J. Child Psyc/ul. PsycUa Vol. 26, No. 5, pp. 811-824. 1985.
Printed in Great Britain
0021-9630/85 13.00 + 0.00
Pergamon Press Ltd.
© 1985 Association for Child Psychology and Psychiatry.
THE DEVELOPMENT OF CONCEPTS OF SIMULTANEITY IN
CHILDREN'S UNDERSTANDING OF EMOTIONS
NADJA REISSLAND
Department of Experimental Psychology, University of Oxford
Abstract—The development of children's understanding of simultaneously occurring emotions was
investigated. A developmental progression was found in their giving examples of ambivalent situations
(e.g. characterised by both happiness and anger); and in their descriptions of situations. The youngest
children (mean age = 5.8) gave as examples of ambivalence two unrelated events associated with
different emotions. At the next stage children (mean age « 7.0) were able to connect sequentially two
events. At a third stage (mean age - 10.1) the children were able to conceive of situations in which
two emotions of opposite valence occurred simultaneously.
Keywords: Simultaneity, ambivalence, emotions, cognition
INTRODUCTION
RECENT research among developmental psychologists has focused on children's
understanding of the relation between different emotions. Harter (1979) has investigated the relation between being happy and being 'mad', 'sad', and scared. Selman
(1980) questioned children concerning their knowledge of the conflict between the
good feeling of friendship and the bad feeling of an event or action which troubled
that friendship. Carroll (1981), Tharinger (1981), Nannis (1983) and Harris (in press)
have examined children's understanding of situations characterised by happiness
and sadness.
Common to much of this research has been the observation that at a certain age
children are able to comprehend ambivalent situations, that is to say, situations
characterised by simultaneously occurring emotions of opposite valence. The ability
to comprehend such situations implies that the children have a concept of simultaneity.
The development of this concept with reference to emotions has been recently
investigated by Harter and Buddin (1983) and by Harris (in press). Harter and
Buddin elicted from children examples of situations, characterised by two different
emotions and they analysed these examples with reference to the valence of each
emotion and the person, or 'target', to whom the emotion was directed. A developmental progression was found in which the children were first able to relate two
simultaneously occurring emotions of the same valence and target (mean ages = 6.5
years) and then two emotions of the same valence but different target (mean
age = 8.0 years). It was not until 10.5 years of age that the subjects were able to
Requests for reprints to: Nadja Reissland, Department of Experimental Psychology, South Parks
Road, Oxford, U.K.
Accepted manuscript received 12 October 1984
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N.REISSLAND
comprehend ambivalent situations in which the two emotions were directed to either
the same or different targets. Harris, on the other hand, presented children with
ambivalent situations and then asked them to identify happiness, sadness, fear
and/or anger in these situations. He found that six year olds had greater difficulty
than ten year olds in admitting that mixed feelings can occur in a single situation,
but both age groups understood that an emotion provoked by a previous situation
may persist in time and 'colour' the feeling provoked by a subsequent event.
In both these studies the main focus was on the development of children's abilities
to comprehend ambivalent situations. It still remains to consider, however, the
conceptual structures by which children relate two co-occurring emotions in
ambivalent situations. The investigation of these structures is of interest, for it not
only has bearing on the development of children's concepts of simultaneity but also
plays an integral, albeit implicit, role in the methods of exemplification and
identification used by Harter and Buddin and by Harris.
One way of elucidating these structures with verbal data is by analysing the
connectives used by children in relating two different events, each of which is
thought to provoke an emotion of opposite valence. These connectives link the two
events in such a way as to form a compound event. By compound event I follow
van Dijk's (1980 : 169) definition: "an event which is constituted by several events
which are linearly ordered but which are perceived or conceived of as one event at a
certain level of description." Diverse connectives may be used to link events and
they may all. for present purposes, be classified into one of three different types:
temporally unrelated connectives, sequential connectives, and simultaneous connectives. Of all these connectives only the simultaneous ones form compound events.
The analysis of children's use of simultaneous connectives enables one to investigate
the conceptual structures by which children understand ambivalent situations; and
the classification of children's responses into temporally unrelated, sequential, and
simultaneous connectives enables one to consider the developmental differences in
children's ability to comprehend situations characterised by two emotions of opposite
valence. In the present paper the results of both these schemes of analysis will be
reported; and the usefulness of these schemes will then be further demonstrated by
applying them to the analysis of the data collected by other researchers in this field.
GENERAL METHOD OF DATA COLLECTION
Subjects
One hundred children were drawn from two primary schools and one secondary school in the Greater
London area and Hertfordshire. The children, of whom there were 48 girls and 52 boys, ranged in
"age from 4.8 years to 14.9 years. They were of similar middle class background and spoke English as
their mother tongue. A distribution of the children by sex and age is shown in Table 1.
Administration of the interview
The children were interviewed individually in their respective schools. During the interviews the
child and the experimenter sat side by side at a table upon which was placed a tape recorder. After
briefly establishing rapport with the subjects, the experimenter explained to each child that the purpose
of the interview was to record what children thought about certain emotions. The children were
reassured that there were only 'right' answers since the experimenter wanted to find out what children
really thought about these matters.
Design and procedure
The interview was designed in two parts. In the first part (questions 1 and 2) the children were asked
to describe a situation in which one could feel happy and afraid or happy and angry at the same time.
The following questions were asked in this part of the interview:
Some children say that you can be both happy and afraid (happy and angry) at the same time.
When can you be both happy and afraid (happy and angry) at the same time?
In the second part of the interview (questions 3, 4, 5 and 6) children were provided with examples of
situations characterised by two simultaneously occurring emotions of different valence and were asked
to identify and explain the emotions present in these ambivalent situations. In Harris' (in press) study
the children were asked to choose from happiness, sadness, fear and/or anger in identifying the
emotions present in an ambivalent situation, but in this study the subjects were not prompted with any
list of emotions from which to choose. This method was adopted in case some children might identify
and explain an ambivalent situation from a wider range of emotions, but nonetheless identify two
emotions of different valence in the situation.
The examples of ambivalent situations had been provided by other children in a previous experiment.
The following questions were asked in this part of the interview:
When I asked other children these questions (referring to the first part of the interview) they gave
me the following examples. Now your task is to tell me what two feelings those children wanted to
express.
3. What two feelings did the child want to express who said: 'It's your first time at swimming
and you don't know how to swim'?
4. Why did the child say he/she felt these emotions?
5. What two feelings did the child want to express who said: 'You had a fight with your friend
and you win'?
6. Why did the child say that he/she felt those emotions?
Stages in the coding and analysis of the data
The interview data was analysed in several ways to bring out different aspects of the development of
children's understanding of co-occurring emotions.
In the first stage of analysis the children's responses to the six interview questions were classified into
simultaneous and non-simultaneous responses to determine whether there was an age basis to the
children's ability to make simultaneous connections between two emotions of opposite valence. In the
second stage of analysis the children's simultaneous responses were analysed according to the types of
temporal connective to ascertain differences in their concepts of simultaneity. In the third stage of
analysis the non-simultaneous responses were also analysed to determine whether there was a progression
in the development of children's ability to understand co-occurring emotions of opposite valence.
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N. REISSLAND
Because each stage in the analysis entailed the use of different methods of coding and analysis, the
methods and results of each stage are presented in turn below.
Classification of children according to simultaneous and non-simultaneous responses
Method. The responses of the children to all six questions were categorised according to a simple
binary taxonomy distinguishing between simultaneous and non-simultaneous responses (Table 2).
This binary categorisation had the virtue of being discrete as well as exhausting the total range of
responses; hence no ambiguity was encountered in the classifaction of responses.
Illustrations of typical simultaneous responses which served as a guide to the classification include
with regard to exemplification: "I'm angry, 'cause my brother is teasing me and I'm happy 'cause
he gets told off" (10.7 girl); or "Well, if you've run away. You're happy that you've run away from
home but you're afraid in case you get in trouble" (13.6 girl). With regard to identification, synonyms
for happiness were overjoyed, pleased, glad, excited, delighted, all-right, nice, o.k., good. For anger
acceptable synonyms were cross, annoyed, frustrated; and for fear acceptable synonyms were frightened,
horrified, worried, scared, small and defenseless. Finally with regard to the explanation of ambivalent
situations typical responses include: "You might feel sorry for them, say they're weaker than you are
THE DEVELOPMENT OF CHILDREN'S UNDERSTANDING OF EMOTIONS
815
and you shouldn't have done it [fought with a friend], so you're angry you did it, but happy that you've
won [the fight] (10.5 boy); or "Glad because you're there [at the swimming pool] for the first time
and you're unhappy 'cause you can't swim and everybody around you can" (10.7 girl).
Results. The experimenter and an independent judge classified the children's
responses (questions 1-6) according to the binary categories of simultaneous and
non-simultaneous responses. There was disagreement in 4% of the cases of
exemplification (questions 1 and 2) and in 3% of the cases of the explanation questions
(questions 4 and 6). There was no disagreement in the classification of the cases of
indentification (questions 3 and 5). All disagreements were resolved by discussion.
Because the children were not grouped a priori but comprised a continuous age
range of children from 4.8 to 14.9 years, a hierarchical cluster analysis was used to
group the children according to their responses. Having translated the children's
responses into binary categories, a similarity matrix for binary data was calculated
by means of a squared Euclidian distance formula (Wishart, 1982). A cluster analysis
based on the similarity matrix derived from the responses of the children to the
interview questions relegated the subjects into only two clusters, one comprising 41
subjects and the other 59 subjects. Thus the similarity between subjects was
based on the subjects' simultaneous or non-simultaneous responses; and the children
falling into the respective groups were most similar to each other. The statistical
details concerning the tests of significance for the number of clusters may be found
in the Appendix.
Having clustered the subjects according to their ability to comprehend two
emotions simultaneously, a test was carried out to check whether the subjects, so
clustered, constituted age groups; that is to say whether their differential ability
indicated a developmental difference. A /-test on the mean age of the subjects in
cluster I and cluster II was significant at the 0.001 level (Table 3).
To establish the age range of the subjects in each cluster, the age range was
calculated that would allow for the maximum number of subjects between the ages
of x and y to be in cluster I or cluster II with a minimum number of exceptions. An
age split appeared at 7.6 years which was then tested for significance by means of a
X2 analysis on age group vs cluster (Table 4). The analysis showed a significant
difference(X2 = 59.58,/><0.001) between the two groups with regard to age range
of the subjects. Only 10% of the subjects offered responses to the interview questions
which did not accord with the responses of their peers. No significant sex differences
were found for the 10 subjects who were not classified with their peers (Table 5).
Chi-siquare tests were then carried out on questions 1-6 to decide whether there
was a significant difference between the two groups with regard to their ability to
comprehend two co-occurring emotions of opposite valence (Table 2). In all cases
there was a significant difference between the two groups at the 1 % level.
In sum, one of the two clusters grouped the younger subjects who gave mainly
non-simultaneous responses and the other cluster grouped the older children who
gave mainly simultaneous responses.
Analysis of different types of simultaneous connectives
Method. In a second examination of the clustered data the simultaneous responses were further
analysed with regard to their particular connectives. This analysis clarified the conceptual structures
by which children comprehend ambivalent situations.
In considering the simultaneous responses (questions 1 and 2) of the older group of children, it
became apparent that these children were able to understand ambivalent situations by making various
types of connections between the two situations which provoke emotions of opposite valence. These
connections were categorised. The types of connectives comprised five categories of intrinsic connection:
present action/ever present state; action/potential outcome; action/intentional outcome; anticipated
action/actual outcome; action/conditional outcome; and a sixth category in which the two events were
extrinsically connected.
By intrinsic connection is meant that the children understood that the two events were connected by
the mental or physical actions of the actors. The first intrinsic category entailed an understanding that
an emotion provoked by a present action could co-occur with an emotion provoked by an ever-present
state. Examples of such ambivalent situations are with regard to happiness and anger (e.g. "Sometimes
I push my friend; I still like her" 4.9 year old girl) and happiness and fear (e.g. "Scared when you
walk across the road and happy when you're crossing it on your own" 6.5 year old girl). In this case
she was always afraid to cross the road but nevertheless happy in those instances when she was 'big'
enough to cross it on her own.
The second to fifth categories of intrinsic connection differ from the first category in that they entail
an understanding of the relation between an action and its outcome. An example of the second
category of action/potential outcome is the response of an 8.1 year old girl who said that one could
experience happiness and fear in the following situation: "Well, our headmaster is quite moody
sometimes and when he is going to take you out for a trip, like you forgot your Wellingtons and you'd
THE DEVELOPMENT OF CHILDREN'S UNDERSTANDING OF EMOTIONS
817
be in a muddy place, you are happy that you are going out and you are scared that he might tell you
off." An ambivalent situation characterised by happiness and anger is: "Well, like if you've taken
something from someone, you'd be really happy if it was your enemy, but then you'd feel angry at them
if they'd say: right I'm gonna tell the teacher. I feel happy for taking it away from them and you feel
angry 'cause they're gonna tell the teacher" (10.9 year old boy).
The third category of simultaneous connective was that of action/intentional outcome. For example,
a 10.5 year old boy said: "You're angry somebody has punched you in the mouth and glad that you
are gonna revenge on him. That you 're gonna fight back on him.''
The fourth category of anticipated action/actual outcome may be illustrated with the response of an
8.0 year old girl who said: "You could be happy when it was your birthday [and you were expecting
a party] and angry that your mother had not let your friends come because you are having a party
just with your family."
Examples of the fifth category of action/conditional outcome include the response of the 10.1 year
old girl who said: "Say you've just got to a new school. You're happy because you've made new
friends, but then the teacher tells you off for not doing your work" [and therefore you are angry as well].
Or the response of a 11.5 year old boy: "When someone's just given you something that you've
always wanted but then you are told at the same time that you can only have it for a day or two, so you're
afraid of losing it again after you've got it but you are happy that it's with you now."
The sixth category comprises those simultaneous responses in which the connection is extrinsic to
the action of the two events; here the two events are fortuitously connected by virtue of having in
common a temporal, local, and subject identity. For example, a 12.2 year old boy said: "Say it's your
birthday [and you 're happy] and you got a test the same day and you "re afraid.''
Results. The classification of children's simultaneous examples of two co-occurring
emotions of different valence according to type of simultaneous connective yielded
the following results (Table 6): 3.7% of all the simultaneous responses fell into the
category of present action/ever-present state; 56% fell into the category of action/
potential outcome; 3.7% into action/intentional outcome; 26.6% into anticipated
action/actual outcome; 5.5% into action/conditional outcome and 4.6% into the
extrinsic simultaneity category.
By comparing the percentage of responses with regard to the co-occurrence of
happiness and anger and that of happiness and fear it became apparent that most
of the responses falling into the action/potential outcome category came from
examples relating happiness and fear simultaneously (90.2%). On the other hand
the categories of action/intentional outcome and anticipated action/actual outcome
contained only responses relating happiness and anger simultaneously. The other
intrinsic categories contained equal numbers of responses for both types of ambivalent
situations. However, slightly more examples of happiness and fear fell into the
extrinsic simultaneity category (60%).
Finally it should be noted that more of the responses fell into the intrinsic
simultaneity category.
Developmental differences in the understanding of co-occurring emotions
Methods. Since the category of non-simultaneous responses was defined with reference to what the
responses were not, rather than to what they were, this residual category did not clarify the nature of
responses and possibly concealed interesting variation. This variation, however, was brought out by
analysing the raw, unclustered data according to the three types of connective: temporally unrelated,
sequential, and simultaneous. Since only the exemplification data were amenable to this classification,
the final stage in the analysis of the results was based solely upon the children's responses to questions
1 and 2.
Responses in the first category of temporally unrelated events include the obvious one of two events
THE DEVELOPMENT OF CHILDREN'S UNDERSTANDING OF EMOTIONS
81
9
having no connection apart from their subject identities. For example, "If you are scared something
frightens you and if you're happy something makes you feel all right" (4.11 girl); or the child might
associate an emotion with one event and another emotion with the negation of that event. Such an
example is given by a 5.2 year old girl who said: "When you can't do things that you want to do
[you're angry] and if you can do things that you want to do [you're happy]." In the absence of any
intrinsic connection the two events lack either a temporal identity (e.g. "When someone has frightened
you, you are scared; and you feel happy when you can do things that you want to do" 5.2 year old girl)
or a local identity (e.g. "You are scared in the brain and then he thinks it is happy in the other brain"
4.10 year old boy). Of particular significance in coding temporally unrelated responses is the fact that
the two conjoint events can be interchanged without loss of meaning. Their commutability indicates
that the two events do not form a compound event but remain separate regardless of the level of
description.
The second type of connective is that in which the emotions of opposite valence are linked sequentially. For example, a 6.1 year old boy said: "You're playing a game and you're happy and someone
messes it up and you're angry". Here the two emotions are linked to form an antecedent and a
subsequent event which by their non-commutative connection indicates a more complex cognition
than the temporally unrelated connectives. The sequential connection does not necessarily imply,
however, that the subsequent event is the outcome of the antecedent, as the example of a 7.11 year old
girl shows: "You've been happy with your friend and you're angry because your mum wouldn't let you
do something else when the friend is gone.''
Finally in the third type of connective the two emotions of opposite valence are linked simultaneously.
An example of this type is: "Happy when your cat's had kittens but afraid that the kittens are going to
go soon" (10.8 girl). Simultaneous connective imply that two separate events are related in such a
way that the subsequent event is the outcome of the initial event; that is to say, that the subsequent is
the consequent of the antecedent. It is by virtue of this connection that the ambivalence of the compound
event can be understood. It is important to emphasise that the simultaneous connection does not entail
merely the understanding of the connection between situation and emotion, rather it necessitates the
ability to comprehend that ambivalent situations depend upon a connection between two different
events, each of which provokes an emotion of different valence.
Results. When the children were asked to give examples of an ambivalent situation,
children of mean age 5.8 years responded with only one emotion or with two emotions
which were associated with unrelated events (Table 7). In contrast with the youngest
group, children of mean age 7.0 years were able to relate temporally two emotions of
opposite valence, but they offered sequential examples. Finally it was not until the
mean age of 10.1 years that children gave examples of situations characterised by
two co-occurring emotions of opposite valence.
GENERAL DISCUSSION
The results of the present study accord, in general, with the findings of Harter
and Buddin (1983) and of Harris (in press). Children undergo a developmental
progression in which they are first able to understand situations non-simultaneously
and subsequently are able to understand them simultaneously. The present study
differs from this other work, however, in the problems investigated by means of these
data. In these other studies it was assumed, for working purposes, that simultaneously
occurring emotions are emotions which occur at the same moment of time. In neither
case, however, were the temporal connectives used by the children analysed. The
analysis of these connectives in the present study suggests that this rough working
definition of simultaneity must be clarified. There are different ways by which
children conceive of simultaneously occurring emotions and these differences have
important methodological and theoretical implications. In what follows I shall discuss
these implications with reference to the findings of Harter and Buddin and of Harris.
One advantage in analysing temporal connectives is that it enables one to clarify
the categories used in the classification of the exemplification data. Harter and
Buddin focus on the degree of difficulty in children's understanding of simultaneously
occurring emotions and go on to categorise the sequential responses together with
the temporally unrelated ones as the non-simultaneous stage from which children
develop an understanding of simultaneously occurring emotions (although Harter
herself did not do this in her 1979 paper). In the present study, however, it became
apparent that there was a difference between the unrelated and the sequentially related
responses which was greater than the difference between the sequentially related and
the simultaneously related responses. In the sequential responses the children
understood at least a non-commutative connection between two events such that one
event was the antecedent and the other was the subsequent. Children at this stage
do not yet realise that co-durationality of these two events such that an event overlaps
with an underlying state or an event is the outcome of an antecedent event. Nor
are they aware of a possible connection through the foreknowledge of a consequent
event, the recall of an antecedent, or the knowledge of an ever-present state. But
still, given the presence of a connection in the sequential understanding between
two emotions of different valence, this level of understanding bears closer affinity
to simultaneous responses than to the responses in which the two events were
unrelated. Thus it would seem that in the development of children's ability to
THE DEVELOPMENT OF CHILDREN'S UNDERSTANDING OF EMOTIONS
821
understand the relation between two emotions it is necessary to distinguish between
temporally unrelated, sequentially related, and simultaneously related responses.
Another category of Harter and Buddin which can be clarified by the analysis
of temporal connectives is that of 'target'. In assessing developmental differences in
children's ability to exemplify co-occurring emotions, they analysed the simultaneous
responses according to the double frame of target (same, different) and valence (same,
different). The same/different valence category specified whether or not the situation
is ambivalent. These binary categories were mutually exclusive and were used
unambiguously in the classification of responses. The category of target, however, is
ambiguous. By target Harter and Buddin meant the object, situation, or person to
which the feelings were directed. As a compound event, however, any simultaneous
response linking different emotions will have a double aspect. This double aspect
may involve ego's relation with two alters; or ego's relation with the same alter in
two contexts over two overlapping periods of time. In this respect the target is always
different, even when it is the same person, for the contexts involving the same
person are different. Without specifying this context the use of the co-ordinate of
target is ambiguous; and in specifying this context it becomes unnecessary, for all
simultaneous responses by virtue of being a compound event will have a double aspect.
Like Harter and Buddin, Harris was also interested in developmental differences
in the understanding of ambivalent situations, but he focused on children's understanding of the link between situation and emotion as a means of investigating
children's theory of mind. Harris found that six year olds had greater difficulty than
ten year olds in admitting that mixed feelings can occur in a single situation, but
both age groups understood that an emotion provoked by a previous situation may
persist in time and 'colour' the feeling provoked by the subsequent event. These
results might be re-analysed in terms of connectives by noting that insofar as children
acknowledge an intrinsic connection between events they recognise that the recall of
the previous action, the recall of a previous anticipation, or the foreknowledge of a
future outcome creates an ambivalent situation in which one feeling 'colours' a
subsequent one.
The fact that these two emotions are provoked by different events and linked
intrinsically in terms of an action and its outcome suggests further that such ambivalent
situations may resolve themselves into those complex emotions, such as guilt,
disappointment and relief, which are identified by children at a later stage of cognitive
development. These 'late' emotions may, for heuristic purposes, be thought of as a
combination of the 'early' emotions of happiness, anger, fear, and sadness. For
example, the happiness of eating biscuits from the biscuit tin and the fear of being
caiight by one's mother resolving itself into guilt; or the happiness of having one's
birthday and the anger of not being able to invite one's friends resolving itself into
disappointment; or the fear of losing one's dog and the happiness of the dog's return
resolving itself into relief. In such instances of an intrinsic connection one might
say, using Harris' terms, that the previous emotion 'colours' the present emotion.
This might explain not only why the child is able to identify 'late' emotions, such as
pride and guilt, only after developing a simultaneous connection between events
(Reissland, 1982); it might also account for the difficulty which Harris' subjects
encountered in understanding single episode mixed feelings. Insofar as such 'mixed
822
N REISSLAND
feelings' were instances of extrinsic simultaneity it is doubtful that they could be
resolved into a complex 'late' emotion. The difficulty which Harris' subjects
encountered in integrating single episode simultaneity lay not in the fact that such
episodes lacked a temporal extension; rather because they lacked an intrinsic
connection.
This analysis in terms of intrinsic and extrinsic simultaneity bears some relation
to other formulations in psychology. Piaget (1969:26), in his research on the development of the child's cognitive awareness of relations in the physical world, distinguished
between co-placement and co-seriality; and similarly Riegel (1977:60) distinguished
between punctiform and extended simultaneity. The difference between these two
types of simultaneity is qualitative rather than quantitative. Punctiform simultaneity
refers to the co-existence of two objects at the same moment in time, but without
any intrinsic connection between them. An example of punctiform simultaneity is
the observation that many stars exist in the sky at the same moment in time although
there is no intrinsic connection between them. Extended simultaneity, by contrast,
includes punctiform simultaneity, but also specifies an intrinsic connection between
the two objects or events. Extended simultaneity has a temporal extension and it
entails the intrinsic interaction of at least two events or objects which take place over
the same duration. Nearly all the simultaneous responses of the subjects in the
present study were instances of extended simultaneity or co-durationality and
they entailed an understanding of the relation between an action and its outcome.
CONCLUSION
In this paper I have demonstrated that specific semantic criteria, namely temporal
connectives, provide a rigorous means of analysing children's understanding of
ambivalent situations. On the basis of this analysis it was found that the youngest
children (mean age = 5.8 years) in this study understood that a situation can provoke
an emotion but were unable to connect two situations in such a way as to form a
compound event and therefore were unable to grasp the ambivalent nature of such
compound events. At the next stage (mean age = 7.0 years) the children were able
to connect two situations sequentially and at a third stage (mean age =10.1 years)
the children showed a simultaneous understanding of the relation between two events.
It is interesting to note that at the initial stage the children's example lacked either
a temporal or a local identity. Had these children, however, been able to meet these
two conditions they would have been able to form an extrinsic simultaneous connection between two events. Such examples would have lacked a temporal extension
but nonetheless would have been adequate examples of ambivalent situations. This
possibility, however, did not occur as only 4.6% of the simultaneous responses fell
into this category and these responses came from the oldest children (mean age =12.1
years). The fact that the simultaneous responses came from the oldest children
whereas the sequential responses were given by the middle group ot children suggests
that children understand a non-commutative connection between two events before
understanding simultaneity as a particular type of connection. This observation
concerning the development of children's understanding of the relation between
emotions bears some relation to the work of Piaget (1969) on children's understanding
THE DEVELOPMENT OF CHILDREN'S UNDERSTANDING OF EMOTIONS
823
of the relation between physical objects. The finding that the children in the present
study first conceptualised the relation between an antecedent and a subsequent
and then transformed the subsequent into a consequent is perhaps just another way
of concurring with Piaget that simultaneity is a limiting case of succession.
Acknowledgements—I am very grateful to Prof. P. Bryant, Dr. P. Harris, Dr. J. Jaspars, and Dr. R.
Burghart for helpful comments on a previous draft of this paper.
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Unit).
APPENDIX
Since the penultimate stage of any cluster analysis entails the formation of two clusters, the problem
then arises whether the two clusters identified were the best split of subjects into clusters. To resolve
this problem the significance of the clusters was tested by a statistical stopping rule, developed by Mojena
(1977), which decides upon the significant number of clusters with a ^-statistic. According to Mojena
statistical rules for selecting the partition which best approximates the underlying population can be
based on the distribution criterion a in which a is defined in general as
d,< = afdps + "As + K» +g\d/>-dt/s\,
where r - index for the new group obtained by fusing p and q; d= measure of association; s = a group
other than the fused group; a for Wards method = (n, + b/>)/(n, + nr); aq for Wards method = (n, +n?y(n, +nr); b
for Wards method = -n/(n, + n,); g for Wards method = 0.
824
N. REISSLAND
Rule 1, which was applied to the data, utilises n - 1 items in the distribution of a by calculating the mean
and standard deviation of the sample. A significant a lies in the upper tail of the distribution. The (statistic is computed with n-2 degrees of freedom by multiplying the realised deviate by the square root
of the number of criterion values. The (-statistic was significant at the 1 % level (Table 3).
This test was corroborated by the variance ratio criterion (VRC). According to Calinski and Harabasz
(1974) a uniform distribution of points in space will usually be reflected by a smooth run of values of the
VRC. However, if the points are grouped into natural clusters with small within cluster variation, a rapid
rise of the VRC will be observed. Thus, they suggest that the value of the VRC for K-2, 3, 4, 5 ........
which has an absolute or local maximum, or at least a comparatively rapid increase, is the value of the
best number of clusters. Furthermore, they suggest that if the values of the VRC increase monotonically
throughout the range of clusters, then no reasonably better partitioning of the points exist than those
into individuals. In examining Fig. 1, one may note firstly that the values of the VRC are decreasing,
secondly that a 'jump' can be observed between k=- 2 and k = 3; and thirdly that a local and it seems
absolute maximum is obtained at k = 2. Hence it can be concluded on the basis of the responses of the
children to all interview questions that there is a significant partitioning of subjects into two clusters.