Psychology of Aesthetics, Creativity, and the Arts
2015, Vol. 9, No. 3, 296 –305
© 2015 American Psychological Association
1931-3896/15/$12.00 http://dx.doi.org/10.1037/a0039006
Pretend Play, Divergent Thinking, and Math Achievement in Girls:
A Longitudinal Study
Claire E. Wallace and Sandra W. Russ
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This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Case Western Reserve University
The present study examined longitudinal relationships among early pretend play, divergent thinking, and
academic achievement in school-age girls. Theoretically, processes in pretend play should relate to
divergent thinking and academic achievement. The aim of the present study was to establish longitudinal
correlates of pretend play in school-age girls. It was hypothesized that early measures of pretend play
would predict divergent thinking and academic achievement, controlling for verbal intelligence, at a
4-year follow-up. Thirty-one girls in the fourth through eighth grades participated in the study. Four years
before the present study, these children received the Affect in Play Scale and a divergent thinking task.
Children in the present study were administered a divergent thinking task (Alternate Uses Task). In
addition, AIMSweb scores of academic achievement in reading and math were collected from school
records. As hypothesized, early pretend play predicted later divergent thinking. Children whose pretend
play was more imaginative and organized generated more alternate uses for common objects. Positive
affect in play predicted originality of responses. In addition, both pretend play and divergent thinking
predicted girls’ mathematics achievement longitudinally. Divergent thinking and play combined accounted for 31% of the variance in math achievement over time. All results remained significant when
verbal intelligence was controlled. The present study provides important longitudinal evidence for the
predictive power of pretend play in children’s development and adaptive functioning, particularly as it
relates to divergent thinking and math achievement in girls.
Keywords: achievement, creativity, divergent thinking, pretend play
recently been criticized as a measure of creative ability, there is
longitudinal evidence for the predictive validity of the Torrance
Test of Creative Thinking, a divergent thinking measure (Kim,
2008). It has predicted creative achievement in adults over periods
of 40 years (Cramond, Mathews-Morgan, Bandalos, & Zuo, 2005)
and 50 years (Runco, Millar, Acar, & Cramond, 2010). In schoolage children, divergent thinking has related to pretend play in a
number of different studies across research laboratories (Fisher,
1992; Hoffmann & Russ, 2012; Kaugars & Russ, 2009; Singer &
Singer, 1990; See Dansky, 1999; Russ, 2004, 2014 for reviews).
Hoffmann and Russ (2012) found positive correlations between
the cognitive and affective domains of pretend play and children’s
divergent thinking abilities, independent of verbal intelligence. In
addition, children who expressed a greater variety of affect categories in their play were better divergent thinkers. A study of
preschool children showed that children who demonstrated more
pretend play and whose play contained a greater frequency and
variety of emotions were able to provide more responses on a
divergent thinking task (Kaugars & Russ, 2009). Other studies
have found similar relations between both positive and negative
affect in play and divergent thinking (Lieberman, 1977; Russ &
Grossman-McKee, 1990; Russ & Schafer, 2006).
Further, some experimental studies have shown that play facilitates the development of divergent thinking skills (Dansky, 1980;
Dansky & Silverman, 1973). Dansky and Silverman (1973) found
that children who were allowed to play with objects gave signif-
Pretend Play and Divergent Thinking
Fein (1987) conceptualized pretend play as a natural form of
creativity. Further, Russ (1993) theorized that pretend play is
important in fostering creativity, as many of the cognitive and
affective processes involved in creativity occur in pretend play.
Cognitive processes such as insight ability, flexibility, and divergent thinking, and affective processes such as the experience of
emotion and incorporation of affect themes from memory or
imagination, are important in both creativity and pretend play (See
Russ, 2004, 2014 for a review). The present study focused on
divergent thinking, which is the ability to generate a variety of
ideas. Pretend play can be considered practice for divergent thinking, as children are mentally transforming toys into a variety of
objects and role-playing different scenarios (Singer & Singer,
1990).
Empirical research supports the theoretical link between pretend
play and divergent thinking. Although divergent thinking has
This article was published Online First March 30, 2015.
Claire E. Wallace and Sandra W. Russ, Department of Psychological
Sciences, Case Western Reserve University.
We appreciate the support and cooperation of the Center for Research on
Girls at Laurel School.
Correspondence concerning this article should be addressed to Claire E.
Wallace, Department of Psychological Sciences, Case Western Reserve
University, Cleveland, OH 44106-7123. E-mail: [email protected]
296
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PLAY, DIVERGENT THINKING, AND ACHIEVEMENT
icantly more uses for those objects than did a control group.
Further, Dansky (1980) extended the previous study to include a
second set of objects that were novel for both the play and control
groups. He found that play had a generalized effect, such that
children in the play group supplied more uses for both sets of
objects than the control group. He also found that free play
facilitated divergent thinking only for children who engaged in
pretend play with the objects. Children’s use of make-believe and
fantasy mediated the relationship between play and divergent
thinking. There is mixed evidence in this area of research, and
some researchers have proposed the existence of some third variable that accounts for the relation between play and divergent
thinking or the presence of experimenter bias to account for
positive results (Lillard et al., 2013). However, there is enough
promising research in this area to merit further investigation using
masked experimenters and new study designs (Russ & Wallace,
2013).
Pretend play has predicted divergent thinking in two longitudinal studies. In a 4-year follow-up study of children, early pretend
play measured by the Affect in Play Scale (APS) related to
divergent thinking fluency (number of different uses generated for
an object) and self-reported coping ability in 5th- and 6th-grade
children, independent of verbal intelligence (Russ, Robins, &
Christiano, 1999). Mullineaux and Dilalla (2009) reported that
realistic role-play at age 5 predicted early adolescents’ performance on a divergent thinking task at ages 10 –15. They concluded
that pretend play observed in preschoolers represents early creativity, which carries through to creativity development measured
in early adolescence.
Gender differences in the correlations between pretend play and
divergent thinking have not been systematically investigated. The
small sample sizes of previous studies did not provide enough
power for meaningful comparisons of sizes of correlations for boys
and girls. In general, there are no mean differences in imagination
or amount of affect expression in the play of girls and boys, with
the exception of affect content. Boys consistently express more
aggression in pretend play than girls (e.g., Fehr & Russ, 2013). It
is important to investigate whether the association between play
and divergent thinking remains stable over time for girls and if
positive and negative affect are differentially predictive.
Pretend Play and Academic Achievement
The relation between pretend play and academic achievement
has theoretical foundations in Lev Vygotsky’s conceptualization of
play as the “leading edge of development” (Vygotsky, 1978).
According to Vygotsky, one function of children’s play is to
develop a symbol system to accompany and enrich their emerging
language learning. Recent research supports the link between play
and language development (Bergen & Mauer, 2000; Christie &
Enz, 1992). Children tend to demonstrate their most advanced
language during play, which is strongly related to early literacy
(Christie & Roskos, 2006). Greater frequency of pretend play is
also linked to better literacy skills (Pellegrini & Galda, 1993;
Roskos & Christie, 2001).
If children’s pretend play relates to emerging literacy, might it
also play a role in the development of reading ability? The majority of studies in this area focus on preschool age children and
conclude that play can provide a context for early literacy learning
297
that leads to reading, such as providing children with exposure to
literacy materials in play environments (Roskos & Christie, 2001).
One theory states that symbolism in pretend play is used in
conjunction with language to convey meaning (Pellegrini, Galda,
Dresden, & Cox, 1991). In play, children must use language to
explain their transformations, thus practicing using language as an
integral part of the representational process. Pellegrini and colleagues’ (1991) longitudinal study showed that preschool children’s use of linguistic verbs in pretend play related to early
reading skills. Specifically, children who used more linguistic
verbs in their play were more likely to use the text on a storybook
page to guide their storytelling efforts, rather than relying on the
pictures. Further, greater use of symbolic transformations in pretend play predicted children’s emergent writing status. Literature
linking pretend play to later reading achievement, separate from
language development and early literacy, is scarce at present.
Research points to links between pretend play and math
achievement. Seo and Ginsburg (2003) found a relation between
play and mathematical skills, observing that 4- and 5- year old
children build knowledge of foundational mathematics concepts
through free play. It may be that the principle of symbolic representation, cited by Vygotsky as linking pretend play and language
development, may also apply to development of early mathematics
skills. A study of preschool children showed that symbolic substitution in pretend play was the strongest predictor of both reading
and math skills (Hanline, Milton, & Phelps, 2008). Specific math
skills tested included number comparison, mastery of number
facts, calculation skills, and understanding concepts. Children who
used more advanced symbolic substitution, such as pretending to
play with an object that was not physically present, had higher
scores on reading and math tests. The authors concluded that the
use of transformations and representations in pretend play may
facilitate the shift from concrete to symbolic thinking that is
necessary to understand written symbols in reading and mathematics.
Other researchers have asserted that the link between play and
academic achievement is mediated by factors such as improved
focus/concentration (Pellegrini & Bohn, 2005) or development of
socially appropriate behavior that facilitates school adjustment
(Golinkoff, Hirsh-Pasek, & Singer, 2006). Although this research
is based more in free play and physical play, research on pretend
play also supports its connection to academic achievement. Singer
and Rummo (1973) found that children whose play contained more
imaginative elements performed better in school, suggesting that
cognitive components of pretend play may translate into the academic setting. This may again reflect symbolic representations
used in both play and reading and math.
Gender differences often arise in discussing academic achievement in children. This is particularly true in regards to math
achievement, as boys have traditionally been perceived as excelling in this area. However, most recent research shows no consistent evidence for gender differences in mathematics ability (Hyde,
2005). In comparing boys and girls, effect sizes for aspects of math
such as computation and problem solving are either small or
nonsignificant (Hyde, 2005). The only areas in which boys seem to
excel are mental rotation and spatial perception, which are often
irrelevant to general mathematics performance (Linn & Petersen,
1985; Voyer, Voyer, & Bryden, 1995). However, both parents and
teachers have been shown to hold biases against girls’ math
WALLACE AND RUSS
298
abilities (Jussim & Eccles, 1992; Tiedemann, 2000). In addition,
girls tend to believe that their math abilities are lower than boys do,
despite equal grades (Lloyd, Walsh, & Yaliagh, 2005; Tiedemann,
2000). The present study sought to understand the longitudinal
relation between girls’ pretend play skills and their academic
achievement in both reading and math.
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Summary
The present study examined longitudinal relationships among
early pretend play, divergent thinking, and academic achievement
in school-age girls. Previous longitudinal studies have found a
relationship between pretend play and divergent thinking, and
research has also demonstrated a link between pretend play and
reading and math achievement. The aim of the present study was
to establish longitudinal correlates of pretend play in school-age
girls. It was hypothesized that early measures of pretend play
would predict scores on measures of divergent thinking and academic achievement, controlling for verbal ability, at a 4-year
follow-up.
Method
Original Study
Participants of the original study were 61 students in a private
school for girls in kindergarten through fourth grade (Hoffmann &
Russ, 2012). The study took place during the 2008 –2009 school
year. Each child was administered the APS and the Alternate Uses
Task in addition to other baseline measures. The Vocabulary
subtest of the Wechsler Intelligence Scale for Children—Fourth
Edition (WISC-IV) was administered to assess verbal ability. The
WISC-IV Vocabulary scores were also used as a measure of verbal
ability in the present study.
Affect in Play Scale (APS). The APS is a standardized
5-minute play task designed to measure various dimensions of
children’s pretend play. Children receive two puppets and three
blocks and are given the following instructions:
I’m here to learn about how children play. I have here two puppets and
would like you to play with them any way you would like for five
minutes. For example, you can have the puppets do something together. I also have some blocks that you can use. Be sure to have the
puppets talk out loud. The video camera will be on so that I can
remember what you say and do. I’ll tell you when to stop.
The child is informed when there is one minute left. If the child
stops playing during the 5-min period, the prompt, “There’s still
time left, keep playing,” is given. The task is discontinued if the
child cannot play after a 2-min period.
The child’s play is scored from the videotape using a criterionbased rating scale. There are five main scores: (a) organization, the
quality of the plot and the complexity of the story, scored from 1
to 5; (b) imagination, the novelty and uniqueness of the play
including the child’s ability to use fantasy elements, scored from 1
to 5; (c) comfort, a global rating of the child’s comfort engaging in
play and their level of enjoyment, scored from 1 to 5; (d) frequency
of affect, a total frequency count of affect units expressed within
the play narrative (e.g., a child might have the puppets say “Yikes,
a monster!” [fear] or “Whee! This slide is fun!” [happiness]); and
(d) variety of affect, a total count of the number of affect categories
out of 11 possible categories, expressed during the play. The 11
affect categories include happiness/pleasure, anger/aggression,
sadness/hurt, nurturance/affection, anxiety/fear, oral, oral aggression, anal, sexual, competition, and frustration/dislike. Affect is
also divided into positive and negative content categories.
A detailed scoring manual for the APS has been developed
(Russ, 1993, 2004, 2014). Past studies have reported the interrater
reliability of the APS to be high, consistently in the .80s and .90s.
Internal consistency for the affect scores on the APS using the
Spearman-Brown split-half reliability is also high (.85; Seja &
Russ, 1999). The APS has a large body of validity studies demonstrating associations with theoretically relevant criteria (see
Russ, 2004, 2014).
Alternate Uses Task. As one measure of creativity, divergent
thinking was assessed using the Wallach and Kogan (1965) adaptation of Guilford’s Alternate Uses Task. The task asks children to
think of uses for six common objects: a newspaper, a button, a key,
an automobile tire, a shoe, and a knife. Two scores are calculated
from the child’s responses to the six items: (a) fluency, the number
of acceptable uses generated by the child, and (b) originality, the
number of acceptable uses given by a child that made up only 1%
or less of all the responses given for an item. The Alternate Uses
Task has excellent reliability and validity, established in many
studies conducted with children (Kogan, 1983; Runco, 1991).
Wechsler Intelligence Scales for Children—Fourth Edition.
The Vocabulary subtest of the Wechsler Intelligence Scales for
Children—Fourth Edition (WISC-IV) was administered as an estimate of children’s verbal ability. Participants were asked to
define words of increasing difficulty and their answers were scored
on a scale from 0 to 2, assessing verbal fluency, concept formation,
and word knowledge. Of all the subtests on the WISC-IV, the
Vocabulary subtest is generally the best estimate of overall intelligence. The Vocabulary subtest has been validated for children
ages 6 to 16 and has demonstrated strong reliability and validity
through correlations with other measures of intelligence and academic achievement (Wechsler, 2003).
Four-Year Follow-Up: The Present Study
Participants. Recruitment letters were sent to parents of the
46 girls who participated in the original study and were still
enrolled at the school. A total of 31 girls returned consent forms
and participated in this study, yielding a participation rate of 67%.
Participants were in the 4th through 8th grades, ages 9 to 14, with
a mean age of 11.1 years. There were 10 fourth graders, four fifth
graders, three sixth graders, six seventh graders, and eight eighth
graders. Information regarding ethnic background or socioeconomic status was not collected in this study, though the private
school has a majority of Caucasian students. This was a private
girls’ school. Thirty-eight percent of the students attending the
school receive financial aid, and this sample was representative of
that number.
A power analysis done with GⴱPower indicated that 31 participants would provide .53 power for a medium effect size. Because
partial correlations were used to control for verbal ability, a degree
of freedom was lost and power may have decreased. This power is
lower than what is preferred for a fair test of all hypotheses, but the
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PLAY, DIVERGENT THINKING, AND ACHIEVEMENT
number of original participants available at the school restricted
the possible sample size.
Procedure. The present study was part of a larger follow-up
assessment examining additional aspects of adaptive functioning
such as coping, affect, and resiliency. The assessment occurred in
the Fall of 2012 and the Spring of 2013, approximately 4 years
following the baseline assessment. Children completed the Alternate Uses Task. Records of each consented participant’s AIMSweb
standardized achievement test scores were released by the school.
Two measures from the original study, the APS and the Vocabulary score from the WISC-IV, were used as predictors in the
present study.
Measures.
Alternate Uses Task. As in the original study, Wallach and
Kogan’s (1965) adaptation of Guilford’s (1950) Alternate Uses
Task was used to measure children’s divergent thinking, although
the present study used a group administration format. Wallach and
Kogan’s (1965) group instructions were used, and children were
given 2 min for each item. The administrator of this divergent
thinking task was blind to children’s early APS play scores.
AIMSweb achievement test scores. AIMSweb is an assessment system designed to measure and monitor students’ academic
performance in Grades K– 8. A series of brief, 1– 8 min tests are
administered to students at various time points during the school
year. All students in the present study are tested three times during
the academic year, and at-risk students may be monitored more
frequently. The present study used the most recent reading and
math AIMSweb scores for each student. September scores were
used for the longitudinal analyses conducted with all students’
scores. January scores were used in concurrent analyses for the 8th
graders, as their concurrent data was collected during the spring
semester.
The AIMSweb system is based on the principle of CurriculumBased Measurement (CBM), which is used by teachers to assess
student progress without readministering time consuming, statewide standardized tests (Shinn & Shinn, 2002). The use of CBM as
a measure of student achievement has been supported across
multiple states who report moderate to strong correlations between
students’ performance on CBM and state achievement test scores
(Powell-Smith, 2004; Shapiro, Keller, Lutz, Santoro, & Hintze,
2006). The present study used AIMSweb tests as measures of
students’ academic achievement in reading fluency, reading comprehension, math calculation, and math problem solving. For each
test, the AIMSweb Technical Manual reports reliability in terms of
Alternate Form, a form of test–retest reliability. It also reports
criterion validity of each test by comparing student performance to
relevant portions of state achievement tests. Reliability and validity of each test is reported below.
The Reading Fluency task (Reading-CMB) measures students’
speed and accuracy in oral reading. Students are required to read
a passage aloud, and their scores reflect the average number of
words read per minute. Alternate form reliability ranges from
correlations of .93 to .95 for students in Grades 4 – 8. Criterion
validity has been established via correlations with state achievement tests, which range from .60 to .72.
The Reading Comprehension task (Maze) measures students’
skills in understanding the meaning of written text. Students read
a passage in which every seventh word is blank, and they must
select from three words to complete the sentences in context.
299
Alternate form reliability ranges from .74 to .78. Criterion validity
is supported, as correlations with state achievement tests range
from .51–.59.
The Math Computation Task (M-COMP) measures skill in
performing basic and complex calculations in areas of addition,
decimals, fractions, and percentages, among others. Student scores
reflect the number of problems they answer correctly. Reliability
ranges from .85 to .90. Criterion validity for this test was calculated by comparing M-COMP scores with scores on the Group
Mathematics Assessment and Diagnostic Evaluation (G-MADE),
given in third and eighth grades. Validity ranged from .73 to .76.
The Math Concepts and Applications test (M-CAP) measures
problem solving and logical reasoning skills. Again, scores reflect
the number of problems solved correctly in areas such as order of
operations, measurement, patterns/relationships, and data. Reliability for students in Grades 4 – 8 ranges from .80 to .88. Validity
data show correlations with state achievement tests ranging from
.57 to .78.
For each subject test, raw scores were transformed into standardized Z scores based on national grade norms (means and
standard deviations) separately for each grade to allow comparison
of scores across grades.
Data Considerations
In this sample of 31 participants there were some missing data.
Three participants from the original sample did not wish to be
videotaped during the pretend play task, leaving 28 participants
with APS scores. Two participants from the original sample did
not complete a second baseline session and thus are missing
baseline divergent thinking scores. A few students were absent on
the days the AIMSweb achievement tests were given, so there are
29 scores for reading fluency, 30 for reading comprehension, and
30 for math concepts/applications. Therefore, each measure had a
slightly different number of participants. Descriptive statistics of
all variables are reported in Table 1. The data were examined for
outliers. No outliers were found that would alter the correlations.
Results
Data Analyses
Data analysis examined longitudinal relationships between early
play and current divergent thinking and academic achievement.1
Additional analyses examined the longitudinal relationship between early divergent thinking and current academic achievement.
Pearson product–moment correlations were used to test for
significant longitudinal associations among the variables, controlling for verbal ability. Hierarchical multiple regression was used to
determine which play variables predicted divergent thinking and
achievement, controlling for verbal ability and age. Baseline divergent thinking was controlled for when investigating the relation
1
To account for missing data, we attempted to use both the multiple
imputation approach and the full information maximum likelihood (FIML)
approach. Because of the small sample size, the data would not converge
in the analyses and neither method was able to produce stable correlations.
FIML did produce a few significant results in the multiple regressions that
were consistent with our findings with the original data analyses.
WALLACE AND RUSS
300
Table 1
Descriptive Statistics of the Sample
Measure
Baseline APS
Baseline divergent thinking
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Current divergent thinking
Achievement: AIMSweb
Variable
n
M
SD
Range
Organization
Imagination
Comfort
Frequency of affect
Variety of affect
Positive affect
Negative affect
Fluency
Originality
Fluency
Originality
Reading fluency
Reading comprehension
Math computation
Math concepts and applications
28
28
28
28
28
28
28
29
29
31
31
29
30
31
30
2.86
3.04
3.36
23.36
3.82
13.07
10.29
15.93
3.28
22.45
5.61
159.17
29.77
37.45
15.90
1.41
1.43
1.42
20.90
2.58
13.17
11.09
6.19
3.40
6.21
3.84
26.43
8.95
12.36
5.63
1–5
1–5
1–5
0–75
0–8
0–45
0–49
6–30
0–12
8–34
0–17
114–208
18–48
10–63
6–30
between pretend play and later divergent thinking. An alpha value
of .05 was used for all statistical tests. Effect sizes reported are
based on Jacob Cohen’s (1992) categorization of small, medium,
and large effect sizes for product-moment correlations. A small
effect size corresponds to a correlation of .10; a medium effect size
corresponds to r ⫽ .30; and a large effect size to r ⫽ .50.
One-tailed tests were used for a priori hypotheses.
ficient that measures absolute agreement rather than just consistency between raters (Shrout & Fleiss, 1979). A two-way random
effects model was used, testing for absolute agreement using a
95% confidence interval. The average scores for the intraclass
coefficients were .94 for organization, .96 for imagination, .95 for
comfort, .96 for frequency of affect, .97 for variety of affect, .95
for positive affect, and .98 for negative affect (Hoffmann & Russ,
2012).
Verbal Ability
Scores on the Vocabulary section of the WISC-IV administered
at baseline were used as an estimate of verbal ability. Verbal
ability was used as a control variable. It was important to demonstrate that relationships among variables were not accounted for by
verbal abilities. In the current sample, participants had a mean
score of 12.29 (SD ⫽ 2.42, range ⫽ 8 to 17). The WISC-IV
Vocabulary subtest has a standardized mean of 10 and standard
deviation of 3, so the present sample’s mean score was approximately two thirds of a standard deviation above average. Verbal
ability did not correlate significantly with pretend play or divergent thinking. As expected, verbal ability did correlate with
achievement variables of reading fluency, r(29) ⫽ .48, p ⫽ .01,
and reading comprehension, r(30) ⫽ .48, p ⫽ .01.
Age
In the present sample, significant relationships emerged among
age and most of the other measures. Children’s age related to the
three pretend play variables of organization, r(28) ⫽ .39, p ⫽ .04;
imagination, r(28) ⫽ .47, p ⫽ .01; and positive affect, r(28) ⫽ .37,
p ⫽ .05. Age also correlated positively with divergent thinking
fluency, r(31) ⫽ .53, p ⫽ .002. Children’s age was related to the
academic achievement scores for math computation, r(31) ⫽ .54,
p ⫽ .002, and math concepts/applications, r(30) ⫽ .53, p ⫽ .003.
No relation was found between age and verbal ability.
Interrater Reliability
Interrater reliability for the APS was calculated for the baseline
sample using 20 randomly chosen participants. Interrater reliability
was assessed using a rigorous form of intraclass correlation coef-
Longitudinal Results
Play and divergent thinking. A major hypothesis was supported in that early pretend play significantly related to divergent
thinking. All analyses involving pretend play controlled for verbal
ability. The cognitive aspects of pretend play, organization and
imagination, related to divergent thinking fluency (see Table 2).
Organization and imagination in play positively correlated with
divergent thinking fluency, r(25) ⫽ .51, p ⫽ .003, and r(25) ⫽ .39,
p ⫽ .02, respectively. Children whose play was rated as better
organized and containing more imaginative elements generated
more responses on the divergent thinking task. The magnitudes of
these correlations were medium to large effect sizes (Cohen,
1992). An examination of affect in play showed that positive affect
in play related to divergent thinking originality, r(25) ⫽ .36, p ⫽
.03. Children who expressed greater amounts of positive affect in
their play generated more original responses on the divergent
thinking task. The magnitude of this correlation was a medium
effect size.
When age was controlled in longitudinal analyses with pretend
play, correlations remained significant between organization in
play and divergent thinking fluency, r(25) ⫽ .45, p ⫽ .01. The
relationship between divergent thinking fluency and imagination
in play dropped below significance, r(25) ⫽ .26, p ⫽ .10, but the
magnitude remained a small effect size. The same was true for the
relation between divergent thinking originality and positive affect
in play, r(25) ⫽ .27, p ⫽ .09.
In examining the longitudinal relation between pretend play and
divergent thinking, it was also possible to take into account children’s initial, or baseline, divergent thinking scores. When controlling for baseline divergent thinking fluency, the relationship
PLAY, DIVERGENT THINKING, AND ACHIEVEMENT
301
Table 2
Longitudinal Pearson Product–Moment Correlations for Pretend Play and Criteria (Controlling Verbal Ability)
Pretend play variables
Criteria
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Divergent thinking
Fluencya
Originalitya
Achievement: AIMSweb
Reading fluencyb
Reading comprehensionb
Math computationb
Math concepts and applicationsb
Org.
Imag.
Comf.
Freq.
Var.
Pos.
Neg.
.56ⴱⴱ (.51ⴱⴱ)
.24 (.18)
.44ⴱⴱ(.39ⴱ)
.31 (.26)
.15 (.13)
.11 (.10)
.15 (.19)
.20 (.23)
.22 (.21)
.20 (.19)
.24 (.30)
.32ⴱ (.36ⴱ)
.00 (.00)
.00 (.00)
⫺.08 (⫺.31)
.17 (⫺.05)
.42ⴱ (.34)
.20 (.14)
⫺.29 (⫺.46ⴱ)
.13 (⫺.01)
.44ⴱ (.40ⴱ)
.12 (.07)
⫺.29 (⫺.35)
.14 (.13)
.23 (.22)
⫺.20 (⫺.22)
⫺.30 (⫺.30)
.15 (.22)
.37ⴱ (.42ⴱ)
⫺.01 (.01)
⫺.23 (⫺.32)
.10 (.04)
.38ⴱ (.37ⴱ)
⫺.04 (⫺.07)
⫺.24 (⫺.22)
.02 (.09)
.47ⴱ (.52ⴱ)
.12 (.14)
⫺.26 (⫺.28)
.23 (.29)
.17 (.18)
⫺.14 (⫺.14)
Note. Partial correlations, controlling for Verbal ability, shown in parenthesis. Org ⫽ Organization; Imag ⫽ Imagination; Comf ⫽ Comfort; Freq ⫽
Frequency of affect; Var ⫽ variety of affect; Pos ⫽ Positive affect; Neg ⫽ Negative affect.
a
n ⫽ 28. b n ⫽ 24.
ⴱ
p ⬍ .05. ⴱⴱ p ⬍ .01.
between early pretend play and current divergent thinking fluency
was again significantly positively correlated. Organization in play
related to divergent thinking fluency, r(23) ⫽ .53, p ⫽ .003, as did
imagination in play, r(23) ⫽ .34, p ⫽ .046. Children whose early
pretend play was rated as more organized and more imaginative
generated more alternate uses on the divergent thinking task four
years later, independent of their baseline divergent thinking skills.
The magnitude of these effects was large for organization and
medium for imagination.
Hierarchical multiple regression was used to determine the
contribution of children’s early pretend play to current divergent
thinking beyond that of age and verbal ability. Verbal ability and
age were entered into Step 1, explaining 39% of the variance in
divergent thinking F(2, 25) ⫽ 7.85, p ⫽ .002. Two predictors were
entered into Step 2 to represent pretend play: organization and
positive affect in play, which accounted for 9% of the variance in
divergent thinking. These predictors were chosen based on a priori
hypotheses predicting their contribution to the variance in divergent thinking as well as their observed correlations with divergent
thinking. Organization in play itself accounted for 8% of the
variance in divergent thinking, but its contribution did not reach
significance. In the final model, age was the only significant
regression coefficient (beta ⫽ .39, p ⫽ .03).
Finally, the longitudinal relation between baseline divergent
thinking and current divergent thinking was examined to determine the stability of the measure over time. Baseline divergent
thinking fluency was related to current fluency score, r(29) ⫽ .34,
p ⫽ .04. Baseline divergent thinking originality was also related to
current originality score, r(29) ⫽ .36, p ⫽ .03. These results
demonstrate that children’s divergent thinking abilities had some
stability, but variation also occurred.
Play and achievement. Analysis of students’ AIMSweb
scores showed that early play predicted math achievement longitudinally. All analyses reported controlled for verbal ability. AIMSweb scores were converted to standard scores to facilitate comparison across grade levels. Imagination in play related to
children’s math computation skills, r(21) ⫽ .42, p ⫽ .03. Organization in play predicted math computation at the trend level,
r(21) ⫽ .34, p ⫽ .055. The affective components of pretend play
also related to math computation scores. Math computation was
predicted by frequency of affect expressed in play, r(21) ⫽ .42,
p ⫽ .02; variety of affect, r(21) ⫽ .37, p ⫽ .04; and positive affect
in play, r(21) ⫽ .52, p ⫽ .005. Children whose early play was
more imaginative and contained more affective elements, especially positive affect, performed better on a test of math computation skills. Pretend play did not predict math reasoning/problem
solving skills (math concepts/applications).
There was no relation between pretend play and reading comprehension. Children’s reading fluency scores, however, correlated
negatively with play scores. Imagination in play correlated in the
negative direction with reading fluency, r(21) ⫽ ⫺.46, p ⫽ .01.
Hierarchical multiple regression tested the contribution of age,
verbal ability, imagination in play, and positive affect in play to
AIMSweb math computation scores. Predictors were chosen based
on observed longitudinal correlations. Results showed that age and
verbal ability accounted for 34% of the variance in children’s math
skills; R ⫽ .59, R2 ⫽ .34, F(2, 25) ⫽ 6.52, p ⫽ .005. In the final
model, age was the only significant regression coefficient, accounting for 16% of the variance in math achievement (beta ⫽ .46,
p ⫽ .02).
Divergent thinking and achievement. Longitudinal relations
also emerged between divergent thinking and achievement. Children’s baseline divergent thinking scores predicted math achievement four years later. Controlling for verbal ability, divergent
thinking fluency predicted math computation, r(22) ⫽ .62, p ⫽
.001. In addition, divergent thinking originality predicted both
math computation, r(22) ⫽ .65, p ⬍ .001, and math concepts/
applications, r(22) ⫽ .35, p ⫽ .047. Children who supplied more
responses, as well as more original responses, in the divergent
thinking task had higher math achievement scores 4 years later.
Play, divergent thinking, and math achievement. Pretend
play and divergent thinking were combined in a hierarchical multiple regression to predict math achievement longitudinally. Positive affect in pretend play and divergent thinking fluency predicted
children’s math skills (math computation), after controlling for the
influence of verbal ability (WISC Vocabulary). Verbal ability was
entered into Step 1, explaining 3.3% of the variance in math skills.
After entry of positive affect in play and divergent thinking fluency at Step 2, the total variance explained by the model as a
whole was 34.3%, F(3, 24) ⫽ 4.17, p ⫽ .02, F change (2, 24) ⫽
5.66, p ⫽ .01. With verbal ability controlled, 31% of the variance
in math achievement was accounted for by divergent thinking and
WALLACE AND RUSS
302
play. In the final model, divergent thinking fluency was the only
significant regression coefficient (beta ⫽ .42, p ⫽ .04).
Concurrent Findings
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Divergent thinking and math achievement. Divergent
thinking related to children’s current math achievement scores.
Controlling for verbal ability, divergent thinking fluency related to
both math computation skills, r(28) ⫽ .47, p ⫽ .01, and math
concepts/applications, r(27) ⫽ .58, p ⫽ .001. Children who generated more alternate uses scored higher on tests of math achievement.
Discussion
The major findings of the present study were that children’s
early pretend play predicted divergent thinking and math achievement over a 4-year period. These longitudinal findings provide
evidence for the predictive power of play. Divergent thinking also
predicted math achievement longitudinally, and the stability of
divergent thinking skills over time was demonstrated. Finally,
concurrent relationships indicated that math achievement is linked
to children’s divergent thinking skills. It should be noted that
verbal ability did not significantly relate to play skills, and all
significant relationships remained significant when verbal ability
was controlled for.
Play and Divergent Thinking
A major finding of this study was that children’s pretend play
predicted their divergent thinking skills over time. Specifically,
children whose play was more organized and imaginative were
able to generate more alternate uses for everyday objects, independent of verbal ability, 4 years later. Further, children who
expressed more positive affect in their play were able to generate
more original alternate uses. Although both cognitive and affective
aspects of pretend play also related to divergent thinking at baseline (Hoffmann & Russ, 2012), their relation was maintained at the
4-year follow-up even when baseline divergent thinking scores
were controlled. At the follow-up, children with better early play
also had better divergent thinking abilities, beyond what their
baseline divergent thinking scores would have predicted. This
indicates that aspects of pretend play predict shifts in divergent
thinking over time. This is the second study to find that early
pretend play predicted later divergent thinking (Russ, Robins, &
Christiano, 1999). Both studies also found divergent thinking to be
relatively stable over time. Even though the task was administered
individually at baseline and in a group format in the present study,
children’s scores at baseline were predictive of their scores four
years later. Both of these longitudinal studies used different administrators for the play and divergent thinking tasks, addressing
recent critiques that significant results found in studies of play and
creativity may be attributed to experimenter bias (Lillard et al.,
2013).
Of the affective components of pretend play, positive affect in
play predicted divergent thinking originality over a 4-year period.
Girls who expressed more positive affect in their play were able to
generate more original uses for everyday objects. A previous study
found similar positive correlations between affect in play and
divergent thinking longitudinally, but correlations did not reach
significance (Russ, Robins, & Christiano, 1999). Negative affect in
play did not relate to divergent thinking. In previous studies with
samples that included both boys and girls, negative affect has
related to divergent thinking (Russ & Schafer, 2006). Perhaps the
relationship was present for the boys but not the girls. Several
studies found relationships between primary process thinking on
the Rorschach (largely aggressive percepts) and creativity for boys
but not for girls (Russ, 1982, 1988; Russ & Grossman-McKee,
1990). It is possible that the use of negative affect in play is
different in girls than in boys. This is an important area to be
studied in the future.
A hierarchical multiple regression analysis was performed to
determine whether pretend play contributed to the variance in
divergent thinking over and above age and verbal ability. Analysis
showed that age accounted for more variance in divergent thinking
fluency than did pretend play. Although age appears to be a
significant factor in children’s divergent thinking abilities, pretend
play still emerged as an important contributor to divergent thinking
and accounted for 8% of the variance in divergent thinking.
Play and Math Achievement
Early pretend play also predicted children’s math achievement.
Imagination in play and the amount of affect in the story, in
particular positive affect, predicted math achievement. Previous
research has supported the relation between play and math
achievement concurrently, but no known research has demonstrated a longitudinal relation between pretend play and math
ability. One possible explanation for our results is the special focus
on science and math in this particular academic setting. This
all-girls’ school strives to stimulate interest in math and science,
areas traditionally dominated by males. The school encourages
experiential, hands-on learning through “tinkering stations” in the
hallways and real-world engineering projects in the community. It
is possible, then, that processes present in pretend play such as
symbolism, organization, and experimentation transfer to math
achievement in a setting where similar processes are emphasized
in math instruction and where girls are encouraged to reach their
full potential in math. Another theory, presented by Hanline and
colleagues (2008), is that practice with symbolic substitution in
play transfers to the symbolic representation skills required in
mathematical reasoning. This is consistent with their findings
demonstrating the association between transformations and representations in play and math skills in preschool children (Hanline et
al., 2008).
Contrary to hypotheses, imagination in play was negatively
related to reading fluency scores. The reading comprehension and
reading fluency scores correlated very differently with play scores.
Although play showed no relation to reading comprehension,
better play seemed to predict lower reading fluency scores. These
findings are not consistent with the play and literacy research and
could be a chance finding. It is also possible that AIMSweb is not
assessing the kind of reading ability that would relate to play.
Specifically, the reading fluency test measures how many words a
child can read correctly within a certain time frame. The reading
fluency score, then, reflects solely the child’s reading speed and
accuracy over one brief period. It does not capture components of
verbal reasoning or unstructured language production. Although a
PLAY, DIVERGENT THINKING, AND ACHIEVEMENT
more comprehensive set of reading/language measures might be
expected to relate to play, it is not surprising that neither imagination nor affect present in play correlated positively with these
brief measures.
Another hierarchical multiple regression showed that the combination of positive affect in play and baseline divergent thinking
significantly predicted math achievement over and above verbal
ability. This confirms correlational evidence that early pretend
play and divergent thinking play an important role in the emergence of mathematical skills over time.
303
variables studied. Second, the sample was made up of female,
mostly Caucasian, students in a private school setting. Ethnicity,
gender, and socioeconomic status were not fully represented. Thus,
the generalizability of these results to other populations may be
limited. Finally, the AIMSweb scores measuring reading and math
achievement may not fully represent students’ ability levels. They
are not considered a gold standard measure of academic achievement, so a more thorough measure may have shifted or strengthened the findings.
Implications
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Divergent Thinking and Math Achievement
The present study found a significant relation between divergent
thinking fluency and originality at baseline and math achievement
scores over time. Children with better divergent thinking skills
scored higher on tests of math computation and math concepts/
applications 4 years later. This suggests that some aspect of divergent thinking may translate into math achievement. The tasks may
share common elements such as nonverbal, fluid reasoning, or
processing speed. One study examining the relation between creativity and achievement measured divergent thinking in groups of
gifted boys. Higher divergent thinking scores were strongly correlated (r ⫽ .68) with membership in the “math and science gifted”
group (Runco, 1999). However, a high correlation was also found
for the “high overall IQ” group. Future research should further
investigate divergent thinking as a potential contributor to children’s math achievement.
Divergent thinking fluency was also positively related to math
achievement concurrently. Even controlling for verbal ability and
for divergent thinking at baseline, children who had higher divergent thinking scores performed better on tests of math skills. This
provides additional support for the idea that similar processes are
involved in generativity or problem solving and mathematics.
Similar to the relation between play and mathematics achievement,
math and divergent thinking may share processes such as advanced
reasoning and thinking “outside the box.” This idea was supported
in a recent study showing that in adults, divergent thinking ability
was specifically related to fluid intelligence (Nusbaum & Silvia,
2011). Although divergent thinking is related to overall intelligence to a certain extent, separating fluid and crystallized intelligence reveals a stronger association with fluid reasoning than with
fact-based knowledge. Further exploration of the processes common to play, divergent thinking, and mathematics skills may yield
interesting ideas about teaching or promoting mathematics
achievement in children.
Limitations
This study has a number of limitations that may have impacted
both the findings and the overall generalizability of results. First,
the longitudinal design restricted the possible sample size. The
resulting sample of 31 children is small, which limits the available
statistical power and consequently the likelihood of finding significant results. It is possible that the contribution of pretend play
to divergent thinking and reading and math achievement in the
multiple regressions may have reached significance with a larger
sample. A small sample size also limited the analyses we were able
to perform to determine the nature of the contribution of age to the
The above results carry implications for how parents and educators view pretend play, creativity, and math achievement. The
present study and others show that a child’s intelligence is far from
the sole determinant of her creative potential or even academic
achievement. A recent meta-analysis showed that divergent thinking is a much better predictor of creative achievement than IQ
(Kim, 2008). It is important for parents and educators to realize
that IQ does not determine a child’s creative potential, and it may
even be possible to promote math achievement in a way that does
not rely so heavily on IQ. Math education that capitalizes on
creative problem solving and manipulation of ideas and images
may help girls to use their divergent thinking skills to improve
their mathematics skills. Approaching math education through the
lens of creative thinking may also engage girls more effectively. A
study of upper elementary school students and teachers showed
that in classrooms where teachers elicited student creativity, students showed the largest gains in academic achievement (Schacter,
Thum, & Zifkin, 2006). This may be a valuable tool to allow
teachers to engage students as well as further their math achievement through different means.
Future Directions
The present study opens the door for several lines of future
research. Replication of results with other more diverse populations would help to clarify the stability and generalizability of the
longitudinal correlates of play. A larger sample size would also
help to confirm these relationships and test for possible mediation
effects. Another research question that emerged is the nature of the
relationship among pretend play, divergent thinking, and math
achievement. Identifying similar processes involved in all three
domains may lead to investigation of ways to utilize pretend play
or divergent thinking in promoting math achievement. This is a
promising idea for teaching girls especially, as the present study
showed significant concurrent and longitudinal relationships in an
all-female sample.
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Received October 22, 2013
Revision received December 18, 2014
Accepted January 20, 2015 䡲