karmiloff-smith’s rrm distinction between adjunctions and ...karmiloff-smith (1990), that young...

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: [email protected]).


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.


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),


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.


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.


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


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


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.


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


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


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]


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.


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


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.


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


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;


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.


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) =


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


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:


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.



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.


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.


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 =


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


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.


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


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


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


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


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


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.


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.


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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


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).


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


Figure 1. Illustrations shown to examples group (from left to right: shape of element

change, deletion, insertion and position-orientation change).


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).


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).


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).


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).


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)

karmiloff-smith’s rrm distinction between adjunctions and ...karmiloff-smith (1990), that young...

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