2011. Vol.2, No.3, 164-173
Copyright © 2011 SciRes. DOI:10.4236/ce.2011.23023
Features of Creativity as Expressed in the Construction of New
Analogical Problems by Intellectually Gifted Students
Rama Klavir1, Malka Gorodetsky2
1The Governmental Excellence Program in the Colleges of Education,
and The Kaye College of Education, Beer-Sheva, Israel;
2Department of Education, Ben-Gurion University, Beer-Sheva, Israel.
Email: Rama_k@macam.ac.il, firstname.lastname@example.org
Received April 7th, 2011; revised May 10th, 2011; accepted May 22nd, 2011.
The present research attempts to provide e mpirical data on creativity features that were employed by gifted stu-
dents, as compared to “regular” ones, in the process of constructing analogical problems. The research is coping
with two major components of creativity: a) Readiness to get involved in the construction of new analogical
problems and b) Creative features in the constructed problems. The results indicate that: 1) Gifted students were
more creative than their age peers on the dimensions that were defined as relative creativity. 2) Relative creativ-
ity was especially salient in tasks that involved insight thinking. 3) Despite the high relative creativity of the
gifted students' their comparative creativity, i.e. their creative capabilities as compared to the optimum, were
limited. The results are coherent with the need and recommendations for progressive nurturing of gifted students
towards fulfilling their creative potential.
Keywords: Intellectual Giftedness, Relative Creativity, Comparative C r eativity, Construc t i o n of Analogical
Problems, R e a diness to Become Creative, Fe atures of Creative Prod ucts
The research literature regarding intellectually gifted children
(high IQ) addresses creativity (e.g. Rogers, 2002: p. 36; Mul-
hern, 2003; Rogers & Silverman, 1998) and divergent thinking
as salient and unique attributes of these children. However, the
connection between intellectual giftedness and creativity seems
to lack conclusive data. Nevo (1997) states a correlation of only
0.32 between creativity and intelligence and justifies this low
correlation by suggesting that a high IQ is probably a necessary
condition for creativity but not a sufficient one. Similarly, Tan-
nenbaum (1983) in his review of the creativity literature till the
80s, states that the correlation between creativity scores and
IQ-s of gifted children vs. “regular” populations, is ranging
from near-zero to high significance. Observations made by
VanTassel-Baska (2001) more than twenty years later led her to
the conclusion: “creativity is an elusive factor in its relation-
ship to giftedness”.
Indeed, this confusing picture can also be found in the review
by Milgram & Livne (2006) regarding creativity in Israel. They
address two articles that originated from the same Israeli re-
search group (Landau, 1981; Landau & Wiessler, 1998). The
1981 study reports that the correlation between intelligence
(high-IQ) and creativity of gifted, as compared to non-gifted
high school students, was found to be zero whereas, the 1998
study that uses different measures for creativity of gifted chil-
dren (fluency and flexibility: Torrance's Circles subset from
1972), reported a positive correlation between intellectual gift-
edness and creativity.
The source for these inconsistencies may stem from a mysti-
fied connection between giftedness and creativity or it may be
the result of the composite nature of creativity which makes its
assessment difficult (Feldman 1999; Hennessey, 2004; Stern-
berg & Lubart, 1996).
This complexity may be due to the multifacedness of the
creativity components and their interrelationships. For example,
Barron (1988) suggests a model of creativity that is based on “a
creative product, produced by a creative person as a result of a
creative process”, i.e. creativity involves a personal features
(e.g. motivation), a process (e.g. the cognitive processes) and
the nature of the creative product. A fourth component that
relates to the context of creativity was added by other research-
ers in this field (Kleiman, 2005; Plucker & Beghetto 2004;
Sternberg and Lubart, 1996). The latter was termed as the Press
component (Basadur & Hausdorf, 1996) and it emphasizes the
connection and dependence of the creative individual on the
unique context (Csikszentmihalyi, 1988), and the activities
she/he addresses (De Souza, 2000).
The ambiguity as to the connection between creativity and
giftedness may stem from other difficulties in the process of
creativity assessment. The features of a creative person are not
easily accessible (Kleiman, 2005) and the nature of the creative
thinking processes can be implied only from the product (Nevo,
1997; VanTassel-Baska, 2001). Thus, the most useful tool left
for the study of creativity is the product. The creative product—
whether it be an actual, physical object or an expressed idea—is
the proof or evidence that creativity has occurred (Kleiman
2005). Because of its tangibility, it is probably the easiest ele-
ment for the assessment of creativity.
Assessing the Q uality of Creative Thinking vi a t he
Assessment of Creative Products
The assessment of creative processes can be deduced from
the features of the creative products. Some of these well-agreed
R. KLAVIR ET AL. 165
upon features are: originality (or newness), appropriateness,
elaborateness and flexibility (e.g. Amabile, 1996; Klavir &
Hershkovitz, 2008; Nevo, 1997; Runco, 2005; Sternberg &
Lubart, 1999): Originality—expresses the deviation of the
product from routine solutions, i.e. being different, unique,
unexpected and/or non-conventional. Appropriateness—re-
flects the attendance of the individual to cope with the con-
straints of the task of creativity. Elaborateness—relates to the
degree the new product is upgraded in comparison to the al-
ready known. The more the product includes new structural
relations the more it is considered to be on a higher thinking
level. Flexibility—relates to the context and the content of the
new product. The more the context and content of the new
product are far removed from the source problem it reflects a
higher flexibility of the individual to shift to new areas, i.e. a
It's important to emphasize that each one of these dimensions
illuminates creative thinking from a different perspective (Bonk,
2003; Guilford, 1967; Klavir & Gorodetsky, 2009; Klavir &
Hershkovitz, 2008) and thus, using only one of these dimen-
sions is not sufficient for deducing neither the creative qualities
of the product nor the quality of the creative thinking process
(Briskman, 1980; Besemer & O’Quin, 1993).
The Readiness to Construct New Products as a Means
to Assess the “Creative Person” (Motivation)
Information regarding the person’s readiness (i.e. motivation)
to get involved in a creative process is simply manifested by the
production of a product (e.g. Feldman, 1999; Sternberg &
Lubart, 1996). This readiness is one of the essential features of
creative people (e.g. Kleiman, 2005; Nevo, 1997; Van-tassel
Baska, 2001; Sternberg & Lubart, 1996). For some the mere
engagement in a creative process itself is satisfying whereas
others are in need of the community’s approval as to their crea-
tiveness (Feldman, 1999). According to Runco (2005), motiva-
tion can influence the thinking processes and lead to the pro-
duction of multiple products that in turn re-influence the think-
ing processes. Meaning, the person’s appraisal regarding his
capability to cope with the task, becomes a source for enhanced
motivation to get involved in further producing original and
new products. Furthermore, people’s negative appraisal of their
capabilities to cope with the task such as lack of required
knowledge, skills or abilities, results in avoiding creative proc-
esses (El-Murad & West, 2004). Thus, for the study of creativ-
ity the choice of an appropriate context and a suitable task that
ensures the manifestation of creative features, is essential.
Features Regarding Appropriate Tasks for the Study
The selection of a task for the assessment of creativity is of
utmost importance. Different kinds of tasks yield different lev-
els of creativity (Mumford et al., 2002). Therefore, the task has
to encapsulate possibilities for activating and expressing crea-
tive modes of thinking. Furthermore, it is advised to use more
than one kind of task in a certain study. The research literature
suggests some well-agreed features regarding appropriate tasks
for the study of creativity. These include the following features:
1) “Open-ended” tasks including complex, ill-defined prob-
lems that are difficult to be solved and for which conventional
responses do not work (Amabile, 1996: p. 41; Mumford, et al.,
2002: p. 707).
2) Tasks that demand previous knowledge. Creativity was
found to depend on specific knowledge in the field of the tasks
(e.g. Runco, 2005; Kleiman, 2005). Thus, the problems have to
be adjusted to the knowledge of the persons performing the
creative processes (Amabile, 1996; Hennessey & Amabile,
1988; Reiter-Palmon, Mumford, O’Connor, & Runco, 1997).
According to Mumford et al. (2002) the person's knowledge is
important since it enables him to redefine the task at hand, to
gather further information for its deep understanding, to com-
bine and reorganize the information in new conceptual combi-
nations and to use analogical reasoning to construct new repre-
sentations towards generating creative ideas.
3) Tasks that involve analogical thinking have the potential
to shed light on the processes involved in the production of
creative ideas (Martindale, 1999). Gentner et al., (1997) suggest
that the construction of new analogical ideas depends on high
cognitive abilities i.e. the ability to draw abstract structural
similarities between analogical problems. Thus the more the
new analogical situations are far removed from the source
problem the more they reflect higher cognitive abilities (Runco,
2007: pp. 12-14) and more creative thinking (Shye & Goldz-
weig, 1999). Following this knowledge the construction of
analogical problems seems to be a suitable task for the study of
creativity especially as this process is associated with cognitive
flexibility and elaboration (Bull, Montgomery, & Kimball,
The present research attempted to assess the nature of crea-
tivity of intellectually gifted students vs. “regular” one, on two
dimensions: 1) assessing their readiness to get involved in the
construction of new product; and 2) assessing the creative
qualities expressed in the constructed products. The research
hypothesis was that the gifted students as compared to the
“regulars” will exhibit a higher readiness to get involved in the
construction of new products (analogical problems) and that
their constructed problems will be found to be more creative
based on criteria for creativity described above. Runco (2005)
found that intellectually gifted children are often appearing to
be “on fire” and strongly engaged in their domains of interest.
Similarly, Winner (1997) found that gifted children derive
pleasure from coping with challenges. This intrinsic motivation
is explained by Winner (2000) and Hennessey (2004) as arising
from their feelings of competence that are nourished from their
past successes in coping with creative tasks. Gifted students
were also found to be characterized by cognitive capabilities
that affect their mode of thinking and lead to creative produc-
tions. These capabilities include generative thinking (e.g., Ward
et al. 1999), analogical complex thinking and insight capabili-
ties (Davidson, 1986; Klavir & Gorodetsky, 2001), flexible
abilities (e.g. Dover & Shore, 1991), high order reasoning as
well as convergent and divergent thinking (Rex, 1996).
Two groups of students were chosen for this task.
The gifted students were seventh and eighth graders with an
IQ defined by the Ministry of Education as being above of 135
(N = 232). They studied in regular high-schools however they
R. KLAVIR ET AL.
were part of an enrichment program catered specifically for
The “regular” students were eighth and ninth graders defined
as neither gifted nor as special education students (N = 229)
that studied in regular classes and were from a similar urban,
middle-class background, and went to the same comprehensive
junior high-schools. The difference in the ages of the popula-
tions was to ensure a similar mental age (Planche, 1985).
The students in both groups were asked to solve only one
problem that was either a mathematical multistage problem, an
insight-mathematical problem, or an insight-non-mathematical
(verbal) problem (see appendix 1). Thus the research relates to
three kinds of problems that were solved by the involved stu-
The mathematical problem: this problem was taken from a
group of challenging problems in a mathematics textbook for
the 8th grade. It was chosen in cooperation with six mathematics
teachers of the 7th-9th heterogeneous classes. The problems
were evaluated by the teachers as being more complex than the
average classroom problems but yet being based on the school-
learned mathematical knowledge.
The mathematical and verbal insight problems: insight prob-
lems that “requires restructuring of a problem space by step-
ping out of the framework provided by the commonly activated
cognitive schemas and acquiring a new perspective on the
problem” (Karimi, Windman, Güntürkün, & Abraham, 2007).
One of these problems necessitated mathematical knowledge
(insight-mathematical problem) while the other was based on
common knowledge (insight-non-mathematical (verbal) prob-
lem). The problems were compiled from a number of puzzle
books (e.g., Lake, 1976) and shared similar attributes, as de-
scribed by Davidson (Davidson, 1986; Davidson & Sternberg,
1984). According to Davidson, the solution of such problems
involves the restructuring of the problem space that is based on
three selective cognitive processes: selective encoding, selec-
tive combination, and selective comparison. The choice of the
specific problems for the study was based on an independent
study in which students were asked to solve five chosen prob-
lems in these categories. The chosen problems for the study
were in the upper quartile (the 75th percentile) of difficulty.
The design included three phases: in the first phase students
received a questionnaire in which they were asked to solve one
problem (source problem). In the second phase, the students
received two solved problems for learning: one problem was
analogous to the source one and the other was a distracting
problem with a similar surface structure but with a different
deep structure. Students were asked to study the solution proc-
esses and then to recite the problems and their solutions in their
own words. This design follows previous researches as a means
to ensure the participants’ engagement in the learning process
(Reiter-Palmon et al., 1997). The third phase was undertaken
two weeks later. At this phase the students were asked to solve
again the source problem and to construct a new analogous
problem of their own that is as far removed from the source one
as possible. Students that didn’t complete the second phase
seriously, meaning there was no indication for a learning proc-
ess of the analogous and the distracting problems, were ex-
cluded from the analysis. Following Mumford (1998), this was
to ensure that all subjects have learned to solve the problems,
i.e. have the appropriate knowledge.
The Defined Variables
1) Readiness to construct a creative product - relates to stu-
dents’ motivation to construct new analogous problems. The
assessment is based on the number of students that constructed
a new analogous problem regardless its quality. All students
that accomplished the three phases were divided into two
groups: those that did construct a new problem and those that
didn't. The group of students that constructed a new problem
was defined as that which expressed readiness to construct a
creative product, whereas the other group was defined as the
2) The creative quality of the new products—was assessed
on the basis of the criteria as suggested above: a) Flexibility:
This criterion relates to the extent of similarity between the
surface structures (content and context) of the constructed
problem to that of the source one. The more the surface struc-
ture of the constructed problem was removed from the source
one it was considered to be more flexible. Three levels of flexi-
bility were defined: completely different, when the content and
context of the story in the constructed problem were completely
different from those in the source problem; similar, when the
content of the story in the constructed problem was different
but its context was similar to that in the source problem; and
identical, when the content and context of the story in the con-
structed problem were identical to those in the source problem.
b & c) Appropriateness & Elaborateness: This variable ex-
pressed the extent of similarity in the solution structures be-
tween the new constructed problem and the source one: The
further the structural elements or relations (logical or mathe-
matical) in the constructed problem were removed from those
in the source problem, the constructed problem was considered
to be more creative (for a similar method, see Bassok et al.,
1998). Since elaboration can be examined only for appropriate
(relevant) problems, these two measures of appropriateness and
elaborateness were combined and appear as a joint variable.
Three levels were assigned for the combined variable: different
was assigned when the solution structure of the constructed
problem was appropriate (relevant) and elaborated; identical
was assigned to constructed problems that their solution struc-
ture was appropriate but was not elaborated; and inappropriate
for cases in which the constructed problems included solution
structures that were irrelevant to the source problem. d) Origi-
nality: This variable expresses the extent to which the con-
structed problems were very original, partially original or not
original. The assessment was based on a subjective judgment
following Amabile’s (1996) instructions: 1) External judges
were asked to grade the originality of the constructed problems
using their subjective judgment without pre-defined criteria. 2)
Then the judges were asked to rate the levels of originality of
each problem relatively to the other constructed ones. e) The
cumulative creativity measure was assigned on the basis of the
above criteria: high cumulative creativity was assigned to
products that included the most creative features as defined
above, i.e. high cumulative creativity was assigned to con-
R. KLAVIR ET AL. 167
structed problems that were assessed as the most flexible, ap-
propriate, elaborated and original. Lower cumulative creativity
was assigned to the rest of the constructed problems. For ana-
lyzed examples, see Appendix 2.
The Process of Analysis
The analysis of the constructed problems was performed by
10 paid graduate students. The assessing students were trained
in a similar manner as described by Reiter-Palmon et al. (1997).
The training session started with all students attending to a
similar questionnaire and attempting to assess the variables
listed above. Then, each of them assessed a questionnaire on
her/his own. After this assessment the students were brought
together to compare their assessments and discuss possible
discrepancies. In the next stage each couple received the same
10 questionnaires for assessment. Then all pairs met for com-
parison of the discrepancies in their ratings. After this training,
they continued the assessment process in couples. Each couple
analyzed all 461 questionnaires separately. The final assigned
values for the constructed problems were those assigned by the
majority of couples and not on the basis of an average as sug-
gested by others (e.g. that of Reiter-Palmon et al., 1997 or
Hennessey & Amabile, 1988).
The Connection between “the Readiness to Create a
New Product” and Creativity
It was found that more gifted students were ready to con-
struct new analogical problems for all three kinds of problems
(Table 1): for the insight-mathematical problem—out of the
number of those who did construct new analogical problems
(45% out of the students), 61% were gifted vs. 39% that were
“regulars”, [X2(1, N = 155) = 9.58 p < .01]; for the mathemati-
cal problem—out of the number of those who did construct
new analogical problems (54% out of the students), 75% were
gifted vs. 25% that were “regulars”, [X2(1, N = 149) = 35.40 p
= .001]; for the insight-verbal problem - out of the number of
those who did construct new analogical problems (31% out of
the students), 78% were gifted vs. 22% that were “regulars”,
[X2(1, N = 157) = 21.13 p = .001].
The results verify that indeed intellectually gifted students are
more prone to construct new analogical problems, i.e. are more
motivated to construct new creative products than the “regulars”.
This difference is valid for all products (in our case: insight-
mathematical, mathematical and insight-verbal problems).
The Connection between Intellectual Giftedness and
Creativity as Manifes ted in the Co nstructed Problems
Five X2 tests were conducted for the five criteria expressing
dimensions of creative quality of the constructed analogical
1) Flexibility (Table 2): the insight-mathematical problem -
25 out of the 43 (58%) gifted students as compared to 8 out of
the 27 (30%) “regular” students constructed a different problem
[X2(2, N = 70) = 5.65 p = .06*] (*with enlarging the Alfa rate);
the mathematical problem—there was no difference between
the gifted students (62%) and the “regulars” (55%); the insight
problem—19 out of the 38 (50%) gifted students as compared
to 2 out of the 11 (30%) “regular” students constructed a dif-
ferent problem [X2(2, N = 49) = 7.70 p < .05].
2 & 3) Appropriateness & Elaborateness (Table 3): the in-
sight-mathematical problem—20 out of the 40 (47%) gifted
students as compared to 21 out of the 27 (78%) “regular” stu-
dents constructed an inappropriate problem, whereas 10 out of
the 43 (23%) gifted students as compared to only 1 out of the
27 (4%) “regular” students constructed a new problem t hat was
appropriate and also elaborated [X2(2, N = 70) = 7.69 p < .05];
the mathematical problem—there was no difference between
the gifted students and the “regulars” as measured on appropri-
ateness and elaborateness of the constructed problems. Only 7
out of the 61 gifted students (12%) and 3 out of the 20 (15%)
“regular” students constructed a problem that was appropriate
and also elaborated; the insight problem—14 out of the 38
(37%) gifted students as compared to 7 out of the 11 (64%)
“regular” students constructed an inappropriate problem, whe-
reas 10 out of the 38 (26%) gifted students as compared to 0 out
of the 11 (0%) “regular” students constructed a problem that
was appropriate and also elaborated [X2(2, N = 49) = 6.39 p
4) Originality (Table 4): the insight-mathematical problem
—17 out of the 43 (61%) gifted students as compared to 1 out
of the 27 (4%) “regular” students constructed a “very original”
problem [X2(2, N = 70) = 13.85 p < .05]; the mathematical
The readiness to construct a new product: the number of students (gifted/“regulars” and beyond) that constructed new problems .
The kind of the problem
I-M1 M I-V
G2 “R” T G “R” T G “R” T
Did construct an analogous problem 43
Did not construct an analogous p r oblem 31
1. I-M: The insight- mathematical problem; M: The mathematical problem; I-V: The insight- verbal problem. 2. G: gifted students ; “R”: “regular” students ; T: Total (be-
yond). a. Within raw; b. Within column.
R. KLAVIR ET AL.
The flexibility levels of the constructed problems by gifted and “regulars”.
Appropriateness & Elaborateness levels o f problems that wer e constructed by gifted and “regulars”.
problem—there was no difference between the gifted students
(31%) and the “regulars” (25%); the insight problem—18 out
of the 38 (47%) gifted students as compared to 4 out of the 11
(36%) “regular” students, constructed a “very original” problem
[X2(1, N = 70) = 5.67 p < .05].
5) The cumulative creativity measure (Table 5): the in-
sight-mathematical problem—8 out of the 43 (19%) gifted
students as compared to 0 out of the 27 (4%) “regular” students
were found as more creative according to this criterion [X2(1, N
= 70) = 5.67 p < .05]; the mathematical problem - there was no
difference between the gifted students (11%) and the “regulars”
(15%); the insight problem—8 out of the 38 (21%) gifted stu-
dents as compared to 0 out of the 11 (0%) “regular” students
were found as more creative on this criterion [X2(1, N = 49) =
2.77 p = .09*] (*with enlarging the Alfa rate).
On the basis of the five creativity features of the constructed
problems, i.e. the creative products, the intellectually gifted
students were found to be more creative than the “regulars” on
the insight problem. The constructed insight analogical prob-
lems (verbal as well as mathematical) of the gifted students
were more flexible, more appropriate, more elaborate, and
original and had a higher level of cumulative creativity. As to
the constructed mathematical analogical problems these differ-
ences between the gifted and “regulars” were not found.
The Connection between Intellectually Gifted and
Creativity beyond the Specific Nature of Problems
For this analysis, the results obtained for the three problems
were combined. It was found that:
Readiness (motivation to create) (Figure 1): out of the 461
students that participated in the task (232 gifted students and
229 “regulars”) 200 (43%) students exhibited readiness to con-
struct a problem: 71% out of them were gifted and 29% were
“regulars”, [X2(1, N = 461) = 60.40 p < .001]. These included
61% of the gifted and 25% out of the “regulars”.
The creative quality of the constructed problems (products)
(Figure 2): a) Flexibility: 58% ( 82 out of the 142) gifted stu-
dents as compared to 36% (21 out of the 58) students con-
structed flexible (different) problems [X2(2, N = 200) = 8.22
p < .05]. b+c) Appropriateness & Elaborateness: 19% (27 out
of the gifted students ) as compared to 7% (4 out of the “regu-
lar” students) constructed new problems that were both appro-
priate and elaborated [X2(2, N = 200) = 11.40 p < .05]. d)
Originality: 38% (54 out of the 142) gifted students as com-
pared to 17% (10 out of the 58) “regular” students were found
to be more original according to this criterion [X2(2, N = 200)
=15.87 p < .001]. e) The cumulative creativity measure: 16%
(23 out of the 142) gifted students as compared to 5% (3 out of
the 58) “regular” students were assessed as having a high cu-
mulative creativity [X2(1, N = 200) = 4.43 p < .05].
These results verified that the intellectually gifted students as
compared to the “regular” ones, did exhibit higher levels of
The paper attempted to answer the question as to the connec-
tion between giftedness and creativity by analyzing students’
R. KLAVIR ET AL. 169
The originality levels of problems that were constructed by gifted and “regulars”.
Very original 17
Partially original 22
Non original 4
The cumulative measure: the number of the most creative analogical problems that were constructed by gifted and “regulars”.
A higher cum ulative
A lower cumulative
The percentages of students (gifted vs. “regular”) that exhibited/didn’t
exhibit readiness (motivation) to construct an a na logical problem.
readiness to construct analogical problems and by assessing the
creative features of these. We have followed some recommen-
dations such as adjusting the context to our students and the
goal of the study. Thus we chose three kinds of problems: in-
sight-mathematical, mathematical and insight-verbal, that on
the one hand have the potential to activate creativity and that
their knowledge-base and complexity matches the high-order
thinking of gifted students. Furthermore, using three kinds of
problems enabled us to expose creative behavior on a few di-
mensions. All subjects, gifted as well as the “regulars”, learned
the problems and only than were asked to construct an analogi-
cal problem. Thus we verified that the subjects had the appro-
priate knowledge to cope with the construction of analogous
problems. Students’ readiness to get involved in this process
and the creative nature of these products were assessed.
The percentages of students (gifted vs. “regular”) that exhibited high
creative qualities in their constructed analogical problem.
We believe that the more comprehensive methodology that
attended to different aspects of creativity supports the connec-
tion between intellectual giftedness and creativity.
The Connection between Intellectual Giftedness and
Creativity—a General Perspective
It was found that creativity as a general feature characterizes
more the intellectually gifted students than the ‘regulars’. This
was reflected in their higher readiness than the ‘regulars’ to as
shown in Figure 1 and in their high level of creativity features
(flexibility, appropriateness & elaborateness, originality and the
cumulative creative quality) in their products (Figure 2).
These results give further empirical support to the claim that
the quality of the product can reflect high order thinking
R. KLAVIR ET AL.
(Briskman, 1980; Besemer & O’Quin, 1993; Klavir & Hersh-
kovitz, 2008; Kleiman, 2005) and that the high order thinking
of gifted students is connected to high creative ability (Klavir &
Gorodetsky, 2009; Shye & Goldzweig 1999). Furthermore, the
present results give empirical support to the claim that the ex-
cellence of gifted students is reflected not only in their cogni-
tive ability (as it is measured by IQ tests) but also in their
higher readiness/ motivation to be involved in complex mis-
sions and in their higher creative ability to refine and produce
new products with high creative qualities. These results are in
coherence with the three-ring theory of Renzulli (1998) who
claims that behavior of the gifted is a combination of three
characteristics (rings): high general ability (intelligence), high
task commitment and high creativity.
Furthermore, the high readiness (motivation) of the gifted
students to get involved in the construction of analogical prob-
lems is in agreement with the claims in the literature as to the
features of populations that express readiness to get involved in
creative processes. Schunk & Pajares (2005) claim that “Indi-
viduals select tasks and activities in which they feel competent
and avoid those in which they do not. Unless people believe
that their actions will have the desired consequences, they have
little incentive to engage in those actions” (p. 87).
The Connection between Intellectual Giftedness and
Creativity—in Contextual Poin t of View
A more detailed analysis indicated that the creativity of the
gifted students was context dependent. The constructed ana-
logical “insight” problems (the mathematical as well as the
verbal) were more flexible, more appropriate and elaborated
and more original (Tables 2-4) than those of the “regulars”.
Moreover, 19% of the gifted students were found to construct
problems with a high cumulative creativity level in the insight-
mathematical problems and 21% in the insight-verbal problems,
whereas none of the “regular” student achieved such products
(Table 5). As to the constructed analogical mathematical prob-
lem no significant differences were found between both groups
that exhibited similar levels of creativity.
These results are congruent with the findings in the research
literature regarding the unique qualities of intellectually gifted
students as being competent in high-order logical and insightful
thinking. It is possible that for the gifted students the mathe-
matical, class-room like problem, was not perceived as a real
challenge. They did show a higher motivation than the “regu-
lars”, to construct an analogical problem but their predisposi-
tion towards the task was as towards a routine, conventional,
familiar and unchallenging assignment. In another study
(Gorodetsky & Klavir, 2003; Klavir & Gorodetsky, 2001) we
have provided gifted student with cartoons and analogical ver-
bal problems for solution. We have found that the cartoons
were more difficult for the gifted than the verbal problems. It
was only after the gifted realized that the cartoons are a kind of
problem and their predisposition towards the cartoons changed,
that their level of success increased.
Of course, it is also possible that the similar performance on
the mathematical problem of the gifted and the “regulars” stems
not from a decrease of that of the gifted but rather from a rela-
tive increase of that of the “regulars”. The increase in the “regu-
lars” creativity may stem from their familiarity with such class-
room encounters. The source problems and the worked out
analogous one were similar to other school mathematical prob-
lems that both groups probably came across in their studies.
Moreover, along their structured learning in school they proba-
bly learned to identify analogical problems, to map their rele-
vant analogical features (surface and deep structure components)
and the possibilities for transfer to new situations. This attune-
ment to the nature of analogical problems probably aided the
“regulars” in the construction of creative mathematical prob-
lems. These findings support the research results by Gentner et
al. (2003: p. 402) that the construction of schemes of the solu-
tion of analogical problems support transfer to new target prob-
Another possibility is that students’ dispositions towards the
mathematical familiar school problems was in favor of the
“regulars” in learning the worked out problems they have been
provided with. The acquired knowledge strengthened their mo-
tivation to get involved in the production of analogous prod-
The Connection between Intellectual Giftedness and
Creativity— a Comparison fr om a Rel a ti v e Poin t of
The creativity of the gifted students’ can be addressed from a
different point of view, not as compared to “regulars” but rela-
tively to themselves, i.e. as compared to the optimum that could
be achieved. Though a high percentage of gifted students ex-
pressed a higher motivation to get involved in the creative
process (in comparison to the “regulars”) and although the fea-
tures of creativity expressed in the constructed problem were
higher than those of the “regulars”, in fact their creativity was
not high. From the 232 gifted students in the initial group, only
142 students (61%) were ready to be involved in the creative
activity (graph no. 1). Furthermore, from this group (142 gifted
students) only 23 (16%) students constructed new problems of
a high cumulative creativity nature. As to their performance on
the specific creativity features only 58% of their products were
highly flexible, 38% were very original and 19% were appro-
priate and also highly elaborated (Figure 2). Thus, though the
gifted expressed a higher creativity as compared to the “regu-
lars”) their relative creativity seems to be quite disappointing.
The results encouraged us to attend to two different measures
of creativity: Comparative Creativity and Relative Creativity.
Comparative Creativity measures the creativity level of gifted
students in comparison to their “regular” peers, i.e. to what
extent are their products more flexible, appropriate & elabo-
rated and original. The results indeed indicate that on these
measures the intellectually gifted students are more creative
than “regular” students. Relative Creativity refers to the crea-
tivity level of the gifted students in comparison to the optimum
of themselves. Form this point of view the gifted students did
not perform on a high level. They did not exhibit a high moti-
vation to construct new problems not were the features of crea-
tivity of the constructed problem on an as optimal level.
Such a differentiation between two measures of creativity,
comparative and relative, may be the reason for some inconsis-
tencies in the research literature.
From the educational point of view, these results strongly
support the need for further educational investment in the gifted
students. It seems that for the development of creativity addi-
tional educational investments are in need. Baer & Kaufman
R. KLAVIR ET AL. 171
(2005) express such a need: “Finding the right conceptualiza-
tion of creativity matters in gifted education because develop-
ing students’ potential as creative thinkers is (or should be) one
of the most important goals of education” (p. 162). Thus pro-
gressive nurturing of gifted students is not only needed for “oc-
cupational” needs in the class-room, but it is essential for their
development as creative students. Education must make efforts
to nurture the creative abilities of gifted students towards their
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The Source Problems
The Insight-Non-Mathematical (Verbal) Problem
Mr. Keidar was the manager of the Sun Furniture Factory.
On Wednesday, at a management meeting, it was decided that
Mr. Keidar would travel to Amsterdam to sign a contract that
had recently been drawn up. The office staff heard about this
plan, and their gossip about this development leaked out, even-
tually finding its way to the ears of Sammy Cohen, the fac-
tory’s night watchman. Panic-stricken, Sammy hurried to the
office the next morning to meet with Mr. Keidar face-to-face.
“Mr. Keidar!” said Sammy, “I heard that you are going to
Amsterdam. Don’t do it! Please, Mr. Keidar, don’t do it! I had
a terrible dream! I dreamed about your trip to Amsterdam all
night long. In my dream, someone came up and shot you to
At that moment, the secretary came in and told Mr. Keidar
that if he wanted to be on time, he would have to hurry to Ben
Gurion Airport. Mr. Keidar paid no attention to his night
watchman’s dream, and traveled to Amsterdam, as planned.
A week later, Mr. Keidar returned from Amsterdam safe and
sound, with the contract signed. The first thing he did upon
returning to his office was to fire Sammy Cohen. Who made a
mistake here, and what was the mistake that led Mr. Keidar to
fire Sammy Cohen?
The Mathematical Problem
French, English, and Hebrew books were purchased for the
new library that was constructed next to the municipality
building. The Hebrew books, which comprised 3/5 of the total
number of books, were arranged on shelves on the ground floor.
The French books, which comprised 15% of the total, were
arranged on shelves on the top floor. The English books, which
comprised 3,500 fewer titles than the Hebrew books, were ar-
ranged on shelves on the middle floor. The average cost of a
Hebrew book was 5 shekels. The cost of a French book was 20
shekels, whereas the cost of an English book was 10 shekels.
What was the total cost of all the books purchased for the new
The Insight-Mathematical Problem
Oded, Ronnie, and Yair were tired and hungry after playing
football. They saw a restaurant on the corner, and went inside.
Oded ordered 10 buns, Ronnie ordered 8, and Yair, who was
the smallest, ordered only 6. Each of them paid for his order,
and they sat down together for the meal.
Suddenly, their cousin Youval showed up. He came directly
from swim practice and was also hungry. Oded, Ronnie, and
Yair invited Youval to sit down with them and to share their
buns with him, equally. Youval agreed, and they split the buns
equally among the four cousins.
When they had finished eating and chatting about sports,
Youval took out 24 shekels to cover the cost of his buns and
R. KLAVIR ET AL. 173
hurried home. Oded, Ronnie, and Yair wondered how to divide
the 24 shekels among themselves in the fairest way.
Examples for the Way of Analysi s of a New
Constructed Insight-Non-Mathematical (Verbal)
An Explained Example
A woman employed a nanny who took care of her baby
every day until she returned home from work. One day the
woman told her nanny that she wanted to go on vacation for a
few days. The next day the nanny advised the woman not to go
on vacation because the previous day, while the baby was
asleep and she was cleaning the neighbours' apartment, she
heard on the news that there was going to be a heat wave the
The woman immediately fired the nanny and deducted a
certain amount from her salary. Who made a mistake here and
what is the nature of the mistake?
1) Flexibility—high (different content and context): The
background to the story is different than the one in the original
problem (at home and relating to a nanny's job replacing the
furniture factory). The content variables are different: Instead
of failing in the duties of a night watchman, the new situation
addresses the nanny’s failure to perform her duties. The reason
for the journey was changed from business to vacation, and the
cause for postponing the journey was changed from assassina-
tion to a heat wave.
2) Appropriateness—high (relevant solution structure): Both
stories deal with workers that expose, unconsciously, their
misbehavior at work and consequently are dismissed by their
3) Elaboration—high (different solution structure): The so-
lution structure is not only relevant, but has also been restruc-
tured meaningfully. Both stories deal with workers who un-
consciously expose their misbehaviour at work and are conse-
quently dismissed by their employers. In addition, the deep
structure of the new problem is restructured meaningfully and
was removed from that of the source problem: the employer
(person B in the scheme below) deducted the payments from
the salary of the nanny (person A). The extended parts of the
deep structure of the solution are depicted in bold letters in the
4) Originality—high (very original): This was determined to
be high on originality since the majority of the judges identified
this problem as being unusual and unexpectedly unique in
comparison to the other newly constructed problems.
Some Additional Examples for the Analysis Process of the
Insight-Verbal New Constructed Problems
1) One day, Rami, a night watchman at a cookie factory,
heard that his manager, Mister “Cookie”, intended to travel to
Switzerland to clinch a deal in the realm of chocolates. Rami
rushed to ask him not to go because he had dreamed at night
Comparison between the solution structure of the source problem and
the solution struct ure of the new constructed problem.
The solution structure of the
the duty of person A is to exe-
person B is responsible, that
person A will execute X,
person A does not execute X,
he himself t ells that to person B,
person B knows that person A is
not perform in g hi s duty and may
The solution structure of the
new constru cted problem:
the duty of person A is to execute
person B is responsible, that per-
son A will execute X,
person A does not execute X,
person A receives payment for
executing X, and also for another
job that is executed during the
same time he was to execute X,
he himself t ells that to person B,
person B knows that person A is
not performing his duty and may
person B can deduct the payments
from the salary of person A.
that someone would murder him in Switzerland. In order to
convince the manager, he added that the secretary shared his
opinion. He told the manager that the secretary had told him
that two days before, when he, the manager, was out of the
factory, she had gone out to buy clothes, and she met someone
who told her about a friend of his who had been murdered in
Switzerland. The manager went to Switzerland and signed the
deal. When he returned he fired the night watchman and the
Flexibility: identical; Appropriateness: relevant; Elaborate-
ness: different; Originality: Partially-original.
2) A mechanic told his boss, the garage manager, that the car
that had been brought in for repair had already been checked by
him, and he had not found any mechanical problems. The
manager took the car and went to test it. When he came back,
he told the mechanic that he had found many mechanical prob-
lems, and fi red him immediately. Why?
Flexibility: different; Appropriateness: irrelevant; Elab-
orateness: Originality: not-original
3) In a hospital in the north, a physician was in charge of the
emergency room during the weekends. One day he heard that
Dr. Levi, the hospital manager, had to travel to Cairo to take
part in the International Medical Committee meeting there. The
ER doctor hurried to his boss, Dr. Levi, and tried to convince
him not to travel to Cairo because the previous Saturday, while
eating lunch in a restaurant with his family, he heard that it was
very dangerous in Cairo. Despite the story, Dr. Levi attended
the meeting. When he returned, he replaced the ER doctor dur-
ing weekends. Was this act justified?
Flexibility: different; Appropriateness: relevant; Elaborate-
ness: identical; Originality: partially-original.