identity and equivalence conservation arc simultaneous in time,
and that the age of equivalence conservation is also the age of identity
conservnt’ion, so t,hat’ it is legit,imate to infer the age of the latter from
the age at which the former is attained” (Elkind, 1967, p. 23). From
Piaget’s view, there is no contradiction in discussing identity conservation processeswhile assessingperformance in an equivalence setting.
In assessingt’he relationship of identity and equivalence conservation,
certain conceptual and methodological distinctions must be considered.
These distinctions center upon the task requirements specific to each
conservation setting. Ideally, equivalence conservation should differ from
the identity case only with regard to the additional logical deduction
sequence. Our problem becomes one of equat’ing the identity and equivalence tasks in terms of all task requirements and perceptual features
except for the latter tasks’ postulated deduction sequence. Identity conservation involves a single stimulus array, subjected to a number of
reversible, physical transformations. For example, colored seeds will be
poured from the initial, st,andard container (A) to a comparison container (C) of taller and narrower dimensions. Following this transforma-
PIAGET’S
CONSERVATION
TASKS
237
tion, the S will be questioned as to the relative amounts of seeds prcsently in container C as compared to the amount previously in container
A. This conception of identity conservation
assessment differs in two
important
aspects from equivalence conservation
as measured in the
conventional
paired-stimulus
format. The latter type of conservation
includes the additional deduction sequence described earlier and presents
the S with an immediate perceptual display in which standard container
A and comparison container C “appear”
markedly
different. This perceptual disparity
(heights or levels of seeds in the present setting) is
considered
an essent.ial aspect of valid conservation
assessment for
Piaget. The S must demonstrate
via his logical explanations, that the
same amount of material is present in both containers in spite of the
perceptual incongruity.
The present identity conservation
task requires the S to “remember”
the situation prior to transformation
or pouring of the seeds, e.g., how
the seeds appeared in standard container A, level attained, etc. Piaget
and Elkind have suggested drawing a reference point or “guideline”
on
the standard container to assist the S in recalling the previous seed level
thus equating the identity task with conventional
equivalence conservation assessment. Another possible solution is to remove the standard
stimulus array from the S’s immediate perceptual field; e.g., place the
standard container A behind an opaque screen immediately prior to t,he
transformation
of the seeds in container B to comparison container C,
thus requiring the S to “remember”
the appearance of container A.
This procedure (termed equivalence conservation I) will be used in the
present research. It is comparable to the identity
conservation
task
format in terms of memory requirements
and perceptual cues presented
to the S. In addition, a conventional
paired-stimulus
format (termed
equivalence conservation
II) as used by Piaget and other researchers
will be included. In this case, all the stimulus arrays will be kept in full
view of the S. Since the t,wo equivalence tasks share the criteria1 logical
deduction sequence, the number of conserving Ss is not expected to
differ for these conditions. Accordingly,
in the analysis to follow, if
equivalence conservation
I is not found to differ significantly
from
equivalence conservation
II, these settings will bc combined to form a
single, overall equivalence conservation condition.
Since the perceptual incongruity
between standard
and comparison
containers is an integral aspect of the conservation tasks (identity and
equivalence cases), it seems appropriate to examine the effects of varying degrees of perceptual disparity upon each of the present conservation
task settings. Piaget has cited cases of chiIdren at the transitional
or
intermediate stage II level who conserve when presented with moderate
238
FRANK
H.
HOOPER
of ~~~weptual
dis~~~trity. ht. who break down and claim different
amounts of mat,erinl are present, when extreme transformations are
performed. This appealY to be one of t,he major aspects of the transitionary stage description; i.e., “an int’crmediate st’agc in which the child
achieves conservation in the simple case, but resorts to intuitive perception for the extreme deformations” (Piaget and Inhelder, 1962, p. 21;
author’s translation). If the amount of conflict,ing perceptual cues is a
major factor, a conservation task with an extreme physical change
should be more difficult than one involving a moderate physical change.
Accordingly, each of the three major conservation tasks conditions,
identity, equivalence I, and equivalence II, will include two degrees of
perceptual transformation or deformation, a moderate and an extreme
romparison container.
tlegrces
METHOD
Subjects
Subjects were drawn from the kindergarten, first, and second grade
classrooms of two clement.ary schools in Mt. Clemens, Michigan. The
schools a,rc in predominantly white, middle-class neighborhoods. Eighteen
males and eighteen females from each grade level were randomly assigned
to the various conservation task conditions. The age means for the three
grades involved were 6, 7, and 8 years, respectively. Teacher-administered Primary Ment,al Abilities (from 7-1901, revised 1964) test
scores indicated IQ means and standard deviations of 111.4 (12.47),
111.8 (12.88)) and 109.2 (12.07) for the kindergarten, first, and second
grades.
Task Materials
The basic task format included plastic bottles containing equal
amounts of small seeds dyed four different colors and glass containers
of constant volume and varying shape. The containers used in each of
the conservation task conditions are described below.
Container
--__-_____
Standard 5%ml beaker
Moderate transformation 50-ml graduate cylinder
Extreme transformation 50-ml graduate cylinder
Dimensions
Height
Diameter
2 inches 13$ inches
2 inches Iv4 inches
8 inches a/4inches
In addition, a plastic funnel, an opaque screen, and a tape recorder
were used.
PIAGET’S
CONSERVATION
TASKS
239
Procedure
An attempt was made to creat,e a relaxed atmosl>here to insure maximal verbalizations
from the children. The Ss received a preliminary
“warm up” experience to familiarize them with the E, the container.5
and seeds, the procedure of seed-pouring,
etc. This introductory
expci,ience used a loo-ml beaker and two smaller 30-1~~1 containers. After the
S had poured the white seeds into the loo-ml beaker, the E poured
unequal amounts of these seeds into the two 30-ml containers. The S
was then asked, “What can you tell me about the seeds in these t’wo
glasses?” Following the S’s indication that one container had more seeds
than the other, the E poured additional seeds into one of the containers,
thus equalizing the amounts. The S again was asked “What can you
tell me about the seeds in these two glasses?” A record was kept,
of those Ss who spontaneously
used the terms “same”
or ‘<equal
amounts”
of seeds. If the S failed to conclude spontaneously
that
the glasses contained equal amounts of seeds, this was pointed out,
with special emphasis on the term “amount.”
In this manner, at
least a rudimentary
understanding
of the criteria1 phrases “more
seeds” and “same amount of seeds” was insured for each S. Following this orientation,
the S received three experimental
trials, each
dealing with different colored seeds. In each inst’ance, the S personally
poured t,he seeds from the plastic bottles to the standartl containers and
from these containers to the appropriate
comparison glasses. M7hen the
initial seed pouring was completed (and an amount-equality
judgment
agreed upon by the S and E for the equivalence conservation
casts),
the transfer to the comparison container took place. Following this, the
criteria1 question specific to each experimental condition was presented,
container)
have the
e.g., “Does this glass (gesture to the comparison
same amount of seeds or more seeds than this glass (gesture toward
standard
container)
has?” The position of the LLmore” and “same”
phrases were alternated from trial to trial in each experimental condition. The S’s objective response and the supporting reasons and explanat,ions for this judgment were tape-recorded.
All test administration
was
done in a room separate from the child’s classroom setting. Total admit)istration time was lo-15 minutes. Procedures specific to the three major
conservation
task-formats
were as follows:
(A) Identity
Conservation-This
case centers on a single, fixed
amount of seeds which was transferred
from the standard 50-m] beaker
to either a graduate cylinder 4 inches in height (moderate transformation) or a graduate cylinder 8 inches in height (extreme transformation).
Following each transformation,
the S was asked, “Does t,his glass (ges-
240
FRANK
H.
HOOPER
ture tmowarcl comparison container)
have the snrrr(’ mm~~nt of seeds 01
‘more s(yxls than this glns;s (gesture towtrcl
the stnntlwrd
container!
had before?” This procedure was repeated with different colored seeds
to yield three Separate trials.
(B) Equivalence Conservation
I-This
case centers upon two identical
50-ml beakers (A and B) with equal amounts of seeds poured into each.
Following S-E agreements regarding this equality, container A was moved
behind the opaque screen and the contrnts of container B were poured
into container C (representing
either a “moderate”
or “extreme”
transformat,ion as described above). The S was then asked, “Does this glass
(gesture toward comparison container c’) have the s(l?tle n~lo~nt of seeds
or more seeds t,han this glass (gesture toward standard container behind
the screen) has?” This procedure was repeated with clifferent colored
seeds to yield three separat,c trials.
(C) Equivalence
Conservation
II-This
case refers to the conventional paired-stimulus
conservation
sctt’ing. Identically
shaped containers A and B (50-ml beakers)
were filled with equal amounts of
seeds. The contents of B were transferred
by the S to container C (repThe S was
resenting either a “moderate”
01 ‘(extreme” transformation).
t,hen asked, “Does this glass (gesture toward comparison container C)
have the same nrno~~~.ntof seeds or ?11ore se& than this glass (gesture
toward standard cont,ainer A) has?” In this condition, all the containers
were kept in full view of the S. This procedure was repeated with
different colored seeds to pick1 t,hree separate trials.
Scoring
All the task sessions were tape-recorded
in their entirety and the final
determination
of response categorization
was done at a later time. Thr
same scoring criteria were applied to all the experimental conditions, and
this included t,he objective response, more or same amount, and the associated rationales offered by the S. In order to pass a given trial, the S
had to make an equality judgment, e.g., same amount of seeds, and support this estimate with an adequate explanation. The 8s’ explanations
were classified as inadequate, e.g., reasons based upon the immediate,
perceptual
features of the t.ask setting or irrelevant
statemcnt,s,
ot
adequate, e.g., Reversibility:
“You can pour the seeds bsck into the first
glass and they would have the same amount”; Statement of the operations performed:
“I just poured these seeds into this glass so they still
have the same amount”; Addition-subtraction.:
“I didn’t add any see&“:
or “We didn’t spill any seeds” or “That glass (comparison
container)
didn’t have any seeds in it before we poured these seeds into it”;
Compensatory
Relations-Proportionalit!/:
“That glass is short and fat.
PIAGET’S
CONSERVATION
241
TASKS
but this one is tall and skinny so they have the same amount”; “Xameness” of seeds: “These are the same seedshere (comparison container)
as we had in here (standard container) “; and References to the previous
amount of seeds or the previous state of equality between containers
A
and B: “This glass has the same amount of seedsas this one (refers to
standard container A and comparison container C) because these two
glasses (refers to standard containers A and B) had the same amount of
seedswhen we started.”
Conservation performance in the present study is viewed as an essentially discontinuous, all or none achievement. Ss who passed two or
three trials are scored as conservers, and this criterion is in accord with
the pass/fail specifications of a number of previous investigators, c.g.,
Kooistra (1964), Shantz and Sigel (1967)) Sigel, Roeper, and Hooper
(1966). No attempt was made to designate an intermediate category or
stage.
RESULTS
Two issues of initial concern are the relationship of equivalence conservation I and equivalence conservation II, and the possibility of
distinctive male vs. female performance patterns. Table 1 presents the
number of males and females passing the conservation tasks for the
various experimental conditions and age-grade levels. Considering, first,
the relationship of the equivalence conservation casesTable 1 indicates
very little difference in the number of conserving Ss for each of these
conditions.
For all ages combined, the percentages of Ss passing equivalence conservation I and II are noticeably similar, e.g., 44.470 and 41.6%,
THE
KUMBER
TABLE
1
OF MALES
AND FEMALES
PAMING
THE CONSERVATION
THE VARIOUS
COSDITIONS
AND AGE LEVELS
Types
Identity
Degree
of
transformation:
Age levels
Kindergarten
First
Second
Grade
grade
Male
Female
Male
Female
Male
Female
of conservation
TASKS
FOR
Equivalence
II
task
Equivalence
I
ext..
Moder.
ext.
3
2
0
1
1
0
0
0
1
3
2
3
3
2
2
0
3
1
2
2
2
2
2
2
3
I
Moder.
1
2
2
Moder.
0
ext.
0
0
2
1
3
1
242
PRANK
H.
HOOPEH
respectivcJy,
(Chi-hquarr, = .056. 1 crf, p < .YO). Considering the various
age levels separately, 66.7%’ of the secorltl graders passed equiralence I
and 66.7O/opassed cquivalcncrl II. For t,he first gradt,rs the values are 50
and 58.3% of the equivalence. I and equivalence II task:: t Chi-square 17
.168, 1 df, p < .70). Although none of the kindergarten Ss passed equivalence II, while 16.7% passed equivalence I, this difference also fails to
reach significance (Chi-square = 2.182, 1 df, p < .20). WC may conclude,
therefore, that t.he two cquivalcncc t,ask formats which share the criteria1
logical deduction scquencc do not differ significantly for the present
sample. Male/female differences, however, are clearly evident in the
present results. Across all conditions and age levels, 64.8% of the male
Ss and 37% of t,he female Ss were conscrvers (Chi-square = 7.262, I df,
p < .Ol) . Consequently, male and female performances will be considered
separately in the following analysis.
For all age levels and task conditions combined, 50.9% of the Ss were
claesetl a8 conscrvcrs and 49.1% as nonconservers. A form of an:+i:
appropriate to this pass/fail classification is the multidimensional Chisquare analysis suggested by Sutcliffe (1957) and Wirier (1962, pp. 629632). The present design conforms to Sutcliffe’s case 2b with certain
restricted classifications and ccrt,ain parameters estimated from the observed data. The partitioning of the overall Chi-square dcrircd from
Table 1 indicated significant main effects for the age-grade levels (Chisquare = 18.301, 2 CEf, ??= < .OOl) , the type of conservation tasks;
idcntit.y condition compared to combined equivalence conditions (Chisquare = 5.353, 1 df? p = < .05), and the male/female dichotomy (Chisquare = 7.262, 1 df, p = < .Ol) . None of the various interaction values
approached significance.
The significant positive relationship between age-grade levels and
conservation ability is primarily due to the differential performance of
kindergarten Ss compared t’o the first and second graders. For all conservat.ion t’ask conditions combined, 22.2, 61.1, and 69.4% of the kindergarten, first and second grade Ss were conservers. Individual comparisons
indicated significant differences between the kindergarten and first grade
(Chi-square = 11.10, 1 df, p = <.OOl) and between the kindergarten
and second grade (Chi-square = 16.17, 1 df, p = < .OOl) . The first grade/
second grade differences wcrc not significant, e.g., Chi-square = .551, 1
df( p = < .50.
Considering the t.ype of consrrvution task, for all ages combined.
66.7% of the identity Ss conserved, compared to 43.170 of those Ss in the
equivalence conservation condit’ions. Thus, equivalence conservation is a
more difficult behavioral achievement than identity conservations, AIt,hough the age/lcrels conservation task-type int,eraction values did not
PIAGET’S
CONSERVATION
TASKS
243
approach significance in the overall contingency analysis, there is some
indication
the relationship
of identity
and equivalence conservation
alters over the present age range. 9.1, 54.2, and 66.7% of the kindergarten, first, and second grade subsamples passed equivalence conservation. These values may be compared to the percentages of Ss passing
identity conservation,
e.g., 50, 75, and 75% for the kindergarten,
first,
and second grades, respectively.
While all these differences favor the
identity conservation
case, only the comparison
for the kindergarten
Ss is significant,
e.g., Chi-square = 8.026, 1 df, p = <.Ol. Thus, the
differences
between identity
and equivalence
conservation
are most
notable at the lower age level, and they tend to diminish as the first
and second grade levels are reached. This is especially true of male subsamples in which the numbers of equivalence and identity conservers are
markedly
different
at the kindergarten
level, but are very closely
matched by the second grade.
As indicated above, male and female performance
patterns
differ
markedly in the present study. Inspection of the pass/fail patterns and
the absence of any significant interactions
indicates a consistent male
performance
superiority.
Considering
the identity/equivalence
distinction, male identity conservation performance is uniform (83.3% passing)
for all three age-grade levels. Adequate equivalence conservation
performance, in contrast, increases sharply from the kindergarten
(8.3%)
to the first grade (67.7%) to the second grade (91.7%). The female Ss
show a similar increase in the number of conservers from kindergarten
to first grade for both identity and equivalence conservation
subtypes,
e.g., 20-67.7s
for identity and 8.3-41.7s
for equivalence conservation.
However, the number of female Ss achieving either type of conservation
does not alter from the first grade to the second grade.
It was expected that greater numbers of conservers would be found for
the moderate degree of physical transformat:on
as compared to the
extreme transformation
cases. This is clearly not the case, for the degree
of physical transformation
shows a notahlc lack of influence on both
identity and equivalence conservation performance. Across all age-grade
levels, task conditions, and subsamples 51.870 of the Ss in the moderate
transformation
conditions conserved as compared to 5C17~
in the extreme
transformation
cases.
In addition to the preceding considerations,
it is possible to examine
the three conservation
task-types
in terms of the logical explanations
offered by the SS. The adequate rationales
supporting
an objective
response of “same amount” may be classified into various sub-categories.
Table 2 gives the relative percentage of satisfactory
explanations for the
identity, equivalence I and equivalence IT conservation
tasks. The per-
244
FRANK
H.
TABLE
PERCENTAGES
OF THE
THREE
MA.J~R
BASIC
ADEQUATE
HOOPER
2
K~TJON.~LE
COXSERVATIOS
TASK
CATE~:ORIEY
FOR
TIIBJ
COKIIITIOSS
Type of conservation task
Explanation
1.
2.
3.
4.
5.
6.
category
Reversibility
Statement, of the operations performed
Addit,ion-subtraction
Compensatory relations-proportionality
“Sameness” of seeds
Reference to the previous state
Identity
Equiv. I
Equiv. 11
4.8
11.1
50.8
25.4
7.9
4.3
-
2.2
-
2.2
17.4
6.5
69.6
6.7
13.3
77.8
in this table are based upon the total number of primary or
final explanations offered by the Ss in question. Children occasionally
offered supplementary explanations in conjunction with the primary
justifications represented in Table 2. There were 17, 7, and 9 of these
mixed response instances in the identity, equivalence I, and equivalence
II conservation cases, respectively.
The patterns for equivalence I and equivalence II are clearly similar.
The type of explanation predominantly given in the equivalence conservation formats is a reference to the previous state of equality between
stimuli arrays A and B. Compensatory relations-proportionality,
and addition-subtraction
explanations also appear as
reversibility,
justification for equivalence conservation but in much lower proportions.
In contrast, the most frequent adequate rationale appearing in the
centages
identity
conservation
case centers
on addition-subtraction
schemas,
e.g.,
“No seedswere added or taken away.” This type of rationale accounts
for only 2.2 and 6.7% of the total number of adequate explanations
offered for equivalence I and equivalence II conservation. Compensatory
relations-proportionality
explanations also appear more frequently in
identity
conservation
as compared
to the equivalence
cases.
DISCUSSION
The present investigation has indicated a conceptual distinction within
conventional Piagetian conservation tasks. Identity
conservation, as
Elkind (1967) has shown, is logically prior to equivalence conservation.
The present results indicate
that identity
conservation
is developrrlentally prior to equivalence conservation. Adequate identity conservation
performance occurred more frequently than equivalence conservation for
all age levels assessed.We may conclude that for discontinuous quantity,
identity conservation is an earlier developmental acquisition than
equivalence conservation.
PIAGET’S
CONSERVATION
TASKS
246
The type of explanations offered in support of objective conservation
judgments also indicate distinctions
between identity and equivalence
conservation.
As Table 2 indicated, the predominant
explanation categories for the identity and equivalence cases were noticeably different.
Approximately
50% of the identity explanations focused upon additionsubtraction
schemas, e.g., “no seeds were added or taken away.” This
response has generally been considered an explicit, logically consistent
justification
and unequivocal
evidence of successful conservation
performance, e.g., Piaget (1952)) Piaget and Inhelder (1962), and Smedslund (1961). Its differential
appearance in the present 8s identity
explanations
adds further
support to the developmental
priority
of
identity over equivalence conservation.
The equivalence conservation
case, in contrast, is usually “solved” by
a reference to the previous state of equality between standard containers
A and B. Acknowledging
the dangers of an uncritical
acceptance of
young children’s
introspective
rationales,
e.g., Piaget (1954)) Werner
(1957), it is noteworthy
how often the present equivalence subjects
offered reasons closely approximating
a logical deduction sequence.
For example, Subject D. H. (Male, 1st grade, Equivalence II) : ‘Cause
this glass and this glass (gesture to standard containers)
had the same
amount and you poured this glass into there and it’s skinnier so it looks
like more. No it doesn’t have more because these two (gesture toward
standard containers)
had the same amount to start out with.” Subject
S. M. (Female, 1st grade, Equivalence II) : “Because that one was the
same amount and we poured it into here-and
the glass is thinner so it
makes it look a little bit more but it’s still the same amount. Because it
was the same as that one (gesture to standard)
before in that glass.”
Thus, the primary
explanation underlying
equivalence conservation
focuses upon the original equality relationship which is an integral aspect
of the postulated logical argument. As described ea’rlier, it is this logical
deduction sequence which formed the basis for a conceptual distinction
between the identity and equivalence conservation
cases. The present
research indicates, in cont,rast to Piaget’s position, that identity and
equivalence are not simultaneous or concommitant
developments. Piaget
is incorrect in attempting to explain equivalence conservation acquisition
solely in terms of identity conservation
mechanisms or processes. Also,
it is clear that the equivalence conservation task format is not the most
appropriate
means of valid identity conservation
assessment.
In view of the heavy emphasis previous investigators
have assigned to
perceptual cues in conservation
task formats. The lack of difference
between moderate and extreme transformations
is surprising.
Although
the present results may he specific to the particular
container sizes and
246
FRANK
H.
HOOPER
mat,erials used, they arc in csscntial accord wit’h Fiegenbaum’s
(19631
finding that no relationship) wa:: prcecnt bctw-cen tliticrc~ntiai comparison
container size and conservation
problem solution. If we accept the
validity of Piaget’s stage descriptions, e.g.. Piaget and Inhclder (1962, p.
21)) the transitional
or intuitive I stage II B‘) lcvcl is not rcprescnted by
the present 8s’ performances.
Conservation
ability was tither complctelp
absent or present in the final.
gcncralized stage which is not subject to
variat.ions in perceptual disparity or task complexity.
The role of perceptual cues is also involved in the lack of differences
found between equivalence conservation
I and cquivalencc conservation
II. The screening of t,he standard stimulus container prior to t,hc transformation
had virtually
no effect on conservation
performance.
Apparently, the “image” of the hidden container was sufficient to produce
the perceptual incongruity
essential to equivalence conservation
assessment. There is also the possibility that subjects utilized the empty standard container B as a guideline or reference in judging the A-C rclationship. It should be made clear that the present screening procedure differs
from Bruner’s format which screened the comparison container ant/ the
results of the transformation,
e.g., Bruncr, Olvcr, and Greenfield (1966).
Nonetheless, reduction of immediate pcrccptual cues was not an important factor in the present study.’
In addition to these primary considerations,
the present research has
revealed notably different male and female patterns. While male and
female Primary Mental Abilities IQ scores were not significantly
different for any age-grade level, male Ss were consistently
superior for all
task conditions and age levels. Not only are the absolute frequency levels
different’, but, of perhaps greater importance, the relationship
between
identity and equivalence conservation
is not the same for males and
females. For the kindergarten
girls, identity and equivalence conservation performances
are at the same lcvcl. The frequency of both conservation
types
increases
from
the kindergarten
t,o first
grade
level
piit
identity showing a marked superi0rit.y. Neither case shows any increase
from the first to second grade level. Thus, the priority of identity conservation as compared to equivalence conservation is not, evident until
the first’-second grade levels for female 8s. For males, in contrast, the
‘At the conclusion of the equivalence I tasks, each S was asked to indicate the
approximate level the seeds would reach if the contents of the hidden container *-I
were poured into the empty standard container B. 91.7% of the Ss nnticipate(1
the level accurately. thus indicating a reasonably clear idea or image of the screened
container’s level. There was lit,tle relationship
between correct anticipation
and
conservation achievement. This agrees with Inhelder’s (1965) report that correct
anbripations
of transformation
outcomes precede adequa.te conservation performance
PIAGET'S
CONSERVATION
TASKS
247
greatest difference between identity and equivalence conservation
tasks
is at the kindergarten
level. As mentioned previously, male equivalence
conservation
performance
levels converge with identity conservation
at
the second grade. In terms of absolute score superiority
and developmental progression, the male Ss appear more advanced than their female
counterparts.
The problem of an adequate understanding
and use of the criterion
relational terms “more” and “same amount” may also be related to the
present sex differences. Thirteen Ss, nine girls and four boys spontaneously and appropriately
used the term “same amount” in the orientation
session which preceded the conservation
tasks proper. All four males
passed their respective conservation
tasks. Eight of the nine females
failed to conserve. Apparently,
the presence of the relational terms in
the 8s’ vocabulary
has a different functional significance for males as
compared to females. This lack of prediction between operational usage
of the relational terms and conservation
performance for the female Ss
supports an earlier finding by Shantz and Sigel (1967).
It should be emphasized that the present distinction between identity
and equivalence conservation
differs considerably
from Piaget’s (1968)
recent statements concerning identity concepts. Piaget distinguishes the
conservation
of quantitative
invariants,
i.e., substance, weight, volume,
number, etc., from qualitative
invariants
which are preoperational
in
nature, The latter category is termed preconservational
identity by virtue
of its lack of quantitative
composition
(compensation
of relations, for
example) and is demonstrated by Ss who assert that, the amount of water
has changed following a reversible transformation
but who maintain it
is the “same water” as before. Piaget states, “In this case, the invariant
is obtained without
quantitative
composition ; there is simply a dissociation between a permanent quality (the same water . . .) and the
variable qualities (the shape or size), but there is no composition of these
variations”
(Piaget, 1968, p. 19). This position is essentially similar to
the Bruner et al. (1966) views on identity concepts as distinct from conservation concepts. The present author’s viewpoint in contrast, to Piaget
and Bruner, distinguishes between two varieties of conservation acquisition (identity vs. equivalence) within the conventional conservation task
format.
The present ident.ity/equivalence
distinction should be examined in additional content areas and task material settings. Insofar as quantity
concepts are concerned, it is probably true that identity conservation
performance will vary depending upon the concept, area in question and
the specific task material used. This has been t,he case with conventional
equivalence conservation,
e.g., the horizontal
dkcalage of substance,
248
FRANK
H.
HOOPER
and vohm~c, and t,he greater difficulty presented by continuous
stimulus material settings a,s compared to discontinuous
materials. The
relationship
between identity
and equivalence conservation,
however.
would not be expected to vary as a function of the conceptual areas 01
task materials.
Methodologically,
a more stringent test of the logical and developmental priority
of identity
conservation
would involve a repeated
measures design with the Ss receiving both identity and equivalence
conservation
tasks. Assuming adequate statistical
control or evaluation
of task carry-over
effects a significant number of Ss who pass identity
and fail equivalence would support the present relationship.
Conversely.
a sizeable number of Ss failing identity and suc,ceeding on equivalence
conservation would be a clear-cut refutation of the present position.
A recent assessment of rural Appalachian children (Hooper and Marshall, 1968) evaluated the identity/equivalence
conservation relationship
utilizing similar task materials and scoring criteria in a repeated measures design. Eighty five- and six-year-old
Ss were tested, and 25%
succeeded on the identity task compared to 13.7570 for the equivalence
conservation
case. More importantly,
while 75% of the Ss failed both
tasks, 13.7570 passed both tasks, and 11.25% passed identity and failed
equivalence, no Ss passed equivalence and failed identity conservation.
These results add considerable support to the present contentions.
Finally, the position of identity conservation
as a central element
within the equivalence task requirements
suggests a possible training or
enrichment
program for promoting
conventional,
equivalence conservation acquisition. Since identity conservation may he viewed as a necessary but not sufficient prerequisite
for equivalence conservat,ion performance, it would seem appropriate
to train children on identity task
settings. This could focus upon the critical physical alteration of stimulus
B to C in the identity setting. A possible training procedure stressing
the
discrimination
of similar spatio-temporal
stimulus transformations
has
been proposed by Watson (1968). General discrimination-memory
training of this type has been found to influence quantity and number conservation acquisition, e.g., Shantz and Sigel (1967).
weight,
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