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Exploring the relationships between analogical, analytical, and creative thinking
Thinking Skills and Creativity 13 (2014) 80–88
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Exploring the relationships between analogical, analytical, and creative thinking Chen-yao Kao ∗ Department of Special Education, National University of Tainan, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 26 October 2013 Received in revised form 18 March 2014 Accepted 25 March 2014 Available online 12 April 2014
Keywords: Analogical thinking Analytical thinking abilities Creative thinking A g factor Intelligence
a b s t r a c t The purpose of this research study was to examine the relationships between analogical, analytical, and creative thinking and other relevant issues through a carefully constructed and self-designed instrument. Participants were 287 six-graders living in an urban area of Taiwan. Major findings are shown as follows. Whereas three factors with larger-than-one eigenvalues were extracted, the g factor can be considered existing in the present study because the variance explained by the first principal factor was much larger than those explained by the other two. The two types of novel analogies were significantly and negatively correlated with each other. Analogical thinking straddles both the fields of analytical and creative thinking. Of the four analogy subscales, the traditional analogical-verbal section was most capable of predicting analytical thinking, creative thinking, and academic achievements. Discussions of the findings were presented in the context of the existing literature. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction Not merely a type of figurative language, analogy is currently considered the core of cognition (Gentner & Kurtz, 2006; Hofstadter, 2001). Analogy is ubiquitous but not many people notice its existence, much less its subtlety. Employing prior experiences in problem solving, learning through comparison (Gentner & Smith, 2012), and the case method in business (Gavetti & Rivkin, 2004) are all important instances of analogy. Gentner, Brem, Ferguson, Wolff, Markman, and Forbus (1997) also pointed out the usefulness of analogy in scientific inventions. Because of analogy’s importance and ubiquity, it is edifying to find out the relationships between analogical thinking and other kinds of thinking. However, there is a paucity of research that addresses this issue. The present study aimed to explore its relationships with analytical and creative thinking and relevant questions to add to the insufficient literature in this field. 1.1. What is analogy? Analogy is a process of establishing correspondences between concepts from different fields of knowledge (Doumas, Hummel, Sandhofer, 2008; Gentner & Smith, 2012). Technically, analogical thinking involves mapping two domains or situations and bringing across inferences from the more familiar domain to the less familiar domain. Mapping requires aligning two domains based on their commonalities. The two domains are referred to as analogs. Of the two domains, the
∗ Correspondence to: 33, Section 2, Shu Lin Street, Tainan, Taiwan, ROC. Tel.: +886 06 2133111x961; fax: +886 06 2130983. E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.tsc.2014.03.006 1871-1871/© 2014 Elsevier Ltd. All rights reserved.
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more familiar or concrete one is also called the base or source, while the less familiar or more abstract one is the target or topic. In general, bases help us explain or better understand targets, for inferences are drawn from bases to address targets (Gentner, 2010; Gentner & Smith, 2012). Moreover, it is the relational or structural similarity that analogical thinking depends on. Matching surface or obvious properties is not necessary for analogy. Analogical thinking can thus be succinctly defined as “the ability to perceive and use relational similarity (Gentner & Colhoun, 2010, p. 35). Analogies differ tremendously in their content, appearance, and usage (Gentner & Smith, 2012). Nonetheless, most of them follow some principles. The principle of one-to-one correspondence denotes that each element in the base is mapped to one and only one element in the target. The connectivity principle suggests that if two predicates or relations are matched, their arguments also correspond with each other (Gentner, 2010). The systematicity principle indicates people’s tendency to choose large, deeply interconnected systems during merge processes, rather than isolated coincidental matches. In other words, when more than one possible interpretation is derived from a certain analogy, the more systematic interpretation is favored. “Our desire for systematicity reflects an implicit preference for analogies that are highly informative and have inferential power” (Gentner & Smith, 2012, p. 132). 1.2. Analogy and analytical thinking Traditional intelligence tests are mainly assessments of analytical thinking abilities (Sternberg, 2003a). From the fact that analogy items are frequently used in the IQ test, we can assume that analogical and analytical thinking are closely related. The standard structure of the analogy test items in the multiple-choice format is A:B = C:D (e.g., Glove is to hand as sock is to foot). According to Sternberg (2002, 2006), analytical thinking involves abilities to (1) take apart a problem and understand its parts, (2) explain the functioning of a system, the reasons why something happens, or the procedures of solving a problem, (3) compare and contrast two or more things, or (4) evaluate and critique the characteristics of something. Obviously, comparison is integral to analytical thinking. On the other hand, comparison is also a signature mechanism in the analogical thinking because during comparison a process of alignment occurs between two represented situations, whereby the common relational structure is made more salient (Gentner, 2010). 1.3. Analogy and creative thinking Analogical thinking is a key process in problem solving and scientific discoveries (Gentner & Smith, 2012). Gentner et al. (1997) made a good use of the works of Kepler to illuminate the processes whereby analogy brings about creativity and changes in knowledge. They continued to argue that distant analogies Kepler used many times could develop a new framework in a certain domain or even form a new domain (e.g., the new science of astrophysics formed by Kepler). In contrast, local or close analogies could be used to fill in a framework in a rather well agreed-on field. As implied in the description above, the more distant the analogies, the more creative the outcomes. Analogical thinking is the pivot of many theories of creativity. Mednick’s (1962) associative theory is an exemplar, which points out that creativity entails a particular sort of response, bringing together apparently irrelevant or remote ideas. As described earlier, analogy is a process of establishing correspondences between concepts from different domains. “Bringing together” can be seen as establishing correspondences or mapping and “irrelevant or remote ideas” can be viewed as concepts coming from different domains. In other words, Mednick’s associative theory refers to transcending surface similarities and identifying a common relational system between two seemingly different domains. Likewise, Koestler (1978) proposed the term bisociation—“perceiving a situation or event in two mutually exclusive associative contexts” (p. 130). This term was coined to distinguish the inflexible thinking fixed on a single plane from the creative thinking operating on more than one plane. The highest level of creative achievement is represented by “the endeavor to bridge the gap between the two planes” (p. 146). “To bridge the gap” can be regarded as establishing a common relational structure through mapping and “two planes” as two domains or analogs. Furthermore, analogy is the mainstay of Gordon’s (1961) synectics, which includes four kinds of analogical methods (i.e., direct, personal, fantasy, and symbolic analogy) applied in problem solving. 1.4. Creative and analytical thinking Creativity and intelligence, which is primarily measured by analytical thinking abilities, are in general regarded as different constructs with a small amount of overlap (Kaufman & Plucker, 2011; Kim, Cramond, & VanTassel-Baska, 2010). According to his own research findings, Cropley (1968) contended that creativity and intelligence are two independent psychological constructs. Torrance (1980) noted low correlations between creativity and intelligence scores. Similarly, Renzulli (1986) makes distinction between schoolhouse giftedness and creative/productive giftedness, based on high intellectual and creative abilities, respectively. As pointed out in Batey and Furnham’s (2006) literature review, IQ can just explain less than 10% of the variance in creativity scores. In a meta-analysis on the relationship between creativity and intelligence conducted by Kim (2005), an average weighted effect size of r = .174 was proposed. However, several creativity researchers, like Silvia and Beaty (2012) and Nusbaum and Silvia (2011), argued that the relationship between creativity and cognitive abilities was underestimated and needed to be revisited. If the argument that overlap between creativity and intelligence is minor is correct, an exploratory factor analysis (EFA) on the test scores concerning both analytical and creative abilities may not result in a predominant first factor (a g factor).
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Carroll (1993) pointed out two major types of creativity, fluency and originality. He also suggested that separate tests for fluency and originality should be provided to make a proper distinction between these two factors. Fluency tests primarily aim at the “quantitative” aspect of creativity because its focus is on great numbers of ideas. On the other hand, originality tests are targeted at the “qualitative” aspect of creativity because its emphasis is on whether ideas possess characteristics of being unusual, novel, and unique. Batey and Furnham (2006) contended that fluency is more closely related to intelligence of the two factors because producing a large number of ideas relies on fluid intelligence (gf), which is in turn based on neural efficiency. On the other hand, originality is more tightly connected to such personality factors as openness to experience and psychoticism. Nonetheless, their argument is inconsistent with Wallach’s (1970) presumption and the findings of the research study conducted by Kershner and Ledger (1985). Wallach mentioned that only fluency is the true measure of divergent thinking and that flexibility, originality, and elaboration basically provided measures of IQ. Comparing the scores of 30 gifted children aged 9–11 with matched controls on IQ and divergent thinking tests, Kershner and Ledger found that the verbal originality scores were greatly affected by IQ. As also demonstrated by their research results, gifted children did not obtain significantly higher scores than average children on figural flexibility and fluency tests. The findings implied that the scores of originality were dependent on IQ but the scores of fluency and flexibility were relatively independent of IQ. The inconsistency above entails further examination on the relationships between two types of creativity and analytical thinking, the backbone of the IQ tests. Based on the literature review above, the following questions guided this research. How many factors with a largerthan-one eigenvalue can be extracted from an EFA on the scores of the test items built on analogical, analytical, and creative thinking? Does the EFA yield a g factor? Does analogical thinking have a higher correlation with analytical thinking or creative thinking? What are the respective relations of fluency and originality tests to analytical thinking? 2. Method 2.1. Participants Three hundred 6th graders were recruited from two municipal elementary schools located in an urban area of Taiwan. Of the 300 participants, 287 students (152 male students and 135 female students) completed all the subtests. Only the data collected from these students were analyzed. Their mean age was 11 years and 10 months (SD = 5 months). The two schools were supportive of this study and helped the researcher obtain consent from the students and their parents. 2.2. Materials To test the delicate relationships between analogical, analytical and creative thinking, a self-designed instrument containing nine parts was used in this study. The first two parts of the instrument were the analytical-verbal section and the analytical-quantitative section, both of which were in the multiple-choice format. Part 1 included 12 items, which required choosing the most suitable word or phrase that could be placed in the blank to make the meaning of the passage complete. Part 2 included 10 items, which required discovering the rule which governed a series of numbers and then figuring out what number should come next in the series. Basically, the first two parts were typical tests for analytical thinking and their items were highly g-loaded. The raw scores of the two sections were converted into two t-scores, which in turn were added up to form the composite score of analytical thinking. Part 3, the analogical-figural section, and Part 4, the analogical-verbal section, were traditional analogy tests in the multiple-choice format. Part 3 included 10 items, which required choosing the shape that went with the shape in the bottom row in the same way that the shapes in the top row went together. Part 4 was comprised of 12 items, which required choosing the word that went with the third underlined word in the same way that the first two went together. Part 5 consisted of 20 novel analogy items in the multiple-choice format. The concept of the novel analogy items was borrowed from the Sternberg Triarchic Abilities Test (STAT). Each novel analogy item followed a counterfactual premise or a “pretend” statement (e.g., Noise can be smelled). Test-takers had to suppose that this statement was true and then solved the following analogy question (Sternberg, Castejón, Prieto, Hautamäki, & Grigorenko, 2001). Novel analogies can be categorized into Type 1 and Type 2 novel analogy items. Type I items (Example 1) are novel analogy questions with a counterfactual premise which does NOT influence the choice of correct answers. Type II items (Example 2) are novel analogy questions with a counterfactual premise which influences the choice of correct answers. Accordingly, Part 5 was further divided into Part 5-1 and Part 5-2, which included Type I and Type II novel analogy items, respectively. In the STAT, Type I and Type II analogy items are mixed in the creative-verbal section and not scored separately. However, in the present study, Type I and Type II analogy items yielded two respective scores. Example 1.
Chimneys are transparent.
Window is to wall as chimney is to . A. glass B. smoke
Example 2.
C. brick
D. roof
Meters are the basic unit for measuring time.
Carat is to diamond as meter is to A. distance
. B. length
C. scale
D. cycle
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Part 6, 7, 8, and 9 were creativity tests in the non-multiple-choice format. At Carroll’s (1993) suggestion, the fluency test and the originality test were separated. Part 6 was composed of two items, which were used to explore test-takers’ verbal creativity ability and focused on the element of fluency. One of the two questions in this section required test-takers to write down as many uses of towels as possible except for drying body parts. The other included a “pretend” situation (Schools exchanged the in-class and between-class time) and test-takers needed to write down as many consequences as possible. The major scoring criterion for this part was the number of meaningful responses. The six items in Part 7 were created by the researcher, theoretically based on Janusian thinking proposed by Rothenberg (1971). Janusian thinking is defined as a creative process that actively conceives “two or more opposite or antithetical concepts, ideas or images simultaneously” (Rothenberg, 1978, p. 175). Janusian thinking is one of a limited number of theories regarding creative thinking processes that is supported by clinical and experimental evidence. Rothenberg (1990) consider it a major mental operation that “distinguishes creative persons from the rest of us” (p. 11). This part was used to explore test-takers’ verbal creativity ability and focused on the element of originality. According to Rothenberg (1990), bringing together opposite concepts can produce an effect of novelty, which causes audience surprise or even shock. The example of this subscale is shown as follows and the answer provided is just for reference. The major scoring criterion was the degree to which each response reflected the meaning of the two antonyms. DIRECTIONS: Please complete the following sentences. There are no standard answers to the blanks. However, your answers need to reflect the meaning of the two underlined antonyms in the sentences. Try your best to make your answers meaningful and original. . Bad habits are both easy and difficult because Bad habits are both easy and difficult because they are easy to get but hard to give up.
Part 8 contained a large number of U-shaped figures, which test-takers needed to use as basis to develop as many pictures as possible. This part was used to assess test-takers’ figural creativity ability and focused on the element of fluency. The primary scoring criterion for this part was the number of meaningful responses. Part 9 comprised four figures, which test-takers needed to use as basis to develop four original pictures. Adapted from Torrance’s TTCT, Part 9 was used to measure test-takers’ figural creativity ability and focused on the element of originality. The main scoring criteria for this part included newness, openness, asymmetry, complexity, unusual visualization, and the profundity of titles. The raw scores of Parts 6, 7, 8 and 9 were converted into four t-scores, which in turn were added up to form the composite score of creative thinking.
2.3. Procedure The test was conducted during regular school hours as an enrichment activity, within the normal context of classes. Because of the hectic schedule of elementary schools in this urban area, two class sessions, with 40 min each session, were allowed for administration of the test. Because of this pragmatic constraint, the test was designed to fit into two class sessions, and every subtest was strictly timed. The test was shorter than the researcher wanted. In addition, to avoid the negative effect of fatigue, the test was administered in two separate class sessions, rather than two consecutive sessions. Parts 1–5 were completed in the first session, and Parts 6–9 in the second session. To implement a standardized administration process, an administration guideline for the test was created for the test administrators to follow. The test was administered by the teachers of these two schools. After the test administration was completed, the participants’ grades of the previous semester were also collected. To minimize the effects of different grading criteria used by two schools, each participant’ semester grade was converted to a t-score on the basis of the same-school participants’ grades.
3. Results 3.1. Reliabilities The internal reliabilities were .709 for Part 1 (12 analytical-verbal items), .757 for Part 2 (10 analytical-quantitative items), and .798 for Part 3 (10 analogical-figural items), .644 for Part 4 (12 traditional analogy items), .805 for Part 5-1 (10 Type I novel analogy items), and .907 for Part 5-2 (10 Type II novel analogy items). The multiple-choice test items were screened by a traditional item analysis before being used in the present study. The inter-rater reliabilities were .901 for Part 6, .960 for Part 7, .924 for Part 8 and, .902 for Part 9. The raters were composed of two graduate research assistants. Before formally engaging in scoring, they were given three training sessions for their scoring. Guidelines for scoring non-multiple-choice items were developed before rating. The final score of each non-multiple-choice test item was the average of the scores given by the two raters.
3.2. Descriptive statistics Table 1 shows the descriptive statistics of the raw scores of subscales. The raw full scores for Parts 1, 2, 3, 4, 5-1, 5-2, and 7 were 12, 10, 10, 12, 10, 10, and 18, respectively. Parts 6, 8 and 9 did not impose limitations on the full mark.
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Table 1 Descriptive statistics.
Part 1 Part 2 Part 3 Part 4 Part 5-1 Part 5-2 Part 6 Part 7 Part 8 Part 9
M
SD
10.33 5.08 7.50 7.22 7.87 3.32 5.36 7.09 6.63 28.29
1.79 2.60 2.45 2.43 2.40 3.46 2.94 3.56 2.93 7.42
Table 2 Correlations between IQ, analogy, and creativity. Part 3 Part 3 Part 4 Part 5-1 Part 5-2 Analysis Creativity
Part 4
Part 5-1
Part 5-2
Analysis
Creativity
.422**
.202** .247**
.223** .320** −.310**
.567** .583** .238** .280**
.250** .406** .188** .158** .384**
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking * p < 0.5. ** p < 0.01
3.3. The results of EFA An EFA was conducted on all the subscale scores and the result indicated that three factors whose eigenvalues were larger than 1 emerged. Eigenvalues for the first three factors were 3.689 (36.889% of total variance), 1.392 (13.918%), and 1.236 (12.365%). The total variance explained by the three factors amounted to 62.547%. A clear break in eigenvalue sizes was shown between the first and second factors, thereby suggesting that a g factor (the first factor) emerged. 3.4. Test correlations Table 2 shows the correlations between the composite scores of analytical and creative thinking and the scores of Part 3, 4, 5-1, and 5-2. As indicated by the correlation matrix, Part 5-1 was significantly and negatively correlated with Part 5-2 (r = −.310). Parts 3, 4, 5-1, and 5-2 were all significantly correlated with analytical and creative thinking, with their correlations with analytical thinking (.567, .583, .238, and .280) being stronger than those with creative thinking (.250, .406, .188, and.158). Of the four analogy subscales, the traditional analogical-verbal one had the highest correlation with both analytical and creative thinking. In addition, the correlation between the composite analytical t-score and the composite creative t-score was .384 (p = .000). The percentage of the variance of creative thinking explained by analytical thinking was the r-squared value, 14.746%. Table 3 shows the partial correlations between the composite score of creative thinking and four analogy subscales with the variance due to the composite score of analytical thinking removed. The partial correlations were significant for the analogical-verbal subscale (Part 4) but non-significant for the analogical-figural subscale (Part 3), the Type I novel analogy subscale (Part 5-1), and the Type II novel analogy subscale (Part 5-2). The analogical-verbal subscale score can significantly predict the composite score of creative thinking, independent of the composite score of analytical thinking; however, the other three subscale scores cannot. Table 4 shows the partial correlations between the composite score of analytical thinking and four analogy subscales with the variance due to the composite score of creative thinking partialled out. The partial Table 3 Partial correlations between analogy and creativity. Controlled variable Analysis
Creativity Part 3 Part 4 Part 5-1 Part 5-2
.43 .243** .108 .057
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking. * p < 0.5. ** p < 0.01.
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Table 4 Partial correlations between analogy and analysis. Controlled variable
Analysis
Creativity
.527** .506** .183** .241**
Part 3 Part 4 Part 5-1 Part 5-2
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking. * p < 0.5. ** p < 0.01 Table 5 Correlations between analysis and creativity subscales. Analysis Analysis Part 6 Part 7 Part 8 Part 9
Part 6
Part 7
Part 8
Part 9
.383**
.487** .522**
.267** .420** .460**
.166** .254** .412** .365**
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking. * p < 0.5. ** p < 0.01.
correlations were significant for all the four analogy subscales. The four analogy subscale scores are significant predictors of the composite score of analytical thinking, independent of the composite score of creative thinking. Table 5 shows the correlations between the composite score of analytical thinking and four creativity subscales (Parts 6, 7, 8, and 9). The verbal creativity subscale focused on originality had a higher correlation with analytical thinking than did the verbal creativity subscale focused on fluency. However, the figural creativity subscale focused on originality had a lower correlation with analytical thinking than did the figural creativity subscale focused on fluency. In addition, significant pairwise correlations between Parts 6, 7, 8, and 9 were computed. 3.5. A stepwise multiple regression Table 6 demonstrates the results of a stepwise multiple regression analysis with the semester grade as a criterion variable and with the composite analytical t-score and the composite creative t-score as predictors. As indicated, the composite creative t-score significantly predicted academic achievement, independent of the composite analytical t-score. Table 7 demonstrates the results of a stepwise multiple regression analysis with the semester grade as a criterion variable and with the composite analytical t-score, the composite creative t-score, and the scores of traditional and novel analogies (Part 3, 4, 5-1, and 5-2) as predictors. As indicated, the scores of traditional analogical-verbal (Part 4) and analogical-figural (Part3) sections significantly predicted academic achievement, independent of the composite analytical t-score. 4. Discussion In this study, three factors with larger-than-one eigenvalues emerged from an EFA on all the subtest scores. The first factor, which was much larger than the rest of the factors, can be regarded as a g factor. It explained 36.889% of the total variance, much lower than the percentage of the variance explained by the first principal factor reported by Koke and Vernon (2003), 51.4%, and Brody (2003), 89%. The variance explained by g fluctuates dramatically due to different measures or scoring criteria employed in assessment. The more heterogeneous the ability measures, the lower the percentage of the Table 6 Results of a stepwise multiple regression (including analysis and creativity). Variables entered
Beta
R square
Adjusted R square
R square change
F change
Sig. F change
Analysis Creativity
.626 .109
.446 .456
.444 .452
.446 .010
227.182 5.223
.000 .023
Table 7 Results of a stepwise multiple regression (including analysis, creativity, and four analogies). Variables entered
Beta
R square
Adjusted R square
R square change
F change
Sig. F change
Analysis Traditional analogical-verbal Traditional analogical-figural
.445 .236 .153
.446 .490 .506
.444 .486 .500
.446 .044 .016
227.182 24.099 8.900
.000 .000 .003
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variance explained by g. It is not uncommon that the g factor can only account for less than half of the variance between measures, which is the case with this study. This unsatisfactory percentage of the variance explained by g leaves intelligence researchers to surmise that other principal factors may exist in parallel with the g factor. Further research is needed to investigate the wide fluctuation of the variance explained by g. The two types of novel analogy items were correlated with each other significantly and negatively. In his previous studies, the researcher tested the homogeneity of the novel analogy items, with Type I and II mixed together, and fixed the number of extracted factors at one. Five items had striking negative factor loadings, which were Type II analogy items. This intriguing result implies that these two types of analogy items in the multiple-choice format may be subsumed under different factors. In a subsequent study, these two types were scored separately and the two scores were correlated with each other significantly and negatively. In the current study, the significant and negative correlation between the two types of novel analogy items was found again. This recurrent finding implied that it was inappropriate of Sternberg et al. (2001) to mix these two types of analogy items in one section and compute a total score. Meanwhile, this finding contradicts the statement of Koke and Vernon (2003) that all mental abilities were positively related. As Sternberg (2003b) noted, some test-wiseness skills underlay multiple-choice tests and made them significantly correlate with each other. Later on, Sternberg (2006, 2010) continued to point out that multiple-choice test items all loaded substantially on a single g-like or analytical factor irrespective of what they were intended to assess. Obviously, the finding is also inconsistent with Sternberg’s claims. In addition, since these two types of analogy were in the verbal form, their negative correlation failed to espouse Gardner’s (2006) contention that verbal demands brought about artificially high correlations among ability tests. The reason for the negative correlation between these two types of novel analogy items may be that the analogy test items with a premise impacting the choice of correct answers demand replacing the original feature by a new one and integrating it into the relational reasoning of the following question. On the other hand, the analogy test items with a premise NOT impacting the choice of correct answers require avoiding or inhibiting interference from irrelevant or inapt features in the process of alignment (Silvia & Beaty, 2012). Integration and avoidance are in different directions. Further studies on these two types of novel analogy items can benefit our understanding of intelligence and creativity. In addition, the four analogy tests were significantly correlated with both analytical and creative thinking, with their correlations with analytical thinking higher than those with creative thinking. This result indicated that analogy was related to both analytical and analogical thinking, with more impact from analytical thinking. Moreover, the analogical-verbal subscale score significantly predicted the composite score of creative thinking, independent of analytical thinking. On the other hand, the four analogy subscale scores significantly predicted the composite score of analytical thinking, independent of creative thinking. It is noteworthy that the traditional analogical-verbal subscale has the strongest power to predict both analytical and creative thinking among the four analogy subscales. The variance of creative thinking explained by analytical thinking in this study was 14.746%. This percentage is again lower than those reported by Silvia and Beaty (2012), 24.3% and by Batey, Chamorro-Premuzic, and Furnham (2009), 17%. As Silvia and Beaty (2012) contended, newer measures of creativity would produce a larger effect of intelligence on creativity. In fact, it is not newness of creativity measures that matters but homogeneity. In their study, metaphor production scores were used as a criterion variable. Metaphor and analogy are very similar in essence because they both can be viewed as cross-domain mapping or alignment (Bowdle & Gentner, 2005; Lackoff, 1992). As aforementioned, analogy involves both analytical and creative thinking, so a substantial contribution of fluid intelligence to the quality of creative metaphors in Silvia and Beaty’s study is a conceivable corollary. The results of the present study basically support the argument that intelligence and creativity are two different constructs with small overlap. In this study, the verbal creativity subscale focused on originality had a higher correlation with analytical thinking than did verbal creativity subscale focused on fluency. However, the figural creativity subscale focused on originality had a lower correlation with analytical thinking than did figural creativity subscale focused on fluency. These results do not support either Batey and Furnham’s (2006) argument or Kershner and Ledger’s (1985) findings. In addition, the result of significant pairwise correlations between two verbal and two figural creativity tests is not congruent with Carroll’s (1993) and Clapham’s (2004) argument that verbal and figural creativity tests are not significantly correlated with each other. These inconsistencies may result from different creativity measures or scoring criteria. The creativity scoring criteria associated with emotion and personality, which are considered non-cognitive, can influence the correlations between creativity and intelligence (or analytical thinking) and those between creativity tests themselves (Gardner, 2006). The stepwise multiple regression analysis including the semester grade (a criterion variable), the composite analytical t-score (a predictor), and the composite creative t-score (a predictor) indicated that the composite creative t-score could significantly predict the semester grade, independent of the composite analytical t-score. This result upholds the argument that creativity performance can explain the variance of academic achievement over and above IQ. As shown in a largescale study conducted by Sternberg (2006), creativity measures significantly augment the SAT in predicting college GPA. However, when the four analogy subscale scores were added to the previous stepwise multiple regression analysis as predictors, the composite creative t-score no longer significantly predicted the semester grade. It was the analogical-verbal and analogical-figural subscale scores that significantly predicted the semester grade, independent of analytical thinking. As implied, it is useful to use the analogical-verbal and analogical-figural tests to explain the variance of academic achievement.
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5. Limitations In this study, the participating schools could only spare two classes for the administration of the test due to the busy schedule of the schools in Taiwan. Because of the limited time for testing, existing instruments for analogical, analytical, and creative thinking were not suitable for use. A self-designed instrument was instead carefully constructed to accommodate this pragmatic constraint. To address the demands of reliability and validity, the multiple-choice items went through such traditional item analysis procedures as examination of the item difficulty and discrimination, the item-total statistics, the item communality and factor loadings, etc. and all the test items were reviewed by two statistics and measurement experts. 6. Conclusion This research study pioneered an examination on the relationships between analogical, analytical, and creative thinking. As shown by the results, analogical thinking straddles both the fields of analytical and creative thinking. Compared with the other three analogy subscales, the traditional analogical-verbal section is more capable of predicting analytical thinking, creative thinking, and academic achievements. Analogy items have great potential of identifying the students with needs for special services and enriching the instructional activities designed to promote not only analytical but also creative thinking. In addition, the specific mechanisms related to creative thinking in analogical thinking need further investigation. Acknowledgement I am very grateful for financial support from the National Science Council, Taiwan (NSC101-2410-H-024-008-MY2). References Batey, M., & Furnham, A. (2006). Creativity, intelligence, and personality: A critical review of the scattered literature. Genetic, Social, and General Psychology Monograph, 132(4), 355–429. Batey, M., Chamorro-Premuzic, T., & Furnham, A. 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Can only intelligent people be creative? A meta-analysis. Journal of Secondary Gifted Education, 16, 57–66. Kim, K. H., Cramond, B., & VanTassel-Baska, J. (2010). The relationship between creativity and intelligence. In J. C. Kauffman, & R. J. Sternberg (Eds.), The Cambridge handbook of creativity (pp. 395–412). New York: Cambridge University Press. Koestler, A. (1978). Janus. New York: Random House. Koke, L. C., & Vernon, P. A. (2003). The Sternberg Triarchic Abilities Test (STAT) as a measure of academic achievement and general intelligence. Personality and Individual Differences, 35, 1803–1807. Lackoff, G. (1992). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor and thought (2nd ed., pp. 1–51). New York: Cambridge University Press. Mednick, S. A. (1962). The associative basis of the creative process. Psychological Review, 69, 220–232. Nusbaum, E. C., & Silvia, P. J. (2011). Are creativity and intelligence really so different? Fluid intelligence, executive processes, and strategy use in divergent thinking. Intelligence, 39, 36–45. Renzulli, J. S. (1986). The three-ring conception of giftedness: A developmental model for creative productivity. In R. J. Sternberg, & J. E. Davidson (Eds.), Conceptions of giftedness (pp. 53–92). Cambridge, England: Cambridge University Press. Rothenberg, A. (1971). The process of Janusian thinking in creativity. Archives of General Psychiatry, 24, 195–205. Rothenberg, A. (1978). Translogical secondary process cognition in creativity. Altered States of Consciousness, 4(2), 171–187. Rothenberg, A. (1990). The emerging goddess: The creative process in art, science, and other fields. Chicago, IL: The University of Chicago Press. Silvia, P. J., & Beaty, R. E. (2012). Making creative metaphors: The importance of fluid intelligence for creative thought. Intelligence, 40(4), 343–351. Sternberg, R. J., Castejón, J. L., Prieto, M. D., Hautamäki, J., & Grigorenko, E. L. (2001). 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Chen-yao Kao is currently a full professor of the Department of Special Education at the National University of Tainan, Taiwan. He teaches the graduate and undergraduate courses regarding gifted education, multiple intelligences and creativity. His research interests include socio-emotional issues of gifted adolescents, creative thinking processes, multiple intelligences, and curriculum and instruction for gifted students.
Contents lists available at ScienceDirect
Thinking Skills and Creativity journal homepage: http://www.elsevier.com/locate/tsc
Exploring the relationships between analogical, analytical, and creative thinking Chen-yao Kao ∗ Department of Special Education, National University of Tainan, Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 26 October 2013 Received in revised form 18 March 2014 Accepted 25 March 2014 Available online 12 April 2014
Keywords: Analogical thinking Analytical thinking abilities Creative thinking A g factor Intelligence
a b s t r a c t The purpose of this research study was to examine the relationships between analogical, analytical, and creative thinking and other relevant issues through a carefully constructed and self-designed instrument. Participants were 287 six-graders living in an urban area of Taiwan. Major findings are shown as follows. Whereas three factors with larger-than-one eigenvalues were extracted, the g factor can be considered existing in the present study because the variance explained by the first principal factor was much larger than those explained by the other two. The two types of novel analogies were significantly and negatively correlated with each other. Analogical thinking straddles both the fields of analytical and creative thinking. Of the four analogy subscales, the traditional analogical-verbal section was most capable of predicting analytical thinking, creative thinking, and academic achievements. Discussions of the findings were presented in the context of the existing literature. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction Not merely a type of figurative language, analogy is currently considered the core of cognition (Gentner & Kurtz, 2006; Hofstadter, 2001). Analogy is ubiquitous but not many people notice its existence, much less its subtlety. Employing prior experiences in problem solving, learning through comparison (Gentner & Smith, 2012), and the case method in business (Gavetti & Rivkin, 2004) are all important instances of analogy. Gentner, Brem, Ferguson, Wolff, Markman, and Forbus (1997) also pointed out the usefulness of analogy in scientific inventions. Because of analogy’s importance and ubiquity, it is edifying to find out the relationships between analogical thinking and other kinds of thinking. However, there is a paucity of research that addresses this issue. The present study aimed to explore its relationships with analytical and creative thinking and relevant questions to add to the insufficient literature in this field. 1.1. What is analogy? Analogy is a process of establishing correspondences between concepts from different fields of knowledge (Doumas, Hummel, Sandhofer, 2008; Gentner & Smith, 2012). Technically, analogical thinking involves mapping two domains or situations and bringing across inferences from the more familiar domain to the less familiar domain. Mapping requires aligning two domains based on their commonalities. The two domains are referred to as analogs. Of the two domains, the
∗ Correspondence to: 33, Section 2, Shu Lin Street, Tainan, Taiwan, ROC. Tel.: +886 06 2133111x961; fax: +886 06 2130983. E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.tsc.2014.03.006 1871-1871/© 2014 Elsevier Ltd. All rights reserved.
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more familiar or concrete one is also called the base or source, while the less familiar or more abstract one is the target or topic. In general, bases help us explain or better understand targets, for inferences are drawn from bases to address targets (Gentner, 2010; Gentner & Smith, 2012). Moreover, it is the relational or structural similarity that analogical thinking depends on. Matching surface or obvious properties is not necessary for analogy. Analogical thinking can thus be succinctly defined as “the ability to perceive and use relational similarity (Gentner & Colhoun, 2010, p. 35). Analogies differ tremendously in their content, appearance, and usage (Gentner & Smith, 2012). Nonetheless, most of them follow some principles. The principle of one-to-one correspondence denotes that each element in the base is mapped to one and only one element in the target. The connectivity principle suggests that if two predicates or relations are matched, their arguments also correspond with each other (Gentner, 2010). The systematicity principle indicates people’s tendency to choose large, deeply interconnected systems during merge processes, rather than isolated coincidental matches. In other words, when more than one possible interpretation is derived from a certain analogy, the more systematic interpretation is favored. “Our desire for systematicity reflects an implicit preference for analogies that are highly informative and have inferential power” (Gentner & Smith, 2012, p. 132). 1.2. Analogy and analytical thinking Traditional intelligence tests are mainly assessments of analytical thinking abilities (Sternberg, 2003a). From the fact that analogy items are frequently used in the IQ test, we can assume that analogical and analytical thinking are closely related. The standard structure of the analogy test items in the multiple-choice format is A:B = C:D (e.g., Glove is to hand as sock is to foot). According to Sternberg (2002, 2006), analytical thinking involves abilities to (1) take apart a problem and understand its parts, (2) explain the functioning of a system, the reasons why something happens, or the procedures of solving a problem, (3) compare and contrast two or more things, or (4) evaluate and critique the characteristics of something. Obviously, comparison is integral to analytical thinking. On the other hand, comparison is also a signature mechanism in the analogical thinking because during comparison a process of alignment occurs between two represented situations, whereby the common relational structure is made more salient (Gentner, 2010). 1.3. Analogy and creative thinking Analogical thinking is a key process in problem solving and scientific discoveries (Gentner & Smith, 2012). Gentner et al. (1997) made a good use of the works of Kepler to illuminate the processes whereby analogy brings about creativity and changes in knowledge. They continued to argue that distant analogies Kepler used many times could develop a new framework in a certain domain or even form a new domain (e.g., the new science of astrophysics formed by Kepler). In contrast, local or close analogies could be used to fill in a framework in a rather well agreed-on field. As implied in the description above, the more distant the analogies, the more creative the outcomes. Analogical thinking is the pivot of many theories of creativity. Mednick’s (1962) associative theory is an exemplar, which points out that creativity entails a particular sort of response, bringing together apparently irrelevant or remote ideas. As described earlier, analogy is a process of establishing correspondences between concepts from different domains. “Bringing together” can be seen as establishing correspondences or mapping and “irrelevant or remote ideas” can be viewed as concepts coming from different domains. In other words, Mednick’s associative theory refers to transcending surface similarities and identifying a common relational system between two seemingly different domains. Likewise, Koestler (1978) proposed the term bisociation—“perceiving a situation or event in two mutually exclusive associative contexts” (p. 130). This term was coined to distinguish the inflexible thinking fixed on a single plane from the creative thinking operating on more than one plane. The highest level of creative achievement is represented by “the endeavor to bridge the gap between the two planes” (p. 146). “To bridge the gap” can be regarded as establishing a common relational structure through mapping and “two planes” as two domains or analogs. Furthermore, analogy is the mainstay of Gordon’s (1961) synectics, which includes four kinds of analogical methods (i.e., direct, personal, fantasy, and symbolic analogy) applied in problem solving. 1.4. Creative and analytical thinking Creativity and intelligence, which is primarily measured by analytical thinking abilities, are in general regarded as different constructs with a small amount of overlap (Kaufman & Plucker, 2011; Kim, Cramond, & VanTassel-Baska, 2010). According to his own research findings, Cropley (1968) contended that creativity and intelligence are two independent psychological constructs. Torrance (1980) noted low correlations between creativity and intelligence scores. Similarly, Renzulli (1986) makes distinction between schoolhouse giftedness and creative/productive giftedness, based on high intellectual and creative abilities, respectively. As pointed out in Batey and Furnham’s (2006) literature review, IQ can just explain less than 10% of the variance in creativity scores. In a meta-analysis on the relationship between creativity and intelligence conducted by Kim (2005), an average weighted effect size of r = .174 was proposed. However, several creativity researchers, like Silvia and Beaty (2012) and Nusbaum and Silvia (2011), argued that the relationship between creativity and cognitive abilities was underestimated and needed to be revisited. If the argument that overlap between creativity and intelligence is minor is correct, an exploratory factor analysis (EFA) on the test scores concerning both analytical and creative abilities may not result in a predominant first factor (a g factor).
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Carroll (1993) pointed out two major types of creativity, fluency and originality. He also suggested that separate tests for fluency and originality should be provided to make a proper distinction between these two factors. Fluency tests primarily aim at the “quantitative” aspect of creativity because its focus is on great numbers of ideas. On the other hand, originality tests are targeted at the “qualitative” aspect of creativity because its emphasis is on whether ideas possess characteristics of being unusual, novel, and unique. Batey and Furnham (2006) contended that fluency is more closely related to intelligence of the two factors because producing a large number of ideas relies on fluid intelligence (gf), which is in turn based on neural efficiency. On the other hand, originality is more tightly connected to such personality factors as openness to experience and psychoticism. Nonetheless, their argument is inconsistent with Wallach’s (1970) presumption and the findings of the research study conducted by Kershner and Ledger (1985). Wallach mentioned that only fluency is the true measure of divergent thinking and that flexibility, originality, and elaboration basically provided measures of IQ. Comparing the scores of 30 gifted children aged 9–11 with matched controls on IQ and divergent thinking tests, Kershner and Ledger found that the verbal originality scores were greatly affected by IQ. As also demonstrated by their research results, gifted children did not obtain significantly higher scores than average children on figural flexibility and fluency tests. The findings implied that the scores of originality were dependent on IQ but the scores of fluency and flexibility were relatively independent of IQ. The inconsistency above entails further examination on the relationships between two types of creativity and analytical thinking, the backbone of the IQ tests. Based on the literature review above, the following questions guided this research. How many factors with a largerthan-one eigenvalue can be extracted from an EFA on the scores of the test items built on analogical, analytical, and creative thinking? Does the EFA yield a g factor? Does analogical thinking have a higher correlation with analytical thinking or creative thinking? What are the respective relations of fluency and originality tests to analytical thinking? 2. Method 2.1. Participants Three hundred 6th graders were recruited from two municipal elementary schools located in an urban area of Taiwan. Of the 300 participants, 287 students (152 male students and 135 female students) completed all the subtests. Only the data collected from these students were analyzed. Their mean age was 11 years and 10 months (SD = 5 months). The two schools were supportive of this study and helped the researcher obtain consent from the students and their parents. 2.2. Materials To test the delicate relationships between analogical, analytical and creative thinking, a self-designed instrument containing nine parts was used in this study. The first two parts of the instrument were the analytical-verbal section and the analytical-quantitative section, both of which were in the multiple-choice format. Part 1 included 12 items, which required choosing the most suitable word or phrase that could be placed in the blank to make the meaning of the passage complete. Part 2 included 10 items, which required discovering the rule which governed a series of numbers and then figuring out what number should come next in the series. Basically, the first two parts were typical tests for analytical thinking and their items were highly g-loaded. The raw scores of the two sections were converted into two t-scores, which in turn were added up to form the composite score of analytical thinking. Part 3, the analogical-figural section, and Part 4, the analogical-verbal section, were traditional analogy tests in the multiple-choice format. Part 3 included 10 items, which required choosing the shape that went with the shape in the bottom row in the same way that the shapes in the top row went together. Part 4 was comprised of 12 items, which required choosing the word that went with the third underlined word in the same way that the first two went together. Part 5 consisted of 20 novel analogy items in the multiple-choice format. The concept of the novel analogy items was borrowed from the Sternberg Triarchic Abilities Test (STAT). Each novel analogy item followed a counterfactual premise or a “pretend” statement (e.g., Noise can be smelled). Test-takers had to suppose that this statement was true and then solved the following analogy question (Sternberg, Castejón, Prieto, Hautamäki, & Grigorenko, 2001). Novel analogies can be categorized into Type 1 and Type 2 novel analogy items. Type I items (Example 1) are novel analogy questions with a counterfactual premise which does NOT influence the choice of correct answers. Type II items (Example 2) are novel analogy questions with a counterfactual premise which influences the choice of correct answers. Accordingly, Part 5 was further divided into Part 5-1 and Part 5-2, which included Type I and Type II novel analogy items, respectively. In the STAT, Type I and Type II analogy items are mixed in the creative-verbal section and not scored separately. However, in the present study, Type I and Type II analogy items yielded two respective scores. Example 1.
Chimneys are transparent.
Window is to wall as chimney is to . A. glass B. smoke
Example 2.
C. brick
D. roof
Meters are the basic unit for measuring time.
Carat is to diamond as meter is to A. distance
. B. length
C. scale
D. cycle
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Part 6, 7, 8, and 9 were creativity tests in the non-multiple-choice format. At Carroll’s (1993) suggestion, the fluency test and the originality test were separated. Part 6 was composed of two items, which were used to explore test-takers’ verbal creativity ability and focused on the element of fluency. One of the two questions in this section required test-takers to write down as many uses of towels as possible except for drying body parts. The other included a “pretend” situation (Schools exchanged the in-class and between-class time) and test-takers needed to write down as many consequences as possible. The major scoring criterion for this part was the number of meaningful responses. The six items in Part 7 were created by the researcher, theoretically based on Janusian thinking proposed by Rothenberg (1971). Janusian thinking is defined as a creative process that actively conceives “two or more opposite or antithetical concepts, ideas or images simultaneously” (Rothenberg, 1978, p. 175). Janusian thinking is one of a limited number of theories regarding creative thinking processes that is supported by clinical and experimental evidence. Rothenberg (1990) consider it a major mental operation that “distinguishes creative persons from the rest of us” (p. 11). This part was used to explore test-takers’ verbal creativity ability and focused on the element of originality. According to Rothenberg (1990), bringing together opposite concepts can produce an effect of novelty, which causes audience surprise or even shock. The example of this subscale is shown as follows and the answer provided is just for reference. The major scoring criterion was the degree to which each response reflected the meaning of the two antonyms. DIRECTIONS: Please complete the following sentences. There are no standard answers to the blanks. However, your answers need to reflect the meaning of the two underlined antonyms in the sentences. Try your best to make your answers meaningful and original. . Bad habits are both easy and difficult because Bad habits are both easy and difficult because they are easy to get but hard to give up.
Part 8 contained a large number of U-shaped figures, which test-takers needed to use as basis to develop as many pictures as possible. This part was used to assess test-takers’ figural creativity ability and focused on the element of fluency. The primary scoring criterion for this part was the number of meaningful responses. Part 9 comprised four figures, which test-takers needed to use as basis to develop four original pictures. Adapted from Torrance’s TTCT, Part 9 was used to measure test-takers’ figural creativity ability and focused on the element of originality. The main scoring criteria for this part included newness, openness, asymmetry, complexity, unusual visualization, and the profundity of titles. The raw scores of Parts 6, 7, 8 and 9 were converted into four t-scores, which in turn were added up to form the composite score of creative thinking.
2.3. Procedure The test was conducted during regular school hours as an enrichment activity, within the normal context of classes. Because of the hectic schedule of elementary schools in this urban area, two class sessions, with 40 min each session, were allowed for administration of the test. Because of this pragmatic constraint, the test was designed to fit into two class sessions, and every subtest was strictly timed. The test was shorter than the researcher wanted. In addition, to avoid the negative effect of fatigue, the test was administered in two separate class sessions, rather than two consecutive sessions. Parts 1–5 were completed in the first session, and Parts 6–9 in the second session. To implement a standardized administration process, an administration guideline for the test was created for the test administrators to follow. The test was administered by the teachers of these two schools. After the test administration was completed, the participants’ grades of the previous semester were also collected. To minimize the effects of different grading criteria used by two schools, each participant’ semester grade was converted to a t-score on the basis of the same-school participants’ grades.
3. Results 3.1. Reliabilities The internal reliabilities were .709 for Part 1 (12 analytical-verbal items), .757 for Part 2 (10 analytical-quantitative items), and .798 for Part 3 (10 analogical-figural items), .644 for Part 4 (12 traditional analogy items), .805 for Part 5-1 (10 Type I novel analogy items), and .907 for Part 5-2 (10 Type II novel analogy items). The multiple-choice test items were screened by a traditional item analysis before being used in the present study. The inter-rater reliabilities were .901 for Part 6, .960 for Part 7, .924 for Part 8 and, .902 for Part 9. The raters were composed of two graduate research assistants. Before formally engaging in scoring, they were given three training sessions for their scoring. Guidelines for scoring non-multiple-choice items were developed before rating. The final score of each non-multiple-choice test item was the average of the scores given by the two raters.
3.2. Descriptive statistics Table 1 shows the descriptive statistics of the raw scores of subscales. The raw full scores for Parts 1, 2, 3, 4, 5-1, 5-2, and 7 were 12, 10, 10, 12, 10, 10, and 18, respectively. Parts 6, 8 and 9 did not impose limitations on the full mark.
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Table 1 Descriptive statistics.
Part 1 Part 2 Part 3 Part 4 Part 5-1 Part 5-2 Part 6 Part 7 Part 8 Part 9
M
SD
10.33 5.08 7.50 7.22 7.87 3.32 5.36 7.09 6.63 28.29
1.79 2.60 2.45 2.43 2.40 3.46 2.94 3.56 2.93 7.42
Table 2 Correlations between IQ, analogy, and creativity. Part 3 Part 3 Part 4 Part 5-1 Part 5-2 Analysis Creativity
Part 4
Part 5-1
Part 5-2
Analysis
Creativity
.422**
.202** .247**
.223** .320** −.310**
.567** .583** .238** .280**
.250** .406** .188** .158** .384**
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking * p < 0.5. ** p < 0.01
3.3. The results of EFA An EFA was conducted on all the subscale scores and the result indicated that three factors whose eigenvalues were larger than 1 emerged. Eigenvalues for the first three factors were 3.689 (36.889% of total variance), 1.392 (13.918%), and 1.236 (12.365%). The total variance explained by the three factors amounted to 62.547%. A clear break in eigenvalue sizes was shown between the first and second factors, thereby suggesting that a g factor (the first factor) emerged. 3.4. Test correlations Table 2 shows the correlations between the composite scores of analytical and creative thinking and the scores of Part 3, 4, 5-1, and 5-2. As indicated by the correlation matrix, Part 5-1 was significantly and negatively correlated with Part 5-2 (r = −.310). Parts 3, 4, 5-1, and 5-2 were all significantly correlated with analytical and creative thinking, with their correlations with analytical thinking (.567, .583, .238, and .280) being stronger than those with creative thinking (.250, .406, .188, and.158). Of the four analogy subscales, the traditional analogical-verbal one had the highest correlation with both analytical and creative thinking. In addition, the correlation between the composite analytical t-score and the composite creative t-score was .384 (p = .000). The percentage of the variance of creative thinking explained by analytical thinking was the r-squared value, 14.746%. Table 3 shows the partial correlations between the composite score of creative thinking and four analogy subscales with the variance due to the composite score of analytical thinking removed. The partial correlations were significant for the analogical-verbal subscale (Part 4) but non-significant for the analogical-figural subscale (Part 3), the Type I novel analogy subscale (Part 5-1), and the Type II novel analogy subscale (Part 5-2). The analogical-verbal subscale score can significantly predict the composite score of creative thinking, independent of the composite score of analytical thinking; however, the other three subscale scores cannot. Table 4 shows the partial correlations between the composite score of analytical thinking and four analogy subscales with the variance due to the composite score of creative thinking partialled out. The partial Table 3 Partial correlations between analogy and creativity. Controlled variable Analysis
Creativity Part 3 Part 4 Part 5-1 Part 5-2
.43 .243** .108 .057
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking. * p < 0.5. ** p < 0.01.
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Table 4 Partial correlations between analogy and analysis. Controlled variable
Analysis
Creativity
.527** .506** .183** .241**
Part 3 Part 4 Part 5-1 Part 5-2
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking. * p < 0.5. ** p < 0.01 Table 5 Correlations between analysis and creativity subscales. Analysis Analysis Part 6 Part 7 Part 8 Part 9
Part 6
Part 7
Part 8
Part 9
.383**
.487** .522**
.267** .420** .460**
.166** .254** .412** .365**
Note: Analysis = the composite score of analytical thinking; Creativity = the composite score of creative thinking. * p < 0.5. ** p < 0.01.
correlations were significant for all the four analogy subscales. The four analogy subscale scores are significant predictors of the composite score of analytical thinking, independent of the composite score of creative thinking. Table 5 shows the correlations between the composite score of analytical thinking and four creativity subscales (Parts 6, 7, 8, and 9). The verbal creativity subscale focused on originality had a higher correlation with analytical thinking than did the verbal creativity subscale focused on fluency. However, the figural creativity subscale focused on originality had a lower correlation with analytical thinking than did the figural creativity subscale focused on fluency. In addition, significant pairwise correlations between Parts 6, 7, 8, and 9 were computed. 3.5. A stepwise multiple regression Table 6 demonstrates the results of a stepwise multiple regression analysis with the semester grade as a criterion variable and with the composite analytical t-score and the composite creative t-score as predictors. As indicated, the composite creative t-score significantly predicted academic achievement, independent of the composite analytical t-score. Table 7 demonstrates the results of a stepwise multiple regression analysis with the semester grade as a criterion variable and with the composite analytical t-score, the composite creative t-score, and the scores of traditional and novel analogies (Part 3, 4, 5-1, and 5-2) as predictors. As indicated, the scores of traditional analogical-verbal (Part 4) and analogical-figural (Part3) sections significantly predicted academic achievement, independent of the composite analytical t-score. 4. Discussion In this study, three factors with larger-than-one eigenvalues emerged from an EFA on all the subtest scores. The first factor, which was much larger than the rest of the factors, can be regarded as a g factor. It explained 36.889% of the total variance, much lower than the percentage of the variance explained by the first principal factor reported by Koke and Vernon (2003), 51.4%, and Brody (2003), 89%. The variance explained by g fluctuates dramatically due to different measures or scoring criteria employed in assessment. The more heterogeneous the ability measures, the lower the percentage of the Table 6 Results of a stepwise multiple regression (including analysis and creativity). Variables entered
Beta
R square
Adjusted R square
R square change
F change
Sig. F change
Analysis Creativity
.626 .109
.446 .456
.444 .452
.446 .010
227.182 5.223
.000 .023
Table 7 Results of a stepwise multiple regression (including analysis, creativity, and four analogies). Variables entered
Beta
R square
Adjusted R square
R square change
F change
Sig. F change
Analysis Traditional analogical-verbal Traditional analogical-figural
.445 .236 .153
.446 .490 .506
.444 .486 .500
.446 .044 .016
227.182 24.099 8.900
.000 .000 .003
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variance explained by g. It is not uncommon that the g factor can only account for less than half of the variance between measures, which is the case with this study. This unsatisfactory percentage of the variance explained by g leaves intelligence researchers to surmise that other principal factors may exist in parallel with the g factor. Further research is needed to investigate the wide fluctuation of the variance explained by g. The two types of novel analogy items were correlated with each other significantly and negatively. In his previous studies, the researcher tested the homogeneity of the novel analogy items, with Type I and II mixed together, and fixed the number of extracted factors at one. Five items had striking negative factor loadings, which were Type II analogy items. This intriguing result implies that these two types of analogy items in the multiple-choice format may be subsumed under different factors. In a subsequent study, these two types were scored separately and the two scores were correlated with each other significantly and negatively. In the current study, the significant and negative correlation between the two types of novel analogy items was found again. This recurrent finding implied that it was inappropriate of Sternberg et al. (2001) to mix these two types of analogy items in one section and compute a total score. Meanwhile, this finding contradicts the statement of Koke and Vernon (2003) that all mental abilities were positively related. As Sternberg (2003b) noted, some test-wiseness skills underlay multiple-choice tests and made them significantly correlate with each other. Later on, Sternberg (2006, 2010) continued to point out that multiple-choice test items all loaded substantially on a single g-like or analytical factor irrespective of what they were intended to assess. Obviously, the finding is also inconsistent with Sternberg’s claims. In addition, since these two types of analogy were in the verbal form, their negative correlation failed to espouse Gardner’s (2006) contention that verbal demands brought about artificially high correlations among ability tests. The reason for the negative correlation between these two types of novel analogy items may be that the analogy test items with a premise impacting the choice of correct answers demand replacing the original feature by a new one and integrating it into the relational reasoning of the following question. On the other hand, the analogy test items with a premise NOT impacting the choice of correct answers require avoiding or inhibiting interference from irrelevant or inapt features in the process of alignment (Silvia & Beaty, 2012). Integration and avoidance are in different directions. Further studies on these two types of novel analogy items can benefit our understanding of intelligence and creativity. In addition, the four analogy tests were significantly correlated with both analytical and creative thinking, with their correlations with analytical thinking higher than those with creative thinking. This result indicated that analogy was related to both analytical and analogical thinking, with more impact from analytical thinking. Moreover, the analogical-verbal subscale score significantly predicted the composite score of creative thinking, independent of analytical thinking. On the other hand, the four analogy subscale scores significantly predicted the composite score of analytical thinking, independent of creative thinking. It is noteworthy that the traditional analogical-verbal subscale has the strongest power to predict both analytical and creative thinking among the four analogy subscales. The variance of creative thinking explained by analytical thinking in this study was 14.746%. This percentage is again lower than those reported by Silvia and Beaty (2012), 24.3% and by Batey, Chamorro-Premuzic, and Furnham (2009), 17%. As Silvia and Beaty (2012) contended, newer measures of creativity would produce a larger effect of intelligence on creativity. In fact, it is not newness of creativity measures that matters but homogeneity. In their study, metaphor production scores were used as a criterion variable. Metaphor and analogy are very similar in essence because they both can be viewed as cross-domain mapping or alignment (Bowdle & Gentner, 2005; Lackoff, 1992). As aforementioned, analogy involves both analytical and creative thinking, so a substantial contribution of fluid intelligence to the quality of creative metaphors in Silvia and Beaty’s study is a conceivable corollary. The results of the present study basically support the argument that intelligence and creativity are two different constructs with small overlap. In this study, the verbal creativity subscale focused on originality had a higher correlation with analytical thinking than did verbal creativity subscale focused on fluency. However, the figural creativity subscale focused on originality had a lower correlation with analytical thinking than did figural creativity subscale focused on fluency. These results do not support either Batey and Furnham’s (2006) argument or Kershner and Ledger’s (1985) findings. In addition, the result of significant pairwise correlations between two verbal and two figural creativity tests is not congruent with Carroll’s (1993) and Clapham’s (2004) argument that verbal and figural creativity tests are not significantly correlated with each other. These inconsistencies may result from different creativity measures or scoring criteria. The creativity scoring criteria associated with emotion and personality, which are considered non-cognitive, can influence the correlations between creativity and intelligence (or analytical thinking) and those between creativity tests themselves (Gardner, 2006). The stepwise multiple regression analysis including the semester grade (a criterion variable), the composite analytical t-score (a predictor), and the composite creative t-score (a predictor) indicated that the composite creative t-score could significantly predict the semester grade, independent of the composite analytical t-score. This result upholds the argument that creativity performance can explain the variance of academic achievement over and above IQ. As shown in a largescale study conducted by Sternberg (2006), creativity measures significantly augment the SAT in predicting college GPA. However, when the four analogy subscale scores were added to the previous stepwise multiple regression analysis as predictors, the composite creative t-score no longer significantly predicted the semester grade. It was the analogical-verbal and analogical-figural subscale scores that significantly predicted the semester grade, independent of analytical thinking. As implied, it is useful to use the analogical-verbal and analogical-figural tests to explain the variance of academic achievement.
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5. Limitations In this study, the participating schools could only spare two classes for the administration of the test due to the busy schedule of the schools in Taiwan. Because of the limited time for testing, existing instruments for analogical, analytical, and creative thinking were not suitable for use. A self-designed instrument was instead carefully constructed to accommodate this pragmatic constraint. To address the demands of reliability and validity, the multiple-choice items went through such traditional item analysis procedures as examination of the item difficulty and discrimination, the item-total statistics, the item communality and factor loadings, etc. and all the test items were reviewed by two statistics and measurement experts. 6. Conclusion This research study pioneered an examination on the relationships between analogical, analytical, and creative thinking. As shown by the results, analogical thinking straddles both the fields of analytical and creative thinking. Compared with the other three analogy subscales, the traditional analogical-verbal section is more capable of predicting analytical thinking, creative thinking, and academic achievements. Analogy items have great potential of identifying the students with needs for special services and enriching the instructional activities designed to promote not only analytical but also creative thinking. In addition, the specific mechanisms related to creative thinking in analogical thinking need further investigation. Acknowledgement I am very grateful for financial support from the National Science Council, Taiwan (NSC101-2410-H-024-008-MY2). References Batey, M., & Furnham, A. (2006). Creativity, intelligence, and personality: A critical review of the scattered literature. Genetic, Social, and General Psychology Monograph, 132(4), 355–429. Batey, M., Chamorro-Premuzic, T., & Furnham, A. 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Chen-yao Kao is currently a full professor of the Department of Special Education at the National University of Tainan, Taiwan. He teaches the graduate and undergraduate courses regarding gifted education, multiple intelligences and creativity. His research interests include socio-emotional issues of gifted adolescents, creative thinking processes, multiple intelligences, and curriculum and instruction for gifted students.