emergence of representation in drawing: the

Cognitive
Development,
0 1998 Ablex Publishing
13, 25-5 1 (1998)
All rights of reproduction
ISSN 0885-2014
reserved.
EMERGENCE OF REPRESENTATION
IN DRAWING: THE RELATION
BETWEEN KINEMATIC AND
REFERENTIAL
ASPECTS
Esther Adi-Japha
Hebrew
University
Iris Levin
Tel Aviv University
Sorin Solomon
Hebrew
University
To identify and characterize early instances in which children attribute
meaning to their drawings, scribbles of 2- to 3-year-olds were examined
from kinematic and representational
perspectives. Scribbles were shown
to be composed of smooth-inertial
and angular-intentional
curves, the
former revealing a systematic relation between curvature and speed (the 21
3 power law). Children tended to attribute a-posterior-i representational
meanings (e.g., an airplane) to angular curves and nonrepresentational
meanings (e.g., a line) to smooth curves, that they have just finished
drawing. They did not do so with reference to scribbles drawn by peers,
by themselves in the past, or by the experimenter
who imitated their
scribbling. Children’s attribution of representational
meanings increased
with age. The phenomenon studied was discussed as a possible precursor
of preplanned representational
drawing, indicating the child’s awareness
of the symbolic function of a line-standing
for itself and signifying a
referent.
This paper is based on the doctoral dissertation conducted by Ester Adi-Japha, collaboratively
guided by Iris Levin and Sorin Solomon. It is included in the list of working papers (no. 97-3) of the
unit of human development and education. Thanks are extended to Norman Freeman.
Direct
all correspondence
Aspects in Education,
to:
Iris Levin,
Tel Aviv University,
Manuscript received September 3,1996;
School
of Education,
Tel Aviv, Israel, 69978
Department
of Devlopmental
<[email protected]>.
revision accepted July 20,1997
25
26
Adi-Japha,
Levin, and Solomon
Researchers agree that drawing evolves from scribbling (e.g., Arnheim, 1956; Freeman, 1993; Gardner, 1980; Kellogg, 1959; Krampen, 1991; Luquet, 1927; Piaget
& Inhelder, 1948/l 967). Scribbling in its initial phases is viewed as a motor activity,
unguided by visual planning, and determined mainly by the mechanical functioning
of the motor system of the arm, wrist and hand. Children show only transient interest in their own scribbles, and often readily move from one scribble to the next
(Gardner, 1980; Golomb, 1992; Thomas & Silk, 1989). With increasing perceptualmotor coordination, the scribbles become complex patterns, guided by visual attention, and determined by esthetic considerations
like that of balance (Arnheim,
1956, 1967, 1969; Golomb, 1992; Kellogg, 1970; Piaget & Inhelder, 1966/1969).
While a full-blown representational drawing-preplanned
by the child and recognizable to an observer-first
appears by 3 to 4 years (Freeman, 1993; Gardner,
1980; Golomb, 1992; Kellogg, 1970; Krampen, 1991; Silk&Thomas,
1986; Thomas & Silk, 1989), preliminary indications of drawing-related symbolic actions can
be traced as early as the second or third year. This suggests that by this age children
are already aware of the dual function of a drawing as a graphic signifier that signifies areferent and as an object existing in reality. Three such early indications have
been described in the literature, all of which were claimed to appear before children
produce planned shapes: action representation, romancing, and guided elicitation.
Action representations, also called gestural drawings, appear both in spontaneous drawing or in response to the request to draw a referent (e.g., an airplane).
Children may accompany scribbling with verbalizations or sounds such as roaring, which indicate that both their motions and the marks emerging from their
drawing-instrument
simulate the motion of an object. Thus, children’s own actions
are combined with marks and sounds to represent the moving-roaring object (Cox,
1992; Freeman, 1993; Gardner & Wolf, 1987; Golomb, 1992; Matthews, 1984;
Wolf, 1988; Wolf & Perry, 1988).
Romancing refers to instances where children name a scribble with a referent,
while an observer has difficulty tracing a graphic resemblance between the drawing and the signified. Romancing has been determined when naming occurs prior
to drawing, concomitantly, or after completion, either spontaneously or elicited by
an adult’s questioning. It included naming of an object, a series of interchangeable
objects, parts of an object, or a fragmented story. The phenomenon of romancing
may be explained in several ways: that the child pretends playfully to be making
a drawing, giving it meaning determined only by his/her intention (stipulation in
Freeman, 1993, p. 122, VV~.V?
in Gardner, 1980, p. 46); that the child intends to draw
something yet the product fails to communicate that intention; that the unintended
shape led the child alone, yet not the observer, to trace a hidden resemblance with
a referent; or that there is an overall spatial signifier-signified
relation, like when
the child indicates the scribble for head above that for legs, though both scribbles
are unrecognizable (Gardner, 1980; Golomb, 1974, 1992).
Guided elicitation is assessed when children, though showing no representational intention in their free scribbling, succeed in producing graphic representation
Emergence
of Representation
in Drawing
27
when assisted. They draw dictated parts in correct spatial relation, they complete
an unfinished drawing provided by an adult, or they create a figurative signifier-signified overall relation when instructed to draw certain objects, like drawing a circle
for bulky objects like a car or house, and a line for linear objects like a worm or snake
(Golomb, 1974, 1992; Kennedy, Nicholls, & Desrochers, 1995).
Concurrent with the emergence of precursors to representational
drawings at
the age of 2 to 3 years, when asked to explain what they drew in their free drawings, children often give no answer at all, or an answer that has no representational
meaning (e.g., a drawing). This may be the case because they are either asked
about, or naturally refer to the entire product which is often free floating and complex, hence not easily suggesting any referent. In contrast, line-sections within
scribbles can suggest simple contours of objects. Therefore, children at such a
young age might successfully attribute representational meanings to line-sections
within their scribbles, if asked about them.
Our inspection of pre-representational
scribbles, led us to conceive of them as
composed of two graphic schemas: an inertial-smooth schema composed of circular lines, and other, more ‘intentional’ schemas like angular forms or dots. Gardner
(1980) suggested a similar distinction with special reference to the motor actions
producing these schemas.
We have noted that certain portions of early scribbling are circular or wavy: in these actions
the child’s elbow remains fixed and his forearm rotates widely back and forth. Such ‘roundish’
forms stand in decisive contrast to a number of other early scribbles. To produce incisive dots,
the child’s entire arm (fingers to elbow) is raised up high and lowered sharply in one movement;...to create angular forms, the orientation of the wrist must be abruptly readjusted halfway through the motion” (p. 44).
Psychophysical studies of both adults and children from age 5 years, instructed
to repeatedly draw or trace ellipses, have shown that the rate at which a particular
section in a drawing is produced depends on its shape (Lacquaniti, Terzuolo, &
Viviany, 1983; Sciaky, Lacquaniti, Terzuolo, & Soechting, 1987; Viviany &
Schnider, 1991). This relationship has been termed the 2/3 power law and its
mathematical formula is:
A(t) = K * C(t)2’3
where
A(t) = the angular velocity
C(t) = the curvature of the section of the figure drawn at time t.
K = constant during the stroke of motion. ’
‘c= I vx*a,-
a, * v? 1I+;
V = (v,* + vv2)“*; A = V* C;
where: V = tangential velocity, vx and v_~= the velocity components in X and Y directions, and a, and
ay for the acceleration components in X and Y directions. (The velocity is the first derivative of the
place, and the acceleration is the second).
Adi-japha,twin,
28
and Solomon
This law has been supported in analyses of the proximal arm area in the motor cortex of monkeys (Schwarts, 1994).
In the study on the law’s applicability to monkeys, the animals had to be trained
to produce elliptic trajectories. In human studies participants were given templates
to trace, or instructed to draw elliptic shapes. Three-year-olds
were excluded
because they were assumed to be “unable to freely draw consistent elliptic patterns” (Sciaky et al., 1987, p. 519). However, we assumed that children younger
than 3 years, though unable to follow instructions to produce ellipses are experienced in producing such curves spontaneously.
EXPERIMENT
1
Aim
To examine the applicability
2-year-olds’ scribbles.
of the 213 power law to inertial-smoo~
sections of
Method
Ten children in the appropriate age range were invited to scribParticipants.
ble. Six (3 boys, 3 girls) who spontaneously produced long enough circular scribbles were included in Experiment I. Their mean age was 2;9 (range: 26-2; 11).
Each child sat at a child sized table with a square
Apparut~~ and Procedure.
digitized tray attached to a computer. The digitizer was a GRAPHTEC digitizer
KD4610A, with a sampling rate of 150Hz and nominal accuracy of 0.025 mm.
The child was provided with an A3 sheet of paper fixed on the tray, and a stylus
whose marks appeared both on the paper and on the computer screen. While children were drawing they could view the marks produced on the paper, and the
image marks emerging on the screen.
No inst~ctions were given other than showing the children how to use the pen.
When they indicated that they had finished a drawing, either verbally or by stopping, a new page was attached to the tray, and they proceeded to the next scribble.
The session was completed upon the children’s request, lasting about 15 min.
All experiments were conducted in Hebrew by the first author.
Results and Discussion
For analyses we used each child’s first two circular scribbles, provided these
contained a smooth section of continuous circular motion, lasting 4-7 set (M =
5.24 set, SD = 0.8 set), which started at least two cycles after onset of motion.
Each circular scribble was smoothed using a digital filter (cut-off frequency
lOHz), and numerically differentiated by using the 5point Lagrange method, providing angular velocity and curvature.
The value of the exponent (beta) was calculated for the two chosen sections per
child, each derived from a different scribble, by a linear regression of 1ogA (angu-
Emergence of Representation in Drawing
29
lar velocity) against 1ogC (curvature). The mean and standard deviation established for beta across the 12 chosen sections was M = -68, SD = .03. This mean is
sufficiently close to two-thirds to validate the law’s applicability to our data. Correlation coefficients (rho) between 1ogA and loge for the 12 curves ranged
between [email protected], with mean r = .93. These fmdings suggest that the 2f3 law holds
true for scribbles produced by children of the age range examined, as iong as it is
applied to the ine~ial-smoo~
sections, free from breaking points.
EXPR~MENT~:
REPRESENTATIONAL
EVOCATIONBYBROKENVS.SMOOTHCURVES
Aim
The aim of Experiment 2 was to examine whether smooth and broken sections
differ in representational evocation.
We expected representational
responses to be attributed to angular sections
more frequently than to smooth curves. This was expected because of the kinematic aspect of broken curves suggesting intentionality to change the direction of
drawing, the higher informational values of broken curves (Attneave, 1954), and
as a result of their relative closure suggesting object contours (Freeman, 1980).
This hypothesis was examined in a two-group design: one group drawing with a
digitizer to examine the kinematic aspect of scribbling, and the other group drawing with a regular pencil on paper to examine the phenomenon in a ‘natural’ context of drawing.
Participants. Children were recruited from nursery schools in middle to high
SES neighborhoods in Jerusalem, Israel.
Two groups of children took part in the experiment. Group 1 which drew with
a digitizer included 12 boys and 16 girls. Group 2 which drew with a regular pencil
on paper included 9 boys and 11 girls. The ages of groups 1 and 2 respectively,
were M = 2;7 and 2;6, SD = 0;3 and 0;3, range 2;3 - 3;0 and 2;l - 3;O.
Pr+oce&re.
In group 1 the procedure with the digitizer was as in Experiment
I. In Group 2 each child was interviewed in his/her nursery, in an isolated,
quiet
site. The child was provided with an A4 sheet of paper and an I-B-2 pencil.
In both groups the children were told to request an&her sheet of paper upon finishing drawing. When a child asked for another sheet, he/she was questioned about
the completed drawing on paper: “What is this ?” Following the child’s response,
the interviewer selected a line section of that drawing, moved her finger along the
line and asked: “What is this?’ To clarify the exact section referred to, she put her
thumb and forefinger at its ends. Following the child’s response (or refusal to
answer) she repeated the procedure l-3 more times on different line sections.
30
Adi-Japha, Levin, and Solomon
Two types of curves, smooth and broken, were selected for query according to
four criteria. First, smooth curves looked smooth while broken curves included a
breaking point. Quantitative validation for this visual distinction is provided
below. Second, each curve was distinctly visible, neither densely crossed nor covered by other curves. Third, selected curves were roughly the same length (M =
5.28 cm, SD = 1.63 cm measured for 106 curves in Group 1). Note that these sections were considerably shorter than the curves used to calculate the curvature and
velocity of lines, for v~idating the 213 power law in Experiment 1 (M = 290 cm,
SD = 56 cm measured for 1’2curves). Finally, each curve selected was graphically
separated from the other selected curves, to allow independent responses. Questions were asked in a sequence alternating smooth and broken curves.
Answers were classified into two categories: (1) nonrepresentational
geometrical (e.g., a line, a circle, a scribble, just marks, dots), and (2) representational-referential (e.g., a kite, an apple, a lion, mom). The following interview with a girl
aged 2;9 illustrates representational
and nonrepresentational
responses given to
smooth and to broken curves:
(C = child; I = interviewer)
(Just before the child stopped the scribble shown in Figure 1, she started hitting
the page with the stylus, saying to herself in a low voice rain)
I:
c:
I:
c:
I:
c:
I:
c:
I:
C:
I:
C:
What is it? (trying to discover what the child was murmuring)
Rain. (She drops the pen).
Would you like to tell me what this is? (referring to the entire scribble).
(Does not answer).
What is this? (indicating with her finger a smooth curve)
A line.
And what is this? (indicating a broken curve).
A kite. This is another kite.
Where is the other kite?
Here (pointing at another broken curve).
And what is this? (indicating a smooth curve).
A line.
The interviewer planned to question the child on two smooth and two broken
curves per drawing, yet this was not always possibie. Some drawings were composed of too short a line to provide several curves, others had no breaking
points. Further, the questioning was stopped when the child refused to answer
and preferred to begin the next drawing, or to end the session. A session was
completed when the child wanted to stop, or after 20 minutes. Children produced between l-8 drawings each. The dialogues were tape- recorded and transcribed
The drawings of Group 1 were recorded by the computer, and the kinematic
aspect of the scribbling was preserved by the digitizer’s plot with dots produced at
equal time spans; the denser~edots,
the slower the motion of the pen (see Figure 1).
31
Emergence of Representation in Drawing
A
,ANOTHER
KITE
(S)
I
0
5
10
15
25
x axis (cm)
20
30
35
40
Notes.
Spontaneous responses given to lines chosen by the girl, rather than the experimenter, are
marked (S). Arrows indicate the line sections which the child refered to, either in response to questions or spontaneously.
The bars designate the ends of the sections chosen by the experimenter.
Figure la.
lb.
A girl’s scribble with her attributions to different curve types.
A digitizer’s plot of the scribble illustrating a smooth curve and a
breaking point
32
Adi-Japha, Levin, and Solomon
Results and Discussion
Curve Smoothness Index:
To validate the visual distinction between smooth
and broken curves (criterion 1, above), we used the digitizer data to develop a
measure for curve smoothness. We calculated the smoothness of each line section the child explained. From the digitized curve with dots equally spaced by
time, we derived a curve with points separated by equal spaces, using linear
interpolation. For each point on the curve, we calculated the angle with respect
to its two neighboring points, situated 10 mm on each side of the curve. The
value of the minimal angle along the selected line section was divided by the
average angle of points, at 3 mm distance on each side of this minimal angle.
The results of this division range from 0 (a sharp angle) to 1 (a straight line or
perfect circle).
Computations were performed separately for two types of curves: line sections
selected by the experimenter and responded to by the children (i.e., elicited
responses) or line sections spontaneously explained by the children (i.e., spontaneous attributions). For each child we computed the average curve smoothness
measure, for elicited responses and spontaneous attributions separately. The number of children for each computation (n) was the number who provided responses
of the type under consideration. Within the category of elicited responses, results
for smooth curves were M = .90, SD = .05, n = 28 and for broken curves A4 = .25,
SD = .14, n = 27. Within spontaneous attributions, results for smooth curves were
M = .89, SD = .03, n = 20, and for broken curves M = .28, SD = 11, n = 17.
One-way Analyses of Variance (ANOVAs) showed that the smoothness index
of the smooth curves was significantly higher than of the broken curves for both
elicited responses, F( 1, 53) = 533.35, p < .OOl, and for spontaneous attributions,
F(1, 35) = 567.98, p < .OOl, supporting our perceptual distinction between these
curve types.
Responses to Whole Scribbles:
The first scribble was a warm-up. Upon completion of the following scribbles the experimenter asked about each entire scribble, “What is this?’ Among 28 and 20 children in groups 1 and 2, respectively, 18
and 13 responded with a nonrepresentational
answer (mostly circles or a drawing),
8 and 5 ignored the question, and 2 in each group provided a representational
answer (e.g., a house). These data strongly suggest that the entire scribbles were
not produced with representational intentions and rarely evoked a representational
answer, when the child was asked what it was.
Following the opening question about each scribResponses to Line Sections:
ble, the experimenter asked the child to interpret selected line sections, as illustrated
in Figure 2.
Group 1 (n = 28) produced 132 scribbles. Overall, the interviewer elicited
124 responses, while 90 attributions were given spontaneously to sections cho-
33
Emergence of Representation in Drawing
B
GIRL
D
BOY
(2;s)
DOLPHIN
IsI
Notes.
Spontaneous responses given to the lines chosen by the children are marked (S).
Arrows indicate the line sections which the children refered to, either in response to questions
spontaneously.
The bars designate the ends of the sections chosen by the experimenter.
Figure 2. Four scribbles
broken curves.
illustrating
children’s
attributions
or
to smooth and to
sen by the children. Elicited responses were given by all the children, while 22
children gave spontaneous attributions.
In Group 2 (n = 20), 71 scribbles were produced. The interviewer elicited
77 responses, and 20 were provided spontaneously
by the children. Elicited
responses were given by all, and spontaneous attributions by 11 children.
Table 1 presents the distribution of responses provided to smooth and broken curves according to response type, i.e., representational
or nonrepresentational. The data suggest that children were inclined to attribute representation
mostly to broken curves, including dots. This trend appeared in both elicited
responses and spontaneous attributions, for drawings on the digitizer as well
as on regular paper. These data could not, however, be statistically analyzed
because of dependence between observations, namely that the same child produced several answers. Hence, for each child we compared the proportion of
representational
meanings given to smooth and to broken curves. Children
were divided into three sub-groups: (1) those who produced a higher propor-
34
Adi-Japha, Levin, and Solomon
Table 1. Distribution of Representational
Given to Smooth and to Broken Curves
(Experiments 2 & 3)
Experiment No.
-2 (Group
Response ‘Qpe
and Nonrepresentational
Responses
Smooth Curve
Broken Curve
Representational
12
51
Nonrepresentational
51
IO
9
52
26
3
_._
1,digitizer)
Elicited
Spontaneous
Representational
Nonrepreselltationai
2(Group 2, pencil)
Elicited
Spontaneous
3 (1 st phase: Interpreting
Elicited
4
28
Nonrepresentational
34
11
Representational
0
I5
Nonrepresentational
4
Representational
peer’s scribble)
6
8
35
33
Representations
12
211
Nonrepresentational
31
23
Represntational
Nonrepresentational
3 (2nd phase: Inte~ret~ng
Elicited
3 (Group 2: Interpreting
Elicited
1
own past scribble)
experimenter’s
improvisation)
Representational
12
17
Nonrepresentational
22
17
tion of representational
meanings to broken curves: (2) those who produced a
higher proportion of representational
meanings to smooth curves; and (3)
those who produced the same proportion of representations
to smooth and broken curves. Children who produced no representations
were not included in
these analyses. This division was carried out separateiy for elicited responses
and spontaneous
att~butions.
Table 2 shows the dist~bution
of children in
Group 1 and in Group 2 into sub-groups with comparisons by sign tests,
We conclude that children of the age range examined tend to attribute representation mainly to broken curves. In contrast, they tend to give geometric responses,
mere descriptions of the curves, to smooth lines. This inclination emerges in regular drawings as well as in drawings produced on a digitizer.
Age Effects:
We examined whether the occurrence of representational
attribution increased with age. To provide sufficient data, Groups 1 and 2 were combined. Children (n = 48) were then divided into two groups, aged 2;1-2;6 and 2;73;0. Of the younger group approximately 70% (25 children out of 35) provided at
least one representationa
meaning, compared to almost the entire older group (20
Emergence
of Representation
35
in Drawing
Table 2. Distribution of Children by Relative Proportion of
Representational Responses Given to Smooth and to Broken Curves
Number of Children Giving Representational
Experiment
Number
More to Smooth
More to Broken
Responses
Same on Both
P<
2. (Group 1 - digitizer)
Elicited
1
19
1
,001
Spontaneous
0
12
5
,001
Elicited
0
12
2
.OOl
Spontaneous
0
8
0
,008
1
4
0
.38
2
6
4
.29
0
2
I
.50
(Group 2 - pencil)
3. (Peer’s scribble)
Elicited
(Past scribble)
Elicited
(Experimenter’s
Elicited
product)
out of 23) children. The tendency to produce representational meanings increased
significantly with age, x2( 1, N = 48) = 4.41, p < .04. There was no significant effect
of gender x2( 1, N = 48) = .20, p > .23.
Repetitions. The higher tendency to attribute representational meaning to broken curves, found above, may indicate a planned attempt on behalf of the child to
represent a particular referent in drawing, or alternatively may be an outcome of
the interviewing process. Children rarely declared in advance what they were
going to draw. Moreover, they rarely attributed any representational
meaning
when asked about the entire scribble. Therefore it seems reasonable to hypothesize
that the representational
attributions to line sections were evoked during the interview. To examine this hypothesis we analyzed the connections between meanings
produced by the same child.
Children often attributed the same meaning to different curves (see also, Gardner, 1980; Goodnow, 1977). Of 48 children, 41 provided identical and/or closely
related meanings, such as an apple and a banana or a rainbow and a star, at least
once over all the scribbles. Four children produced a single response each. Analyses pertained to 37 children who repeated the same exact answer, at least once.
We classified all of a child’s responses into two groups: originals and repetitions.
A response was considered original if it appeared only once, or for the first time in
the child’s protocol (i.e., the entire corpus of responses). A response was considered a repetition if an identical response had appeared already in the child’s protocol. Overall 167 originals and 144 repetitions were identified. Of 201 elicited
responses, 129 were originals; of 110 spontaneous attributions, 38 were originals.
36
Adi-Japha, Levin, and Solomon
Since we hypothesized that responses were more often triggered than preplanned, we expected that originals should appear more often among elicited than
among spontaneous attributions, as the curves for the former were selected by the
interviewer while the latter were chosen by the child.
Of 37 children who produced repetitions, only 28 gave both elicited and spontaneous meanings; these were included in the first analysis. We computed for each
child (1) the proportion of original responses of the total number of elicited
responses; and (2) the proportion of original responses of the total number of
spontaneous responses. We divided the children into three groups: (a) those who
produced a higher proportion of originals among elicited responses, (b) those who
produced a higher proportion of originals among spontaneous attributions, and (c)
those who produced an equal proportion of originals among elicited and spontaneous responses. The same analyses were carried out for 18 children who gave
representational repetitions, and for 17 who gave nonrepresentational
repetitions
(partly overlapping groups). Sign tests indicated that children tended to produce
originals significantly more often among elicited than spontaneous responses,
both overall and on representational attributions, see Table 3.
Repetitions were classified into immediate and separated repetitions. An immediate repetition was defined as a response immediately following the identical
response. Repetitions were considered separated when other responses were given
between them. Of 144 repetitions, 90 were immediate and 54 were separated. We
expected that repetitions should be more often immediate than separate, if
responses were evoked by the interview rather than preplanned. Immediate repetitions were primarily given to the same drawing, but also included identical attributions produced as the last response to one scribble, and as the first response to
the next scribble. The following analysis pertained only to immediate repetitions
produced to the same drawing, since unlike immediate repetitions pertaining to
successive scribbles, these constitute a clearer case of immediacy.
A total of 25 children produced repetitions for the same drawings. Six of them
could not have produced separated repetitions, as they only gave 2 answers per
drawing. The following analysis therefore refers to 19 children, all of whom produced representational repetitions, and 15 of whom produced nonrepresentational
Table 3. Distribution of Children by Relative Proportion of
Originals Among Elicited and Spontaneous Responses Overall, for
Representaional and for Nonrepresentational Responses
Higher proportion of originals on
Elicited
Overall
22
Spontaneous
5
Same Proportion
PC
1
.002
Representational
14
3
1
.Ol
Nonrepresentational
11
4
2
.12
Emergence
of Representation
37
in Drawing
repetitions. For each child we calculated (1) the proportion of immediate repetitions out of possible immediate repetitions; and (2) the parallel proportion of separated repetitions. Possible immediate repetitions within the same drawing equals
n-l for each drawing, summed over all drawings, where n is the number of
responses given by the child for each drawing. The possible separated repetitions
equals 1+2+3...+ n-2 for each drawing, summed over all drawings. The same analysis was carried out on representational
and nonrepresentational
attributions.
Table 4 presents the results. Sign tests indicate that repetitions tended to appear
more often immediately than separately, significantly overall, and for representational as well as for nonrepresentational
attributions.
In sum, when asked ‘what is this?’ on line-sections, children came up with original responses mainly to sections that the interviewer had chosen. Immediately
thereafter, they often gave the same response to sections that they themselves
selected. These data lend support to the claim that the meanings attributed were
triggered by the interview, rather than preplanned.
The triggering of responses during the interview may have three grounds: First
the visual features of a curve that includes a breaking point may trigger attribution
of representation more effectively than those of a smooth curve. A curve with a
sharp turn is naturally more closed, thus likely to suggest the contour of an object
(Freeman, 1980; Gardner, 1980). From a different perspective, broken curves may
deliver more information than smooth curves (Attneave, 1954; Hoffman & Richards, 1985), with most information
supplied by segments evenly distributed
between the peaks of curvature (Kennedy & Domander, 1985). If in fact visual
features are related to representation,
we can expect that children will attribute
representational
meaning to broken curves, regardless of whether they are drawn
by themselves or by someone else.
Second, the act of drawing a breaking point may indicate an intention to change
the direction of drawing, and this intention increases the child’s attention to the
segment produced. Further, drawing a breaking point is accompanied by proprioceptive feedback that may increase attention to the segment being drawn.
Increased attention to a segment may, in turn, make the segment isolated from the
scribble, hence inviting representational attribution. In this case it is expected that
Table 4. Distribution of Children by Relative Proportion of
Immediate vs. Separated Repetitions Overall, for Representaional
Nonrepresentational Responses
and for
Higher proportion of repetitions on
Immediate
Separated
Same Proportion
14
3
2
Representational
16
3
0
.004
Nonrepresentational
12
1
2
,003
Overall
PC
.Ol
Adi-Japha,Levin,and Solomon
38
children will attribute representational meanings to broken curves, so long as these
remain distinct for the child, isolated from the rest of the drawing (e.g., on scribbles they just drew, rather than those drawn a month earlier).
Third, watching the act of drawing a breaking point may increase attention to
the part being drawn, due to its unexpected direction and/or to the slowing down
in producing the breaking point (note the power law). This increased attention may
isolate the segment drawn from the scribble, calling for an attribution of representation to it. In this case it is expected that children will attribute represen~tion~
meanings to broken curves, as long as they remember watching them being drawn,
no matter who drew them (either themselves or someone else in their presence
e.g., the experimenter).
Tn Experiment 2 all the above features were present, and the outcome was representational attribution to broken curves. By separating features in Experiment 3
we examined whether specific features are sufficient for the phenomenon to occur,
or whether their combination is necessary.
EXPERIMENT 3
Aim
Inte~reting
peer’s drawings,
menter’s imitated drawings.
children’s
own previous
drawings,
and experi-
Method
Participants.
1.
2.
3.
Group I- 1st phase:
From the children who drew on the digitizer in
Experiment 2, 10 boys and 10 girls participated in Group 1,2-3 weeks later.
In phase 1 they interpreted drawings produced by their peers in Experiment
2. Their mean age was 2;7 (SD = 0;3, range 2;3 - 3;O).
Group I- Zymase:
Of these 20 participants, 10 boys and 9 girls served
in phase 2, 2-3 weeks later. The missing girl was replaced by a boy who
took part in Experiment 2, but not in the phase 1. They interpreted their own
drawings produced 4-5 weeks earlier, in Experiment 2.
Group 2: The 20 children who drew with regular pencils on paper in
Experiment 2, served as group 2, 2-3 weeks later. They interpreted drawings produced by the experimenter who imitated their own immediate
drawings, again produced with regular pencils on paper.
Procedure.
1.
Group J-Phase
I: The experimenter reminded each child of the previous time s/he drew on the digitizer. Each child was then told that another
child had done the same, and was shown a few drawings on papers pro-
Emergence
2.
3.
of Representation
in Drawing
39
duced by a peer. S/he was asked ‘what is this?’ referring to 4-6 smooth and
broken curves, which had been previously used in interviewing children
who drew them. Children were randomly paired, each responding to the
drawings of his/her counterpart. They were questioned in an alternating
sequence of smooth and broken curves.
Group I-Phase
2:
A couple of weeks later they again came to the laboratory and were presented with their own drawings on paper. They were
shown drawings about which they and their peers had previously been
questioned. They were questioned on 4-6 curves in an alternating sequence
of smooth and broken curves.
Group 2: These children were interviewed in the nursery, as they were in
Experiment 2. After each child scribbled with a pencil on an A4 paper, the
interviewer improvised a scribble in a similar style. She subsequently
selected 4-6 smooth and broken curves in her scribble, and asked the child
‘what is this?‘, alternating for smooth and broken curves. When the number
of responses failed to reach four, the interviewer produced a second imitated scribble and questioned the child about additional sections.
Figure 3 presents two scribbles produced by two children, and two improvised
by the experimenter in a similar style, to illustrate the resulting degree of resemblance.
Results and Discussion
1.
2.
Group I-Phase
I:
Twenty children provided 82 responses to 35 drawings produced by their peers a couple of weeks earlier. Responses were predominantly nonrepresentational,
for both smooth and broken curves, as
shown in Table 1. Among these, 22 responses were “I don’t know”. This
answer was very rare in all our other studies. Most children, namely 15 out
of 20, gave no representational answers at all, as indicated in Table 2. While
there was a slight tendency to give representational
answers to broken
rather than to smooth curves, no significant difference emerged between
the responses given to these curve types.
Group I-Phase
2:
A couple of weeks later the children provided 86
responses to 37 drawings that they had produced 4-5 weeks earlier.
Responses included both representational
and nonrepresentational
attributions. While representational
responses were given slightly more often to
broken curves and nonrepresentational
to smooth (Table l), this difference
was not significant (Table 2), with many children (8 out of 20) giving no
representational
attributions at all.
In sharp contrast to Experiment 2, no child provided a spontaneous response
when asked about a peer’s drawings, and only one child did so when asked about
his previous drawings.
40
Adi-Japha, Levin, and Solomon
To clarify the difference between those results p~~aining ta drawings just produced by the child (Experiment 2), and those done either by a peer (Experiment 3Phase 1) or by the child hi~~rself
a few weeks earlier (Experiment 3-Phase 2),
we compared the data provided by the 20 children who participated in these two
experiments. For each child we compared the proportion of representational
answers given to broken curves out of the total number of answers given to such
curves in Experiment 2, to these proportions in Phase 1 and Phase 2, separately.
Concerning Phase 1, children were divided into those whose proportion was
higher for their own drawings than the peers’ drawings (14) those whose proportion was higher for the peers’ drawings (0) and those who had the same proportion
for both { 1). Concerning phase 2, children were divided into those whose proportion was higher for just completed drawings (9), those whose proportion was
higher for their own past drawings (0), and those who had the same proportion for
both f7). Five and four children respectively, gave no representational meanings to
broken curves in either of the experiments.
One tailed sign tests comparing the data of Experiment 2 with Phase 1 and 2
separately indicated significant differences @ < .OOl, p < .002). It is concluded
that the tendency to attribute representation to broken rather than to smooth curves
GXPERIMENTER’S
[MITPATION
EXPERIMENTER’S
[MITIATION
II
Figure 3. Two scribbles produced by children and their imitations improvised by
the experimenter.
Emergence of Representation in Drawing
41
is higher in reference to children’s own immediate drawings, than both to peer’s
drawings and to their own past drawings.
Having children interpret their own drawings twice, both immediately after
production and after 4-6 weeks, provided an opportunity to examine whether they
tended to give the same representational meanings to the same line sections. Only
25% of the children gave the same meaning to the same line-section in both sessions at least once. For each child we computed the proportion of responses in the
second session that duplicated responses given to the same line section in the first
session. This proportion was below 50% for 13 of 15 children, indicating that most
responses in the second session were new (p < ,002, by sign test); Thus, one curve
was often given different meanings by the same child on separate occasions.
The finding of a higher tendency to attribute representations to broken curves
for just finished drawings than for past drawings or peer drawings, raises the question whether children tend to attribute representation to broken curves when they
recall the curves being drawn, or whether they need to recall how they personally
produced the curves for the phenomenon to occur. Group 2 was designed to distinguish between these possibilities.
3. Group 2: Twenty children responded to questions on 68 line sections
from 30 scribbles drawn by the experimenter imitating their scribbles.
Many children (11 out of 20) gave no representational
attributions at all.
While representational
meanings were given slightly more often to broken
curves, and nonrepresentational
meanings to smooth curves (Table l), this
difference was not significant (Table 2). No child provided a spontaneous
response in this experiment.
To clarify the difference between tendencies emerging from Experiment 2 and
Experiment 3 group 2, we compared the data collected in the two experiments. For
each child who participated in both, we compared the proportion of representational meanings given to broken curves out of the total number of attributions
given to such curves in these experiments. Children were divided into those whose
proportion was higher for their own drawings (9) those whose proportion was
higher for the experimenter’s drawings (2) and those who had the same proportion for both (6). Three children gave no representational
attributions to broken
curves in either of the experiments. A one tailed sign test (p < .033) indicated that
the difference between experiments was significant.
These results suggest that the tendency of children to attribute representation to
broken curves is not an outcome of having just perceived the act of drawing. They
must recall the experience of drawing these curves on their own.
EXPERIMENTS
Aim
Experiment 4 had two related goals: (a) to test whether children’s attribution of
representational
meaning to broken rather than smooth curves is intuitively
42
Adi-Japha, Levin, and Solomon
expected by
adults, and (b) whether children’s specific representational responses
given to certain curves are intuitively recognized by adults.
Adults may view broken curves as more meaningful either because they are
more closed (Freeman, 1980; Gardner, 1980) or convey more information (Attneave, 1954; Hoffman & Richards, 1985, Kennedy & Domander, 1985). Further,
if adults can recognize the particular meaning attributed by children to curves, this
might mean that children take into account the curve’s specific shape when attributing meaning. A similar question was posed by Freeman (1993): “Is it really the
case that ‘anything goes,’ that any product is as good as any other for pretending
to be an artist?’ (p. 123).
Since parents of young children can be expected to be more familiar with children’s scribbles than same aged people without children, and since such familiarity may affect intuitions about scribbles, our sample was designed to vary on
parenthood and gender.
Method
Participants.
Forty university students in their twenties took part in the study.
This sample included 10 mothers and 10 fathers, all married and raising their own
2- to 3-year-old child. The children of these parents were not included in our
experiments. The 20 childless singles were also equally divided by gender.
Apparatus.
Scribbles produced by 15 children with the digitizer in Experiment 2 were used to prepare 45 10 x 7 cm. cards. From each child’s scribbles, three
cards were prepared: two with broken curves that had previously elicited representational attributions, and one card with a smooth curve that had elicited a nonrepresentational attribution. Figure 4 presents one smooth and two broken curves
produced by the same child (aged 2; 11). The meanings attributed by him to the
broken curves were an ant and a dolphin, and to the smooth curve a line. The numbers on the axes, shown in Figure lB, indicate centimeters along the axes of the
digitizer tray, running O-30 cm and O-45 cm on the x and y axes, respectively.
The broken curves were randomly divided into two sets, with one broken curve
per child included in each set. In phase 1 each adult dealt with 30 cards: 15 of broken curves and 15 of smooth. All the adults dealt with the same 15 smooth curves,
and half of each group-i.e.,
mothers, fathers, childless women and childless men,
dealt with one set of broken curves. In phase 2 each adult dealt with the set that he/
she did not treat in phase 1. The two sets were used to enable generalization across
sets.
The experimenter acquainted the participants with the procedure
Procedure.
of Experiment 2. She told them that 2- to 3-year-olds had scribbled with a digitizer
and then asked what particular curves of their scribbles were. The adults were
shown a typical digitized scribble (see Figure 1B) and the experimenter explained
the meaning of the density of the dots.
Emergence of Representation in Drawing
20.0
20.0
Figure 4.
43
27.5
35.0
Three cards based on two broken and one smooth curve of the same child.
44
Adi-Japha, Levin, and Solomon
The experimenter then explained the classification of children’s responses into
representational
and nonrepresentational
meaning, the former referring to actual
objects, and the latter to graphical forms. Representational
meaning was illustrated by a banana, an apple, a lion or a kite, and nonrepresentational
meanings by
a circle, a line, or a triangle. The response triangle was included because it may
suit a broken curve. All these responses were given by children.
The assessment involved three phases. In the first phase of uninformed classification 30 cards, half including broken curves and half smooth, were presented in
a random sequence. The participants were asked to classify them into those given
representational
responses by the children, and those given nonrepresentational
responses.
Participants then proceeded to the second phase, that of informed classification.
They were told that the curves could be classified as either smooth or broken, and
were shown a typical curve of each type. They were informed that children attributed representational
meaning to broken curves and non representational
to
smooth. They were asked to classify the cards again into those likely to have been
given representational and nonrepresentational
answers.
In the third phase, the participants were presented with a new set of 15 broken
curves and were asked to decide which of two representational
meanings was
given by the child to each curve. The correct response was that elicited from the
child for that curve, while the incorrect response was that elicited from the child
for the curve included in the other set.
Results and Discussion
The number of correct classifications of cards in the first and second phases into
those given representational and nonrepresentational
attributions was analyzed by
a four-way ANOVA: 2 (phase: uninformed and informed), by 2 (parenthood: parents and childless singles), by 2 (gender), by 2 (set of cards), with repeated factor
on phase. This revealed significant effects of both phase, F( 1, 32) = 255.95, p <
.OOl, and parenthood, F( I, 32) = 9.11, p < ,005) as well as a significant interaction
between these factors (F( 1, 32) = 4.44, p < .04. All other effects were not significant.
The mean number (and range) of correct classifications of 30 cards in the uninformed phase was 17.70 (1 l-22) for singles and 19.95 (17-22) for parents. In the
informed phase the numbers increased to 25.65 (23-28) and 25.30 (23-28), respectively, where each of the participants performed better when informed. Parents
outperformed singles in uninformed classification, but this difference vanished
when informed. This suggests that parenting a child of the age range examined
promotes awareness of the representational
meaning for children of broken
curves, and the lack of such meaning as regards smooth curves. Even parents,
though, did not use this criterion systematically, unless provided with it explicitly.
Given the information, parents and childless singles alike could distinguish well
between the two types of curve.
Emergence
of Representation
45
in Drawing
In the third phase, the mean number (and range) of correct recognitions of
meanings attributed to the broken curves was 11.28 (9- 14) of a maximum of 15. Of
40 participants, 17 succeeded significantly above chance (p < .05), responding
correctly to at least 12 cards. Data were analyzed by a two-way ANOVA, 2 (parenthood: parents and singles) by 2 (gender). No effects were significant. Thus, parents and singles were equally inclined to select the correct meaning out of two
possibilities. Needless to say, the referents attributed to the curves by the children
could not be recognized by an uninformed observer. Only when the possible referents were limited to two, were curves often recognizable.
The referents of some curves were easier to assess than others. Figure 5 presents
two curves. The first curve shows a ‘difficult’ item, with eight adults choosing the
correct response (a watch) and 12 the incorrect (a sun). The second illustrates an
‘easy’ item, with 16 adults choosing the correct response (Q banana) and four
choosing incorrectly (a kite).
GENERAL DISCUSSION
The major findings in the present series of studies relate kinematic aspects of
scribbling to precursors of graphic representation. We found that children, 2- to 3years-old, produce scribbles that include two types of graphic schemas: smoothinertial and angular-intentional.
The distinction between the two types of line sections was originally described on the basis of impressionistic
observation as
involving different motor actions (Gardner, 1980). The present studies have shown
them to differ dynamically: smooth curves obey the 2/3 power law, while angular
curves do not. This describes the formal relation between curvature and drawing
speed found in adults’ ‘inertial’ drawing (Lacquaniti et al., 1983; Sciaky et al.,
1987; Viviany & Schnider, 1991).
24.3
2 1.0
22
A SUK\A
WATCH
27
32
A BANANA \ A KITE
Figure 5. Two cards illustrating a “difficult” and an “easy” item, and their possible
responses.
46
Adi-Japha, Levin, and Solomon
The two types of schema are usually both present in scribbles of this age group.
During inertial action, the motion of the drawing instrument is characterized by a
simple kinematic relation between speed and curvature. These motions are separated by discrete events characterized by a break in the continuity of both speed
and direction. The breaking point is reflected predominantly by angular sections,
and sometimes by dots or short lines produced by powerfully hitting the page. The
child is inclined to attach representational
meaning to the breaking points in his/
her drawing while treating the ‘smooth-inertial’ parts as nonrepresentational.
The link between broken curves and representational meaning was found in our
study to appear only when children interpret scribbles that they themselves have
just finished drawing. This link did not appear when children were asked to interpret line sections of scribbles either drawn by peers, by themselves a few weeks
earlier, or by an experimenter who scribbled in their own style .
Attention to broken curves may be higher than to smooth curves due to intentional change of direction involved in their drawing, a slowing down of production, proprioceptive feedback, or a combination
of the above. This increased
attention to broken curves may isolate them from the background swirls. But why
do segments attended to invite representational attribution?
We suggest that the visual features of these curves play a role in the emergence
of representational
attributions. Sections including breaking points convey more
information (Attneave, 19.54), and being relatively closed suggest the contour of
an object (Freeman, 1980). Moreover, it seems that the particular shape of the
curve surrounding the breaking point, determines to some extent the referent
attributed to it. For instance, an enclosed roundish region may suggest a bulky
object like a car or a house, a slim region may call for a narrow object like a banana
or an ant, and a tail may suggest a kite (Kennedy et al., 1995). However, the visual
features of these curves are not sufficient to invite representation. Only when combined with increased attention do they provide the context for early emergence of
representation.
Furthermore, our findings strongly suggest that the attributed referent is not
present in the child’s mind prior to or in the course of drawing. It is invented during
the interview when the child is inspecting a particular curve. We conclude this
from the following findings: (1) the answers to the opening question referring to
the entire scribble ‘what is this?’ were rarely referential, (2) original referential
attributions were mostly given to lines selected by the interviewer, and not by the
child, and (3) repetitions occurred more often spontaneously, to self-selected lines,
immediately following elicited responses.
While representational attributions are a by-product of the interview, the referents chosen are not entirely arbitrary. There was often a figurative connection
between the shape of the curve and the attributed referent. This conclusion derives
from our finding that approximately half the adults sampled chose-a
percentage
above chance level-the
referent attributed by the child to his/her line-sections,
out of two possible referents. It is nevertheless obvious (see Figures 1, 2) that the
Emergence
of Representation
in Drawing
47
line-sections were not full-blown representational
drawings, recognizable by an
observer. The children who drew them, when asked to interpret the same lines
twice a few weeks apart, more often than not came up with different referents.
Studies that analyzed the favorite referents of children’s drawings examined
representational
drawings of 4-year-olds. They unanimously
concluded that the
prevalent referent of spontaneous drawings is that of the human figure (Ballard,
1912; DiLeo, 1970; Lark-Horovitz, Lewis, & Luca, 1967; Lukens, 1896; Maitland, 1895), to the extent that this became the typical object of analysis of the
development of drawing (Cox, 1992, 1993; Freeman, 1977, 1980; Golomb, 1974;
Harris, 1963; Koppitz, 1968, 1984; Silk & Thomas, 1986; Sitton & Light, 1992).
We examined whether the human figure was the prominent referent in our studies, and whether other referents mentioned by our participants appeared in the literature on early drawing (Cox, 1992; Gardner, 1980; Koppitz, 1968; LarkHorovitz et al., 1967).
A total of 76 different referents were mentioned in Experiment 2, among 171
representational
responses. We classified them into ‘inanimate objects’ including
tools and toys (53 responses) and vehicles (18); ‘animate objects’ including animals (46) and plants (36); and celestial bodies (18). Human figures appeared
rarely, three times only (e.g., mom).
These data suggest that children’s preplanned representational drawing is a different phenomenon from the post hoc representational
attributions studied here.
Children from about age 3, when drawing a preplanned referent, tend to prefer to
draw the human figure. This does not mean that their first graphic concept is that
of a human figure. On the contrary, at a younger age they tend to grasp how simple
lines capture graphic features of various referents, but the human figure is frequently not included among them. It is the first object, though, that they are motivated to draw once they reach the stage when their drawings become preplanned.
Figure 6 was drawn by a girl, 3; 1 years old. She took part in Experiment 2, but
was later removed because she was too old for our study. Her scribble includes referents attributed to line-sections, along with a preplanned drawing of a human figure. It illustrates a transitional
point between precursors, and full blown
representation. Preplanning will gradually predominate.
Note that the referents mentioned by our subjects were not necessarily representative of objects in the children’s immediate physical environments,
such as a
table or a bottle. Children had probably been acquainted with many of the referents, like a snake or a dolphin, via TV or children’s books. Assuming that TV and
books capture a child’s imagination, it may be suggested that meanings attributed
to drawings reflect topics that arouse children’s imagination. It is also possible that
exposure to two-dimensional
drawings of a referent on paper (as in books) facilitates children’s ability to trace graphic resemblance with that referent in their own
scribbles.
Children’s responses consisted mostly of single nouns standing for whole
objects, that are concepts at the basic level (Brown, 1958; Rosch, 1978; Rosch,
Adi-Japha, Levin, and Solomon
48
GIRL
1:
(3;I)
AN
IRON
(S)
,
Note.
Spontaneous
2:
responses given to lines chosen
A
HOUSE
by the girl are marked
(S)
Figure 6. A scribble of a girl with her attributions, including a representational
drawing of a man.
Mervis, Gray, Johnson, & Boyes-Braem, 1976). These are the type of nouns frequently found in children’s early language (Nelson, 1973), and in mother-toddleidiscourse (Mervis & Mervis, 1982; Shipley & Kuhn, 1983). Parts of objects were
rare (8 cases), and if mentioned, followed the whole object (e.g., a banana then a
peel or an elephant and a trunk). This mirrors the way parents introduce parts of
objects when talking to young children, first naming the whole object and then its
parts (Shipley, Kuhn, & Madden, 1983). No scenes were mentioned of a series of
objects relating to each other, as in the previously described phenomenon
of
romancing. Nouns were rarely followed by adjectives. Only four objects were
described as big or small. Thus, it seems that young children look for ‘graphic concepts’ rather than for a detail of a drawing on the one hand, or a full scale drawing,
on the other.
IMPLICATIONS
FOR
FUTURE
STUDIES
What are the educational implications of our findings? Parents and teachers often
ask young children who have completed a scribble, ‘What is this drawing?’ This
common adult reaction has been criticized as inhibiting the child’s creativity
(Kellogg, 1970). It seems that such questions, when posed to a 2- to 3-year-old
child, often do lead to a dead-end. Questions about line-sections, in contrast, often
elicit meaningful responses, and do not stop the child from going on with scrib-
Emergence
of Representation
in Drawing
49
bling, or from attributing more interpretations.
Further studies should explore
whether eliciting representational
attributions to line sections included in prerepresentational scribbles could promote representational
drawing.
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