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Representational Flexibility Over Time 1
Running Head: REPRESENTATIONAL FLEXIBILITY OVER TIME
Karmiloff-Smith’s RRM distinction between adjunctions and redescriptions:
It’s about time (and children’s drawings)
Steve Hollis and Jason Low*
Victoria University of Wellington, New Zealand
In Press with British Journal of Developmental Psychology
(Accepted 11 January 2005)
The data contributed in part to a thesis submitted to Victoria University of Wellington
in fulfilment of the requirements for the degree of Master of Arts in Psychology by
Steve Hollis under the direction of Jason Low. The research was supported by a VUW
URF Grant 1-36 to Dr Jason Low. *Requests for reprints should be addressed to Dr
Jason Low at School of Psychology, Victoria University of Wellington, PO Box 600,
Wellington, New Zealand (e-mail: Jason.Low@vuw.ac.nz).
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Representational Flexibility Over Time 2
Abstract
A sample of 315 children aged between 6- and 9-years participated in a 5-month
longitudinal study aimed at investigating constraints on representational flexibility as
observed in drawing behaviour. The study specifically looked at how external
interventions affected children’s representations over time. The intervention involved
showing children various examples of pretend people in relation to Karmiloff-Smith’s
(1990) task of requesting children to operate on their normal person-drawing
procedures. The study confirmed that knowledge introduced exogenously was only
beneficial immediately after the intervention. Over time, in contrast to the older
children, the younger children reverted back to their internal representations that were
specified as sequentially fixed lists. The intervention did not promote transfer of
learning to the analogous task of drawing pretend houses. The study suggests that
exogenous provocations of behaviour are driven by adjunctions, and that reiterated
cycles of representational redescription must occur before the externally mediated
knowledge becomes flexibly manipulable.
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Representational Flexibility Over Time 3
Following Karmiloff-Smith’s (1990) seminal work, the present study aims to
investigate children’s drawings as a source of evidence with respect to the more
general process of representational change, that is, the way in which knowledge in the
mind becomes transformed into knowledge to the mind. Karmiloff-Smith found that
young children’s internal representations are governed by a sequentially fixed list and
it is only with subsequent representational redescription that the constraint relaxes to
become a flexibly ordered set of manipulable features. Since then, researchers have
argued that flexibility in drawing (conceptual and procedural) can be found at a much
younger age when external input is considered (e.g., simplifying task materials and
instructions). Our study will, however, not focus on whether Karmiloff-Smith has
underestimated young children’s competency. We will instead investigate whether we
can overestimate the effects of external input in driving representational change.
RRM and Children’s Drawings
In early studies relating to language and naïve physics, Karmiloff-Smith
reported that when procedurally embedded knowledge undergoes first-pass
representational redescription, it might still be somewhat rigid in nature (e.g.,
Karmiloff-Smith, 1986; Karmiloff-Smith & Inhelder, 1974). To verify the general
process-oriented framework of her representational redescription model (RRM),
Karmiloff-Smith (1990) investigated the issues of internal representational change
and the constraints involved by asking children between the ages of 5- and 11-years to
draw a man, and then, a man that did not exist. In keeping with RRM, children from
the ages of 5 upwards were selected because behavioural mastery is a prerequisite for
the first level of representational redescription to take place. Indeed, she noted that a
majority of the children were able to draw pictures of normal men and executed these
sequential procedures easily. The modifications found in the creative drawings
included: shape/size of element changes (e.g., one arm in the shape of a triangle),
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Representational Flexibility Over Time 4
shape of whole changes (e.g., the whole is drawn as a series of triangles), deletions
(e.g., one arm was deleted), insertions (e.g., extra head was added), position-
orientation changes (e.g., legs were drawn where arms are meant to be and vice versa)
and cross-category changes (e.g., half man and half animal). The results revealed that
all age groups were able to make the first three types of modifications, but only a few
of the 4- to 6-year-olds were able to make changes involving the last three types. She
also reported that younger children finished their drawings after making a deletion,
while older children continued their drawings after deleting an item. Finally,
Karmiloff-Smith reported that the majority of the participants in the younger age
group could not interrupt their sequential drawing of a man even when she asked them
to draw a man with two heads. All but one participant from the younger age group
ended up drawing two people instead of one.
Having accomplished behavioural mastery, the younger children were viewed
to have gone through the first round of representational redescription. At this level,
their knowledge remains sequentially specified, inheriting a procedural constraint
from the behavioural mastery phase. Hence, children are able to make modifications
that do not interrupt the procedural sequence (e.g., element changes) but find it
difficult to make modifications that involve insertions of sub-routines in the drawing
procedure (e.g., position-orientation changes). Furthermore, at the first level of
redescription, children’s knowledge has not become available as data structure to
other parts of the cognitive system. Hence, young children made few modifications
that combined concepts about personhood with concepts about animalhood. It is only
with additional rounds of redescription that the sequential constraint further relaxes,
and knowledge becomes available across domains. Other laboratories have, however,
emphasised a different picture of representational flexibility in children’s drawings.
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Representational Flexibility Over Time 5
Research Post-Karmiloff-Smith (1990)
While Karmiloff-Smith interpreted her findings to support the presence of an
endogenous cognitive constraint upon representational change (i.e., a sequential
constraint), Zhi, Thomas and Robinson (1997) decided to test whether the constraint
is instead exogenous and task related. Three- and four-year-olds were asked to draw a
man with two heads. Half the participants were shown a picture of a woman with two
heads, while the other half was not shown an example. The majority of the children in
the illustration group successfully drew a two headed person and performed the
insertion in the middle of the drawing sequence, while none of the children in the no-
illustration group completed the drawing successfully. Elsewhere, Spensley and
Taylor (1999) tested the effects of highly specific verbal prompts (e.g., draw a man
with legs coming out of his arms) amongst 4- to 6-year-olds and replicated Zhi et al.’s
findings of task considerations promoting flexibility. All these results suggest that
conceptual and procedural flexibility may be observed earlier in development and that
young children may have misunderstood Karmiloff-Smith’s (1990) instructions.
Why are young children reliant upon external prompts in order to adopt
flexible drawing strategies? Berti and Freeman (1997) explained that when children
attempt a solution to Karmiloff-Smith’s creative generation task, the first aim is to
make the picture recognisable as a man. The problem that arises, they suggest, is that
in trying to accomplish this first goal, the child may fall short of the second (i.e., the
picture should also contain fictional features). The result is that the picture looks like
a normal man. They argue that dual recognition can be accomplished “when [the
child] can envisage picking out from each category the distinctive shapes that will
trigger the two recognitions” (p. 409). Hence, young children are able to demonstrate
graphic flexibility when they are provided with explicit instructions as to what they
need to present to the viewer.
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Representational Flexibility Over Time 6
Finally, Picard and Vinter (1999) questioned the specific Karmiloff-Smith
(1990) finding that younger children finished their drawings after making a deletion
and instead suggest that task parameters can also limit intra-representational
flexibility. Five- and nine-year-olds were shown a drawing of a house and a television
and told that “a magician had tried to make the objects invisible, but had failed, and so
the objects were finally only partially invisible” (p. 608). Children received one of
two subsequent instructions: “we only see a few bits of it” or “we can’t see all of it
anymore”; these instructions were labelled ‘pieces’ and ‘parts’ respectively.
Participants were required to erase some features of the object in accordance with
either the ‘parts’ or the ‘pieces’ instruction. Picard and Vinter found that younger
children were able to make deletions targeted to the whole object upon receiving the
‘parts’ instruction as compared to the ‘pieces’ instruction, suggesting, contra
Karmiloff-Smith (1990), that young children are not constrained to making deletions
at the end of the drawing sequence.
Responses from Karmiloff-Smith
Researchers have argued that since young children can draw novel innovations
to the human form after being asked to come up with a particular category or shown a
visual example, RRM has underestimated the age at which representational flexibility
can be observed. In response, Karmiloff-Smith (1992, 1994, 1999; Spencer &
Karmiloff-Smith, 1997) explains that critics of her 1990 drawing study appear to be
arguing that there is no change in representational format during development and all
that changes with age is that greater amount of information can be brought to bear in
working memory. Even in the original 1990 report, Karmiloff-Smith argued that when
young children are successful at drawing or copying, for instance, a two-headed man
after being shown a visual example, they are not using the flexibility of a redescribed
procedure that can be pursued rapidly. Instead, under these externally provoked
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Representational Flexibility Over Time 7
circumstances, young children are creating de novo a new and independent procedure
(an adjunction). This needs to be contrasted with the explicit representational format
that sustains behaviour amongst older children whereby they can spontaneously insert
sub-routines into their drawing procedure. She explained that it would be an error of
confounding external product and internal representation to think that the same
product (e.g., finished drawing of a two-headed man) is necessarily generated from
identical representations. Even when change is exogenously triggered, subsequent
internally provoked representational change must still take place. Change via
representational redescription is not to be equated with change via representational
adjunction (i.e., adding a new solution on the basis of external stimuli that remains
unconnected with existing knowledge available to the mind). To consolidate her
argument, Karmiloff-Smith (1990) referred to drawing research revealing that even
when behavioural change can be induced exogenously, the transfer of training effect
has been weak, if any (e.g., Cox, 1985, Pemberton and Nelson, 1987).
The Present Study
RRM predicts that external solutions in the form of visual examples are only
temporarily helpful because they are stored as adjunctions and therefore not processed
as deeply as representational redescriptions would be. Further internal reformatting of
the externally promoted solutions must still occur before young children can reliably
call upon advanced representations, and even when behavioural change can be
induced immediately after the introduction of visual examples, the transfer of training
effect is limited. We tested these RRM predictions by charting representational
changes between an examples condition with two control conditions: (a) children
working on drawings of pretend men in the presence of an experimenter but without
visual examples (draw alone condition); and (b) children working on an unrelated task
in front of the experimenter (distracter condition). This design has been successfully
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Representational Flexibility Over Time 8
used by Peters, Davey, Messer and Smith (1999) to investigate how internal
representational change occurs despite exogenous provocations in the block balancing
task, and correspondingly, we felt that it would enable us to compare the effects of
visual examples with a period of task related practical experience and with a period of
being with the experimenter, but engaged in a non-drawing activity.
The present study is the first, then, to investigate whether children’s internal
representations seen through Karmiloff-Smith’s (1990) drawing task might change
over time (approximately five months), and whether redescription of external
knowledge (via visual examples) must still take place before it is generalised and
available for wider use. The first phase of the experiment asked children to draw a
person and a pretend person. One week later, an intervention phase took place. As
mentioned, this intervention involved allocating participants into one of three
conditions: distracter, draw alone and examples. This was followed by three further
drawing phases, which took place one week, five weeks and seventeen weeks
respectively after the intervention. In the last phase, we looked at transfer of learning
across tasks, by introducing a new but similar problem: drawing a pretend house.
If the ability to introduce innovations with sub-routines in the middle of the
drawing procedure is independent of the distinction between representational
adjunctions and redescriptions, young children who are argued to be unable to
complete Karmiloff-Smith’s (1990) drawing task because of information processing
demands (e.g., lack of prompts) should perform better in the examples condition as
compared to their counterparts in the draw alone and distracter conditions. More
specifically, there should be no developmental difference between the younger and
older children’s representations in the examples condition across all time points, and
both groups should also exhibit transfer of learning when invited to complete the
analogous task of drawing pretend houses.
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Representational Flexibility Over Time 9
In contrast, to the extent that advanced and generalised representations only
occur after there has been sufficient developmental time for representational
redescription to take place (Karmiloff-Smith, 1981, 1990, 1992), children in the
examples group should only outperform their same-age counterparts in the other
conditions for a brief period of time after the intervention. Similarly, since RRM
views externally provoked behavioural change to be a product of representational
adjunctions that themselves still need to undergo redescription, young children in the
examples group should only show behavioural patterns similar to their older
counterparts for a brief time after being shown the visual examples. The 17-weeks
post-intervention time frame should not be sufficient to wash out approximately six
years of reiterated rounds of redescription as found by Karmiloff-Smith (1990)
between 5- and 11-year-olds. Extending from RRM predictions, then, as time passes,
young children in the examples conditions should return to a lower level
representation that is similar to their pre-intervention performance, and also similar to
their same age counterparts’ performance in the draw alone and distracter conditions.
Moreover, it should be the case that there would be little (if any) transfer of learning
exhibited by young children in the examples group when drawing pretend houses.
Method
Participants
A total of three hundred and fifteen children across five age groups
participated in the experiment. The younger children comprised of 5- to 7-year-olds
(84 boys and 87 girls; M = 78.85 months, SD = 10.45 months). The older children
comprised of 8- to 9-year-olds (73 boys and 71 girls; M = 107.73 months, SD = 7.17
months). Following Karmiloff-Smith (1990), to investigate representational change,
we selected children from 5-years onwards since children from this age exhibit
behavioural mastery when drawing people and houses and have adequate conceptual
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Representational Flexibility Over Time 10
knowledge of such categories. The sample came from two large primary schools
located in suburban areas of Wellington, New Zealand. The sample represented
middle-class socio-economic backgrounds and was culturally diverse: Pakeha (New
Zealanders of European descent, 43%), Maori (13%), Pacific Islander (39%) and
Other (5%). There was 100% retention across all phases of the experiment. All
participants spoke English.
Procedure
The procedure for the intervention and each time point of the experiment will
be described separately. All participants were interviewed individually. The identity
of the experimenter and the location of the testing room remained constant over the
course of the study. All participants were provided with drawing paper and pencils.
Time 1. We followed Karmiloff-Smith’s (1990) procedure by first asking
children to copy drawings of four geometric forms to ensure that none of the
participants had motor or planning problems. All children succeeded in copying the
geometric forms. Then participants were asked to draw a picture of a person and a
house on separate pieces of paper. While the children drew, the experimenter took
notes on the sequence by which children drew the components of the people and
houses. After these drawings were put away, the experimenter invited each child to
play the ‘Rocket Drawing Game’. Participants were presented with a cardboard rocket
with a removable conical top. When the top is removed, drawings can be rolled up
and placed into the hollow of the rocket’s main cylinder. Participants were instructed
that the game was to draw a pretend looking person to go back to live on a planet
different to earth. Taking our lead from Karmiloff-Smith, to ensure that the
participants understood what was expected of them, several additional locutions were
used with every child in random order, such as a person “that doesn’t exist”, “that you
invent”, and “that you have never seen before”. Participants were instructed that a
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Representational Flexibility Over Time 11
clock (placed in front of them) would ring after five minutes and it would be time for
the rocket to take off. The experimenter took notes of the sequence in which the
various parts to the pretend person were drawn. All children finished their drawings
before the clock rang. When the clock rang, participants were instructed to roll up
their drawings and place them into the rocket. The experimenter simulated rocket
take-off sounds. After the rocket “blasted off”, the experimenter removed the
drawings from the rocket, placed them on the table, and invited participants to
describe their drawings. All responses were noted. Then children were thanked for
their participation.
Intervention. One week after Time 1, participants took part in the intervention
phase. Participants from both age groups were randomly allocated into one of three
conditions. In the distracter condition, participants were asked to build something
using lego bricks. They were instructed that a clock (placed in front of them) would
ring in five minutes and it would be time to finish their lego construction and tell the
experimenter what they had made. Participants in the draw alone condition were
invited to play the rocket drawing game again, with the explanation that the goal was
to draw a pretend looking person to go back to live on yet another planet different to
earth. The rocket had a different coloured removable top and different stickers. The
experimenter recorded the order in which participants drew components in their
pictures. Participants in the examples condition were shown four different examples
of pretend people (see Figure 1). The examples were printed on separate pieces of
paper, and presented individually, in random order. Over a period of five minutes, the
examples were explained to the participants. For instance, with respect to the deletion,
the experimenter said, “This is a pretend person because part of this person’s body has
been removed.”
[Insert Figure 1 here]
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Representational Flexibility Over Time 12
We used four examples in our study: two representing low-category modifications
(shape of element change and deletion), and two representing high-category
modifications (insertion and position-orientation change). We did not show examples
of shape of whole and cross-category changes to keep from overly taxing children’s
attention in processing the features. More importantly, Karmiloff-Smith (1994) has
explicitly reiterated that her 1990 data showed no developmental sequence between
elements/whole/deletion, nor between insertions/position-orientation/cross-category;
the former three occurred simultaneously in younger children’s drawings while the
latter three occurred simultaneously in older children’s drawings (p. 738).
Time 2. One week after the intervention, the experimenter returned and said
that the rocket drawing game was lots of fun and asked the children to play it again.
The procedural details for the rocket drawing game were similar to those carried out
in Time 1. The experimenter explained that the task was to draw a pretend person to
go back to live on yet another planet that was different to earth. The rocket had a
different coloured removable top and different stickers. While participants drew their
pretend people, the experimenter recorded the order in which participants drew the
various components in their pictures.
Time 3. Testing at Time 3 took place one month after Time 2. The aim of this
test phase (and the subsequent test phase) was to examine representational changes
over longer periods of time. At Time 3, all children were invited to play the rocket
drawing game again. The experimenter said that the game was lots of fun and the task
was to draw a pretend person to go back to live on yet another different planet. The
rocket had a different coloured removable top and different stickers to all rockets used
before. While participants drew their pretend people, the experimenter recorded the
order in which the various components in the pictures were drawn.
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Representational Flexibility Over Time 13
Time 4. Three months after Time 3, children participated in the Time 4
session. All children were invited to play the rocket drawing game once again. The
experimenter said that the game was lots of fun and the task was to draw another
pretend person to go back to live on yet another different planet. Just before children
in the examples condition completed the rocket drawing game, they were randomly
divided into two sub-groups. One group (no reminder about training) received the
same instructions as all the other participants, while the other group (reminder about
training) received slightly different instructions. This latter group was shown the four
examples of pretend people in random order and asked to think about them as they
played the game again. The examples were then removed. The reminder manipulation
served to check, if children in the examples group showed regressions in their
representational levels, whether such a trend might be attributable to a lack of
imagination in young children per se. As per usual, the rocket had a different coloured
removable top and different stickers to all rockets used before. While participants
drew, the experimenter recorded the order in which participants drew the various
components in their pictures. After this, to assess transfer of learning, the
experimenter said, “Let’s play a different kind of rocket drawing game. Now I would
like you to draw a pretend house to put on a planet that is different to earth.” The rest
of the procedural details to the house version of the rocket drawing game were similar
to the pretend people version of the rocket drawing game.
Results
The appendix contains examples of children’s generations for the draw a
pretend person task. Some children drew more than one picture of a pretend person at
the various time points. In the results presented here, only the first drawings generated
by the participants were included for analysis. The results are presented as follows.
First, we present results concerning conceptual flexibility as expressed in the
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Representational Flexibility Over Time 14
drawings. Following this, the results concerning procedural flexibility in the execution
of the modifications in the creative drawings will be presented. This is followed by
results linking conceptual and procedural flexibility. Preliminary analyses revealed no
significant effects involving gender or ethnicity of participants, and so these factors
will not be discussed further. Preliminary analyses also indicated no significant
difference between the performances of 5-, 6- and 7-year-olds, and no significant
difference between the performances of 8- and 9-year-olds. Hence, responses from 5-,
6- and 7-year-olds constituted data for the younger age group while responses from 8-
and 9-year-olds constituted data for the older age group.
Conceptual Flexibility
Two independent judges coded 25% of children’s pretend drawings for the
two categories of modifications as stipulated in Karmiloff-Smith (1990, 1994): low-
category modifications (elements/whole/deletions) and high-category modifications
(insertions/position-orientation/cross-category). There was 95% overall agreement.
All differences were resolved upon discussion. The remaining drawings were then
coded by one of the judges. The categories were not treated as mutually exclusive
given that children often introduced several types of changes in their drawings (e.g.,
changed the shape of the head and then drew a fruit for the body). However, similar to
Karmiloff-Smith’s (1990) own findings, even when we treated the categories as
mutually exclusive (coding only the most advanced type of modifications) the pattern
of results was the same. Figure 2 gives the percentage of children attempting the two
categories of modifications by time and condition.
[Insert Figure 2 here]
For each condition, Cochran’s Q Test was applied to the frequencies of low-
category modifications in younger and older children’s drawings across the five
sessions (pretend house drawing included). For younger children in each of the three
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Representational Flexibility Over Time 15
conditions, there was no significant difference in the occurrence of low-category
modifications over the five sessions (Qdistracter = 8.03; Qdraw again = 3.54; Qexamples = 5.11;
all ps > .05). Similarly, for older children in each of the three conditions, there was no
significant difference in the occurrence of low-category modifications over the five
sessions (Qdistracter = 5.50; Qdraw again = 6.23; Qexamples = 1.55; all ps > .05). As indicated in
Figure 2, across the three conditions, both younger and older children were able to
generate low-category modifications across the drawing sessions.
Turning to high-category modifications, Cochran’s Q Test was also applied to
compare the frequencies of such modifications across the five sessions in each of the
three conditions.
For younger children in the distracter and draw again control conditions, there
was no significant difference in the occurrence of high-category modifications over
the five sessions (Qdistracter = 2.02; Qdraw again = 7.19; all ps > .05). As shown in Figure 2,
high-category modifications did not significantly account for younger children’s
drawings in the control conditions across the five sessions. However, for younger
children in the examples condition, there was a significant difference in the
occurrence of high-category modifications over the five sessions (Qexamples = 29.75, p <
.001). Post-hoc McNemar Tests with Bonferroni adjustments revealed that the
following pairwise comparisons were significant (all ps < .01). There were more high-
category modifications generated at Time 3 (56%) than Time 1 (25%). There were
more high-category modifications generated at Time 2 (51%) and Time 3 (56%) than
at Time 4 (21%). Finally, there were more high-category modifications generated
during the pretend man drawing session at Time 3 (56%) than during the pretend
house drawing session at Time 4 (28%).
For older children, there was no significant difference in the occurrence of
high-category modifications over the five sessions (Qdistracter = 2.93; Qdraw again = 8.74;
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Representational Flexibility Over Time 16
Qexamples = 1.01, all ps > .05). As illustrated in Figure 2, high-category modifications
appeared consistently and prominently in older children’s drawings in each of the
three conditions across the five sessions.
Procedural Flexibility
We next examined whether children displayed a flexible or a rigid sequencing
of movements when making graphic modifications. We specifically looked at the
moment in the course of the drawing activity when interruptions were executed to
make alterations to the human (or house) form. Three types of procedural
interruptions were observed: at the beginning – the modification was performed while
the child was drawing the first graphic unit; at the middle – the child began his or her
drawing as usual (according to baseline) and then executed the graphic modification
and then went on to finish the drawing as per usual (according to baseline); and at the
end – the child started as usual and once the graphic modification was performed, did
not draw any more. Karmiloff-Smith (1990) and Picard and Vinter (1999) have
successfully used this coding scheme. Two independent judges coded 25% of
children’s drawings according to these criteria and achieved an overall 98%
agreement. One of the judges then coded the remaining drawings. Figure 3 depicts the
proportions of the three types of procedural interruptions by age group, time and
condition.
[Insert Figure 3 here]
The proportions of the three types of interruptions executed for pretend
people drawings were submitted into a 2 (age: younger & older) x 3 (condition:
distracter, draw alone & examples) x 3 (interruption: beginning, middle & end) x 4
(time: Time 1, 2, 3 & 4) multivariate ANOVA with age and condition as between-
subject variables and interruption and time as within-subject variables. There were
significant main effects of age (F(1, 309) = 25.36, p < .001), interruption (F(2, 308) =
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Representational Flexibility Over Time 17
48.99, p < .001) and time (F(3, 307) = 3.40, p < .05). There were also significant two-
way interactions involving: age x interruption (F(2, 308) = 6.63, p < .001); condition
x interruption (F(4, 616) = 7.45, p < .001); and interruption x time (F(6, 304) = 55.69,
p < .001). The two-way interactions were further qualified by a three-way time x
interruption x condition interaction (F(12, 608) = 2.77, p < .01).
To interpret these interactions, the proportions of the three types of
interruptions at Time 1, Time 2, Time 3 and Time 4 were each analysed in a 2 (age:
younger & older) x 3 (condition: distracter, draw alone & examples) x 3 (interruption:
beginning, middle & end) ANOVA with age and condition as between-subject
variables and interruption as within-subjects variable. All significant interactions were
further interpreted through simple main effects analyses followed by pairwise
comparisons with Bonferroni adjustments. The significant findings from these
subsequent analyses are summarised in Table 1.
[Insert Table 1 here]
At Time 1, there was a significant interaction between age and interruption.
End of sequence interruptions accounted for proportionally more of the younger
children’s drawing behaviour (M = 0.43) than middle of sequence (M = 0.27) or
beginning of sequence interruptions (M = 0.11). In contrast, middle of sequence
interruptions accounted for proportionally more of the older children’s drawing
behaviour (M = 0.51) than end of sequence (M = 0.25) or beginning of sequence
interruptions (M = 0.19).
Turning to Time 2, the following two-way interactions were significant:
between age and interruption, between condition and interruption, and between
condition and age. The age by interruption interaction can be interpreted as follows.
For younger children, there were proportionally fewer modifications made at the
beginning of the drawing sequence (M = 0.11) than at the middle (M = 0.37) or end of
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Representational Flexibility Over Time 18
the drawing sequence (M = 0.41). In contrast, middle of sequence interruptions
accounted for proportionally more of older children’s drawing behaviour (M = 0.61)
than beginning of sequence (M = 0.18) or end of sequence interruptions (M = 0.15).
For the condition by interruption interaction, for both the distracter and draw
alone conditions, there were proportionally fewer interruptions made in the beginning
than the middle or end of the drawing sequence (distracter: Mbeginning = 0.17; Mmiddle =
0.38; Mend = 0.32) (draw alone: Mbeginning = 0.13; Mmiddle = 0.41; Mend = 0.37). However,
middle of sequence interruptions accounted for proportionally more of the examples
condition’s drawing behaviour (M = 0.66) than beginning of sequence (M = 0.13) or
end of sequence interruptions (M = 0.20).
With respect to the condition by age interaction at Time 2, older children
carried out more modifications overall (M = 0.32) than younger children (M = 0.26) in
the distracter group. There was no difference in the overall proportion of
modifications made between younger (M = 0.30) and older children (M = 0.29) in the
draw alone group. Furthermore, there was also no difference in the overall proportion
of modifications made between younger (M = 0.33) and older children (M = 0.33) in
the examples group.
The procedural flexibility results at Time 3 were similar to those observed at
Time 2. At Time 3, the age by interruption interaction can be interpreted as follows.
Beginning of sequence interruptions accounted for proportionally less of younger
children’s drawing behaviour (M = 0.10) than middle (M = 0.39) or end of sequence
interruptions (M = 0.36). For older children, proportionally more modifications
appeared in the middle (M = 0.56) than at the beginning (M = 0.17) or end of the
drawing sequence (M = 0.22). In terms of the condition by interruption interaction, for
both the distracter and draw alone conditions, modifications were proportionally
fewer in the beginning than in the middle or end of the drawing sequence (distracter:
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Representational Flexibility Over Time 19
Mbeginning = 0.14; Mmiddle = 0.39; Mend = 0.32) (draw alone: Mbeginning = 0.11; Mmiddle =
0.40; Mend = 0.36). However, for the examples condition, modifications were
proportionally more frequent in the middle (M = 0.62) than at the beginning (M =
0.14) or end of the drawing sequence (M = 0.21).
At Time 4, the two-way age by interruption interaction can be interpreted as
follows. End of sequence interruptions accounted for proportionally more of younger
children’s drawing behaviour (M = 0.46) than middle of sequence (M = 0.27) or
beginning of sequence (M = 0.12) interruptions. With older children, middle of
sequence interruptions accounted for proportionally more of drawing behaviour (M =
0.53) than end (M = 0.25) or beginning of sequence interruptions (M = 0.19).
For the analogous task of drawing pretend houses at Time 4, the proportions of
the three types of interruptions were analysed through a 2 (age: younger & older) x 3
(condition: distracter, draw alone & examples) x 3 (interruption: beginning, middle &
end) ANOVA with age and condition as between-subject variables and interruption as
within-subjects variable. There was a significant two-way age x interruption
interaction (F(2, 308) = 19.58. p < .001). Beginning of sequence interruptions
accounted for proportionally less of younger children’s drawing behaviour (M = 0.09)
than middle of sequence (M = 0.31) or end of sequence (M = 0.45) interruptions. In
contrast, middle of sequence interruptions accounted for proportionally more of older
children’s drawing behaviour (M = 0.59) than end of sequence (M = 0.22) or
beginning of sequence interruptions (M = 0.14).
Representational Level
The final section of the results looks at the representational level of children’s
drawings, that is, the overall link between the type of modification children made and
the location in the drawing sequence where the modification was made. Table 2
presents the coding scheme used to score children’s representational level.
-
Representational Flexibility Over Time 20
[Insert Table 2 here]
To assign representational level scores, two judges independently coded 25%
of children’s drawings and achieved 100% agreement. One judge coded the remaining
drawings. The mean representational level scores by age group, time and condition
are shown in Figure 4.
[Insert Figure 4 here]
Children’s level scores for the pretend people drawings were analysed in a 2
(age: younger & older) x 3 (condition: distracter, draw alone & examples) x 4 (time:
Time 1, 2, 3 & 4) multivariate ANOVA with age and condition as between-subject
variables and time as a within-subjects variable. There were significant main effects
of age (F(1, 309) = 167.37, p < .001), condition (F(2, 309) = 4.50, p < .05) and time
(F(3, 307) = 12.76, p < .001). The two-way condition x time interaction was also
significant (F(6, 614) = 3.98, p < .01). Finally, these effects were qualified further by
a significant three-way age x condition x time interaction (F(6, 614) = 2.39, p < .05).
To interpret the three-way interaction, children’s level scores were further analysed in
separate age x condition ANOVAs for each time point. All significant two-way
interactions were then further interpreted through simple main effects analyses
followed by pairwise comparisons with Bonferroni adjustments. The significant
findings from these subsequent analyses are summarised in Table 3.
[Insert Table 3 here]
At Time 1, there was only a significant main effect of age. The mean level
score for the younger children (M = 1.35) was lower than the mean level score for the
older children (M = 2.18).
At Time 2, the age by condition interaction stemmed from a significant simple
main effect of condition for the younger children but not for the older children. The
mean representational level score for younger children in the examples condition (M =
-
Representational Flexibility Over Time 21
2.24) was significantly higher than the mean level scores obtained by their same age
counterparts in the distracter (M = 1.42) and draw alone (M = 1.57) conditions. There
was no significant difference between the mean level scores amongst older children
between the three conditions (distracter M = 2.41; draw alone M = 2.39; examples M
= 2.58).
Turning to Time 3, the two-way age by condition interaction was similarly due
to a significant main effect of condition for the younger children but not for the older
children. The mean representational level score for younger children in the examples
condition (M = 2.28) was significantly higher than mean level scores obtained by their
same age counterparts in the distracter (M = 1.58) and draw alone (M = 2.28)
conditions. There was no significant difference between the mean level scores
amongst older children between the three conditions (distracter M = 2.49; draw alone
M = 2.47; examples M = 2.48).
By Time 4, analyses revealed only a significant simple main effect of age. The
mean level score for the younger children (M = 1.51) was lower than the mean level
score for the older children (M = 2.50). These results mirror those seen at Time 1
where only a main effect of age was observed.
When we performed an age x condition ANOVA upon the representational
level scores of children for the drawings generated also at Time 4 for the analogous
task of drawing pretend houses, the analyses revealed a significant age x condition
interaction (F(2, 309) = 3.34, p < .05). This two-way interaction for the pretend house
drawings was due to a non-significant main effect of condition for the older children
but a significant main effect of condition for the younger children. For younger
children, participants in the draw alone condition had a lower mean level score (M =
1.14) than participants in the distracter (M = 1.51) or examples (M = 1.58) conditions.
For older children, the mean level scores for participants in the three conditions were
-
Representational Flexibility Over Time 22
not significantly different from each other (distracter M = 2.40; draw alone M = 2.47;
examples M = 2.31). Nevertheless, at Time 4, the overall pattern of performance in
the analogous task of drawing pretend houses reflected the performance of drawing
pretend people at Time 1: young children in the examples condition no longer
outperformed their same age counterparts in the control conditions, and had lower
representational level scores compared to older children.
It is reasonable to ask whether prominent main effects of age at Time 4 might
be due to a simple lack of imagination in young children. To check this possibility, we
remind the reader that we had also randomly divided participants in the examples
condition at Time 4 into a reminded sub-group and a non-reminded sub-group.
Children’s level scores from the examples condition at Time 4 were entered into a 2
(age: younger & older) x 2 (reminder status: reminded and non-reminded) x 2 (task:
pretend man drawing & pretend house drawing) ANOVA with age and reminder
status as between subject variables and task as within-subjects variable. The mean
representational scores at Time 4 for the example condition as a function of age and
reminder status are depicted in Figure 5.
[Insert Figure 5 here]
Reminder status did not turn out to be a significant main effect (F < 1) and did
not interact with age (F(1, 101) = 1.25, p > .05) or task (F < 1). The three-way age x
reminder status x task interaction was also not significant (F(1, 101) = 1.53, p > .05).
In short, the reminder did not reactivate representational flexibility at Time 4.
Summary
The results can be summarised as follows. At Time 1, younger children show
greater conceptual and procedural rigidity in their drawings than compared to their
older counterparts. However, at Time 2 and Time 3, compared to the distracter and
draw alone control conditions, younger children in the examples condition like their
-
Representational Flexibility Over Time 23
older counterparts generally, executed high-category graphic modifications in the
middle of the drawing sequence. However, the benefits of the examples proved to be
short-lived. By Time 4, children reverted to the patterns exhibited at Time 1 –
younger children tended to make low-category modifications and execute their
graphic modifications at the end of the drawing sequence while older children tended
to make high-category modifications in the middle of the drawing sequence. The
pattern persisted even when children were examined in their performance on the
analogous task of drawing pretend houses.
Discussion
The present study specifically investigated whether children’s internal
representations seen through the Karmiloff-Smith (1990) drawing task might change
over time (approximately five months), and whether representational redescription of
external knowledge (via visual examples) must still take place before it is generalised
and available for wider use. Before the intervention, we found developmental patterns
similar to those reported by Karmiloff-Smith (1990). Compared to older children,
younger children demonstrated significantly more conceptual and procedural rigidity.
We found that a week after having seen examples of pretend people, the measures of
young children’s conceptual and procedural flexibility were higher in comparison
with their baseline measures. There was also no significant difference between the
representational scores of younger and older children one week after the intervention.
In this manner, the results concerning immediate performance after exogenous
provocations confirm extant research showing that young children’s representations
benefit from external supports (e.g., Berti & Freeman, 1997; Spensley & Taylor,
1999; Zhi et al., 1997). While these results would confirm criticisms of Karmiloff-
Smith’s (1990) study that representational flexibility in children’s drawings of novel
-
Representational Flexibility Over Time 24
forms has been underestimated, such data alone would confuse the external drawing
product with the internal cognitive formats that drive behaviour.
Our study through its longitudinal nature, then, makes important contribution
to knowledge in the area of representational flexibility by showing how externally
provoked behavioural change may be a product of representational adjunctions that
themselves still need to undergo representational redescription. We found that young
children in the examples group only showed behavioural patterns similar to their older
counterparts for a brief time after being shown the visual examples. Over the five
months (by Time 4) young children in the examples conditions slowly returned to a
lower representational level that was similar to their pre-intervention performance,
and also similar to their same age counterparts’ performance in the draw alone and
distracter control conditions. Reminder status at Time 4 did not turn out to be a
significant main effect and did not interact with age group. Hence, it seems reasonable
to conclude that the appearance of the significant age group difference at Time 4 is
not due to a simple lack of imagination in young children. Finally, since redescription
of external knowledge (via visual examples) must still take place before it is
generalised and available for wider use, there were also convergent findings of poor
transfer of learning effects exhibited by young children in the examples group when
completing the analogous task of drawing pretend houses (see also Davis, 1985,
Pemberton and Nelson, 1987, Phillips, Inall, & Lauder, 1985 for parallel findings).
Why did the younger children in the examples group only show flexible
drawing behaviour for a short period of time? Younger children in the examples
group may have consciously abstracted and rehearsed locally defined rules and
heuristics from the example set (e.g., draw a triangle for the leg, delete the right leg
and so on) and stored it in short-term memory as a representational adjunction that is
unconnected with other existing computational acts in order to rapidly gain, albeit
-
Representational Flexibility Over Time 25
limited, success in their generation of types of changes for the task. The upshot of this
representational adjunction is that the embodied skills may be prone to rapid decay
and forgetting over time, and are difficult to transfer to new domains (i.e., draw
pretend houses). These suggestions raise two further important issues about the
trajectories of representational flexibility as a result of external provocations.
First, if behaviours driven by representational adjunctions are not long lasting,
why did our reminder of the training event not reactivate flexibility in young
children’s drawings? There are two possibilities. One answer may have to do with the
time window from the onset of the initial training event, within which subsequent
information may activate or be integrated with the representation of that event. Work
on time windows and early learning by Rovee-Collier and her colleagues (e.g.,
Rovee-Collier, Evancio, & Earley, 1995) suggest that only representations that are co-
active in short-term memory will improve processing, and that new information
encountered after a time window has closed will be treated as new and not accrue
beneficial reactivation effects. It is possible that our reminder may have occurred
outside of the time window from the training event, not permitting the reminder to
activate the training event, limiting young children in the example group from
sustaining a learning advantage. The implication then, is that for young children
whose knowledge base is still being formed, new information targeting
representational flexibility may be more efficiently acquired and remembered when
the training examples and reminders are arranged to occur closer together in time. An
alternative account for the lack of effects at Time 4 may be the result of children’s
lack of motivation for a task that had grown stale. The representational scores for the
older children do not show any significant differences that would reflect a loss of
interest, but perhaps only the younger children who were more challenged by the task
would be more susceptible to repeated testing. In order to determine whether repeated
-
Representational Flexibility Over Time 26
testing may have played a role in the representational scores of younger children,
future replications would need to include an additional control condition that perhaps
receives only the initial test, the reminder and the final test.
Second, if representational adjunction driven behaviours are short-lived, can
example priming be designed to maximise the stability of flexible behaviour? In our
study, the example training manipulation only scaffolded the representational
trajectory for five weeks (up to Time 3). This may be partly attributable to young
children in the examples group seeing a diverse range of solution patterns, and as a
result they generated an unstable adjunction based on local ad-hoc hypotheses. It may
be possible to help children generate flexible drawing strategies and sustain them for
longer periods of time by first training them with exemplars containing only the
simplest patterns and culminating with the more complex patterns. A hierarchically
organised exemplar training programme may assist the progress of representational
redescription by decomposing the task into an ordered series of sub-features that
partition the problem solving space (e.g., first introducing size and shape variables,
second introducing addition or deletion variables, and third introducing variables
based on ontological category shifting) (see Elman, 1993, for the potential utility of
hierarchically organised training in neural network learning).
The present findings further suggest that the ability to manipulate a
representation may not have a very strong relationship with procedural rigidity given
that visual examples can serve as cues for behaviour change. This may very well
indicate, as Karmiloff-Smith (1992, 1999) has suggested, that the sequential
constraint may be weaker than she originally proposed. However, this seems a limited
way to theoretically expand RRM. Previous observations of children’s drawings
reveal that there are significant variations in how children from five years of age draw
normal human figures, ranging from simple additive combination of shapes to
-
Representational Flexibility Over Time 27
visually realistic contours with internal differentiation of parts (e.g., Bassett, 1977;
Lange-Kuttner, Kerzmann & Heckhausen, 2002). These observations are important
because they raise the issue of needing to discover what exactly is the important
recognisable point of behavioural success that is followed by RR during micro-
development. Moreover, aside from a sequential constraint, future researchers may
uncover that procedural rigidity may also be understood in terms of spatial layout and
how it sustains the symbolic meaning of a drawing. Spatial layout may be a fruitful
index of first-pass redescriptions that contain constraints on problem solving since it
pertains to spatial locations of elements (e.g., drawing the head first can affect size
scaling) and captures geometrical placement relations (e.g., whether chimneys are in
perpendicular orientation to the roof of a house), both of which have been found in
young children’s drawings to contain a great deal of error (e.g., Ibbotson & Bryant,
1976; Low & Hollis, 2003; Thomas & Tsalimi, 1988; Vasta & Liben, 1996).
Our results indicate that while task manipulations can promote flexibility,
young children, over time, do continue to use their normative representations while
older children are able to sustain high-level representations. Since our findings not
only support Karmiloff-Smith’s RRM contention that there is a difference between
behaviours driven by adjunctions and redescriptions, but also support information-
processing researchers’ emphasis on task parameters and flexibility (e.g., Berti &
Freeman, 1997; Zhi et al., 1997), RRM needs to evolve into some integrative form
whereby information processing developments concerning source monitoring,
executive functioning and task complexity are considered. For example, perhaps
redescription might also occur when executive functioning capabilities are sufficiently
mature to permit the operation of less compacted information. It is important to start
exploring links between redescription and information processing factors and how
they unfold and interact over time.
-
Representational Flexibility Over Time 28
In conclusion, this research adds further evidence to that which already exists
regarding internal constraints and representational flexibility as seen in the drawing
domain. While external aids can affect young children’s representational flexibility,
such behaviour should not be equated with the graphic behaviours amongst older
children that are sustained by redescribed representations. Young children’s graphic
flexibility seen immediately after external provocation was only short lived. These
children slowly returned to using their baseline internal representations. As a result,
the findings indicate that the momentary flexibility amongst young children was
driven by representational adjunctions. Most importantly, the findings confirm RRM
predictions that children really do need to develop beyond behavioural success.
-
Representational Flexibility Over Time 29
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Representational Flexibility Over Time 32
Table 1. Age, interruption and condition interactions and simple significance effects
for procedural flexibility in pretend people drawings across the four time points:
Degrees of freedom, F values and significance levels
Sources of variation d.f. F p Time 1 Age x Interruption 2, 308 14.05
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Representational Flexibility Over Time 33
Table 2. Coding scheme for assigning representational level scores to children’s
drawing strategy
Strategy Score
[Normal person drawing] 0
[Just C1 change at end] or
[Both C1 & C2 change at end] or
[Just C2 change at end] 1
[Just C1 change in beginning / middle] or
[C1 change in beginning / middle & C2 change at end] or
[C1 change at end & C2 change in beginning / middle] 2
[Both C1 & C2 change in beginning / middle] or
[Just C2 change in beginning / middle] 3
Note: C1 refers to low-level modifications (change of elements, change of whole,
deletions) and C2 refers to high-level modifications (insertions, position-
orientation changes, cross-category changes).
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Representational Flexibility Over Time 34
Table 3. Age and condition interactions and simple significance effects for
representational scores in pretend people drawings across the four time points:
Degrees of freedom, F values and significance levels
Sources of variation d.f. F p Time 1 Age 1, 309 70.08
-
Representational Flexibility Over Time 35
Figure 1. Illustrations shown to examples group (from left to right: shape of element
change, deletion, insertion and position-orientation change).
-
Representational Flexibility Over Time 36
Younger Children
0 20 40 60 80 100
LowT1
HighT1
LowT2
HighT2
LowT3
HighT3
LowT4
HighT4
LowT4H
HighT4H
Typ
e o
f ch
an
ge b
y T
ime
Percentage of occurrence
ExamplesDraw AloneDistracter
Older Children
0 20 40 60 80 100
LowT1
HighT1
LowT2
HighT2
LowT3
HighT3
LowT4
HighT4
LowT4H
HighT4H
Ty
pe
of
ch
an
ge
by
Tim
e
Percentage of occurrence
ExamplesDraw AloneDistracter
Figure 2. Percentage of low- and high-category modifications by age, condition &
time (Note: T4H = pretend house drawing at Time 4).
-
Representational Flexibility Over Time 37
Younger Children
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
BT1
MT1
ET1
BT2
MT2
ET2
BT3
MT3
ET3
BT4
MT4
ET4
BT4
H
MT4
H
ET4
H
Interruption by Time
Pro
po
rtio
n o
f O
ccu
rren
ce
Distracter
Draw Alone
Examples
Older Children
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
BT1
MT1 ET
1BT
2M
T2 ET2
BT3
MT3 ET
3BT
4M
T4 ET4
BT4H
MT4
H
ET4H
Interruption by Time
Pro
po
rtio
n o
f O
cc
urr
en
ce
Distracter
Draw Alone
Examples
Figure 3. Percentage of each type of graphic interruption by age, time & condition
(Note: B = beginning; M = middle; E = end and T4H = pretend house drawing at
Time 4).
-
Representational Flexibility Over Time 38
0
0.5
1
1.5
2
2.5
3
T1 T2 T3 T4 T4H T1 T2 T3 T4 T4H
Time
Me
an
Re
pre
se
nta
tio
na
l S
co
reDistracterDraw AloneExamples
Younger Children Older Children
Figure 4. Mean representational scores by age, time & condition (Note: T4H =
pretend house drawing at Time 4; error bars = 1 SEM).
-
Representational Flexibility Over Time 39
0
0.5
1
1.5
2
2.5
3
T4M T4H T4M T4H
Pretend drawings at Time 4
Me
an
Re
pre
se
nta
tio
na
l S
co
reReminder
No-Reminder
Younger Children Older Children
Figure 5. Mean representational scores by reminder status and age for examples
condition at Time 4 (Note: T4M = pretend man drawing at Time 4; T4H = pretend
house drawing at Time 4; error bars = 1 SEM).
-
Representational Flexibility Over Time 40
Appendix
Illustrations of types of modifications made in children’s drawings
Changes to Shape of Element Insertions of elements from
same category “His head is a funny shape.” “He has four eyes and four
arms.” (Child, 5- to 7-Year-Old Group) (Child, 8- to 9-Year-Old Group)
Changes to Shape of Whole Position-Orientation Changes “His whole body is a star shape.” “His top body is floating.” (Child, 5- to 7-Year-Old Group) (Child, 8- to 9-Year-Old Group)
Deletions Cross-Category Changes “He has no body.” “She’s got a tail.” (Child, 5- to 7-Year-Old Group) (Child, 8- to 9-Year-Old Group)
top related