From pentagon to triangle: a cross-cultural investigation of an implicit theory of giftedness. (International Perspectives).

Confucius's philosophy of education, "You Jiao Wu Lei," is found in Chapter XXXVIII of the Confucian Analects (see Legge, 1970). Originally, this phrase means that in teaching, there should be no distinction of classes. In modern time, it has also been interpreted as inclusive education. For thousands of years, this philosophy of education has exerted great influence upon Chinese education, and it has also been one of the major forces shaping the implicit theories of giftedness in China.

Nearly two decades after its inception in mainland China, gifted education is still very limited. There are still no policies on or institutions for the education and training of gifted students. As noted by Stevenson (1998), despite the interest of the Chinese governments, both at the national and provincial levels, in providing gifted students with special educational opportunities, the gifted programs mainly served secondary school students. Furthermore, only a small percentage of students were enrolled in programs or classes for gifted students. Stevenson also predicted that there would be no great expansion of gifted programs in the near future.

Given that China, with the largest population on earth, has such underdeveloped gifted programs, it makes sense to understand the Chinese people's conceptions of giftedness. Moreover, because teachers are usually the ones making decisions on which child should be enrolled in a gifted program, it is their conceptions of giftedness that need to be examined, yet, no such study has been conducted in mainland China.

Studies on conceptions of giftedness have been abundant elsewhere in the world (e.g., Buckley, 1994; Busse, Dahme, Wagner, & Wieczerkowski, 1986; Lee, 1999; McBride, 1988; Persson, 1997; Rohrer, 1995; Solow, 1999; Wellisch, 1997; Wolfe & Southern, 1991; Yang & Sternberg, 1997). Most focused on teachers' or parents' conceptions of giftedness. For example, after interviewing 16 teachers, Lee concluded that teachers perceived giftedness as a series of conceptions: excellence, potential, rarity, behavior, innate ability, motivation, and asynchrony. Solow studied four parents of intellectually gifted students from different family backgrounds and found that these parents focused on more than just their children's intellects. They also viewed their children's giftedness in emotional, humanistic, moral, social, and spiritual terms.

The common goal in the above studies was to understand people's implicit theories of giftedness. Implicit theories are not public or formal. Rather, they are intellectual constructions residing in the minds of individuals (Sternberg, 1985a; Sternberg, Conway, Ketron, & Bernstein, 1981) and are discovered by questions and inference and are often revealed by behavior.

The importance of understanding people's implicit theories of giftedness cannot be overemphasized. Sternberg and Zhang (1995; also see Zhang & Sternberg, 1998) proposed five reasons for understanding people's conceptions or implicit theories of giftedness. For example, Sternberg and Zhang argued that people's generalized implicit theories of giftedness determine how decisions about identification of gifted students are made. In addition, Solow (1999) noted that there was evidence that parents' implicit theories of giftedness influenced their behavior toward, and decision making about, their children.

The Pentagonal Implicit Theory of Giftedness

Sternberg and Zhang (1995) proposed a pentagonal implicit theory of giftedness in which there are five criteria that are individually necessary and jointly sufficient for a student to be identified as gifted. The first criterion is excellence--one must be superior in some dimension or set of dimensions. The second criterion is rarity--the excellence must be relative to peers, not just to any comparison group. If every one in a peer group were judged to do superior work (criterion 1), no one would stand out as gifted. The third criterion is demonstrability--the superiority of the individual on the dimension(s) that determine(s) giftedness must be demonstrable through at least one test that is valid. The fourth criterion is productivity--the dimension(s) along which the individual is evaluated as superior must lead to or potentially lead to productivity. The fifth criterion for a person to be viewed as gifted is value--the superior performance shown by a person must be along a dimension that is valued by his or her society.

The pentagonal implicit theory of giftedness has been operationalized through a test (see the section on measures), which was administered to three different groups of people. A first group was 24 students at Yale University. A second group was 39 parents of gifted children in Connecticut. A final group was 72 in-service and preservice teachers from the University of Hong Kong. Results from multiple-regression analyses suggested that there was a good fit between the pentagonal model and the data collected from all three groups of research participants. All three groups of participants used the five specified criteria when they identified individuals as gifted (Sternberg & Zhang, 1995; Zhang & Sternberg, 1998). However, it should be noted that all three groups of participants believed that only they themselves would take demonstrability (i.e., test validity, criterion 3) into consideration whereas schools would not take demonstrability into account when making judgment about giftedness. Furthermore, almost identical results were obtained from the United States and from Hong Kong except that in Hong Kong (Zhang & Sternberg) participants took productivity into account more for boys than for girls.

The Present Study

The present study extends the previous work based on the pentagonal model with an investigation of a group of preservice teachers from mainland China. The major aim here was to find out if the pentagonal implicit theory can be validated among this population. Apart from cross-cultural validation of the pentagonal theory, there are at least three good reasons for conducting the present research. First, previous work related to the pentagonal theory did not control variables that could have easily affected the participants' conceptions of giftedness. The present study controlled such variables as participants' gender, age, self-rated abilities, and socioeconomic status. Second, an investigation of a group of preservice teachers in China is particularly important, as such research participants are future teachers and some of them may become policy makers for the education of the gifted and talented in China. The way they define giftedness is most likely to affect the way they make policies about identification of, curricula for, and instruction of gifted students. As Kelly (1970) argued, perceptions drive actions. Third, as mentioned earlier, gifted education in mainland China, a country with the largest population in the world, is still in its infancy. If the concept of giftedness were to become increasingly important in education, a first and most important task is to understand people's conceptions of giftedness.

No specific hypothesis was made in the present study. However, given that definitions of giftedness may vary across time, culture, and even persons within a culture (Csikszentmihalyi & Robinson, 1986; Hunsaker, 1995; Yang & Sternberg, 1997), it was anticipated that the results from mainland China would be different from those found in the United States and Hong Kong.

Method

Participants

One hundred and eighty-nine (74 male and 115 female) second year students from China Central Teachers' University volunteered to participate in this research. The participants' ages ranged from 18 to 23, with an average of 20 years. Participants were studying natural sciences, social sciences, and humanities.

Measures

The original inventory (Sternberg & Zhang, 1995) assessing the pentagonal model was based on the five criteria of giftedness described earlier. Participants are asked to indicate the extent to which each of the criteria of the model contributed to their judgment, and to what they believe to be the judgment of their schools, in labeling children as gifted.

The questionnaire is composed of 60 cases, each describing a child. Each case consists of six statements. The first statement is based on the "excellence" criterion, the second on "rarity," the third on "demonstrability," the fifth on "productivity," the fourth and sixth on "value." Each of these statements carries a pre-assigned value of the extent to which it satisfies the corresponding criterion. Furthermore, each case involves a different hypothetical test. The names of the tests were invented. These different tests are of five types: achievement, creativity, intelligence, motivation, and social skills. The number of tests of each type is the same. There are two forms of the same inventory, one with hypothetical children given male names (Boys' Form) and the other with hypothetical children given female names (Girls' Form).

Participants are asked to read each case and to rate on a Likert scale (from 1 to 6, with 1 = poor, and 6 = superior) the likelihood that the child involved would be identified as gifted, both from the participants' own viewpoint (my judgment) and from their perception of their school's viewpoint. Here is a sample case:

1. Alice's score on the Hunter Creativity Test was excellent.

2. This score was in the top 5% of her school.

3. The Hunter Creativity Test has been found to be accurate in predicting gifted performance for 60% of students.

4. The school considers the Hunter Creativity Test to be a fair measure of giftedness.

5. Alice submitted 3 independent projects.

6. The school believes that independent projects are an excellent measure of giftedness.

My judgment (3) School judgment (4)

The first 30 cases were translated and back-translated between Chinese and English and were employed in the present study. The reduction of cases was in order to fit testing into the time available. In the Chinese version of the inventory, Western names are replaced by names that are common in the Chinese culture so that each case looks more authentic and that the participants have Chinese children in mind when evaluating the cases. The 30 cases were balanced across the five types of tests and across the pre-assigned values. Among the 189 participants, 93 responded to the Boys' Form and 96 responded to the Girls' Form of the questionnaire.

To cross-validate the finding that preservice teachers took more than just excellence into account in their judgment of giftedness, a simple questionnaire (added to the end of the 30 cases) was administered. This questionnaire was also included with prior groups of research participants. The participants were asked to rate, on a 6-point Likert scale, how reliable they thought each of the six kinds of tests and each of the six kinds of products are for use in identifying gifted students. The six kinds of tests are intelligence, creativity, motivation, academic achievement, social skills, and curiosity tests. The six kinds of products are art projects, athletic prizes, essays, science projects, debating prizes, and performing arts prizes, which are common products in Chinese schools.

Apart from responding to the 30 cases assessing the pentagonal implicit theory of giftedness and the simple questionnaire on the tests and products, the participants also rated themselves on a 10-point Likert scale about their abilities (analytical, creative, and practical abilities, Sternberg, 1985b). Furthermore, data on the participants' socioeconomic status (as measured by family income level) were also collected.

Data Analysis

First, the consistency of the research participants in rating the 30 cases was examined. Following that, group differences in mean rating on the 30 cases were examined based on the participants' gender, age, family income level, and on their self-rated analytical, creative, and practical abilities. A multiple-regression analysis was conducted to find out the extent to which these preservice teachers took into account the five criteria specified in the pentagonal model when they made judgments about school children's giftedness. Raw data on the simple questionnaire about the 6 kinds of tests and 6 kinds of products were converted into 12 homogeneous subgroups and compared independently. The results are structured this way because the present study focuses not on how each individual participant rated the tests and products, but on how this whole sample rated the tests and products and on any significant difference in the rating of the tests and products.

Results

Reliability

The Cronbach alpha coefficients for "my judgment" and "school judgment" of the 30 cases are .85 and .77, respectively. These data on internal consistency were considered sufficiently high for conducting the remaining statistical analyses.

T-Test and One way ANOVA 

Results from t-test and one way ANOVA indicated that research participants did not significantly differ in making judgments about giftedness as a function of participants' age, gender, family income level, and self-rated abilities. Table 1 presents the summary statistics of these analyses.

Multiple-Regression Analysis

Results from the multiple-regression analysis were both similar to and different from those found in Sternberg and Zhang's (1995) study of American university students and parents of gifted students and those found in Zhang and Sternberg's (1998) study of Hong Kong in-service and preservice teachers. To facilitate comparison, Table 2 reproduces the results from the two previous studies and includes the results of the present study.

The results of the multiple-regression analysis only lent partial support to the pentagonal model. Support for the pentagonal model would derive from statistically significant [R.sub.2] and statistically significant [beta] weights corresponding to each of the criteria.

As shown in Table 2, there are both similarities and differences among findings from the three different cultures (the U.S., Hong Kong, and mainland China). The major similarity is that for all three cultural groups, the excellence, productivity, and value criteria showed statistically significant [beta] weights in all the multiple regressions (with the exception of Hong Kong participants who did not take productivity into account in their judgment of giftedness for girls). The major difference is that whereas all five criteria resulted in significant [beta] weights in the U.S. and Hong Kong data sets, the criteria rarity and demonstrability did not enter the regression models at all in the mainland China data set. It should be noted, however, that the [beta] weights for demonstrability were not statistically significant for the "school judgment" in any of the previous research participating groups, either, including the U.S. university students, the parents of gifted children, and the Hong Kong preservice and in-service teachers.

Means for Homogeneous Subgroups

Tests on the 12 homogenous subgroups (6 kinds of tests and 6 kinds of products) resulted in significant differences. A Tukey post-hoc test indicated that the participants rated creativity tests (M = 4.80), science projects (M = 4.44), and curiosity tests (M = 4.17) as significantly more reliable in the identification of gifted students than they did intelligence tests (M = 3.84). In addition, participants rated achievement tests as one of the bottom 3 kinds of tests/products of the 12 (M = 3.11 for achievement tests, M = 2.93 for performing arts prizes, and M = 2.53 for athletic prizes). Table 3 presents the results of this test. This finding confirmed the ones obtained from using the pentagonal model in the sense that these preservice teachers perceived products as equally, if not more, important than tests in making judgments about giftedness.

Discussion

A primary goal of this study was to examine the validity of the pentagonal implicit theory of giftedness among preservice teachers in mainland China. Results indicated that these in-service teachers held a triangular, rather than a pentagonal, implicit theory of giftedness. The two angles that the present data did not capture are rarity and demonstrability. These results were obtained when the following variables were taken into account: participants' age, gender, family income level, and their self-rated abilities.

The fact that these in-service teachers considered at least 3 of the 5 criteria in the pentagonal model in making judgments of giftedness suggests that there is a certain amount of cross-cultural generality in people's conceptions of giftedness. As acknowledged in our previous work (Zhang & Sternberg, 1998), each of the five criteria in the pentagonal model can be identified in other implicit theories of giftedness. For instance, virtually every theory of giftedness, explicit or implicit, takes excellence into account. The productivity criterion also can be found in the work of many scholars (e.g., Abra & Valentine-French, 1991; Feldhusen & Hoover, 1986; Lee, 1999; Tannenbaum, 1983). The value criterion is best embodied in the work of Hunsaker (1995). Therefore, the present finding regarding the excellence, productivity, and value criteria lent support to both theoretical arguments and empirical research in the literature.

However, in the literature, the other two criteria (rarity and demonstrability) were also given much attention in the evaluation of giftedness. For example, rarity has been suggested to be important in the definition of giftedness by a number of theorists and researchers (e.g., Feldhusen & Hoover, 1986; Lee, 1999; Sternberg, 1993; Tannenbaum, 1983). The demonstrability criterion (or validity of tests) also has been addressed in the literature, although not many works have been identified (e.g., Abra & Valentine-French, 1991).

As mentioned earlier, research participants in previous studies (Sternberg & Zhang, 1995; Zhang & Sternberg, 1998) took all five criteria into account when they evaluated giftedness. However, again, one exception should be noted. Participants in both previous studies thought that, even though they themselves took the validity of tests (demonstrability) into consideration, their schools would not. In the present study, the demonstrability criterion did not enter the regression model at all. Neither the participants themselves took it into account nor did the participants think that the schools would take it into account. Thus, it seems justified to say that test validity tends to be ignored by people from all samples of research participants investigated so far using the pentagonal model. Furthermore, the prevailing perception is that schools tend to ignore test validity.

One possible explanation of the fact that participants tended not to consider test validity in their judgment of giftedness is that participants may think that gifted students should score high on all sorts of tests, no matter what the tests are. In fact, this explanation has been confirmed by a group of 11 in-service teachers in Hong Kong during an informal interview. This tendency to de-emphasize test validity is, indeed, not unusual. Even though there has been much concern in the literature regarding the misuse of tests, especially the use of tests that are not valid, using invalid tests remains a problem (see Abra & Valentine-French, 1991; Dellas & Gaier, 1970; Hickcox, 1995).

However, not taking rarity into account in the evaluation of giftedness seems to be less common. Data collected from the three cultures using the pentagonal model indicated that the mainland Chinese group was the only group of participants who did not think that rarity is an important criterion for being gifted. Perhaps the philosophical basis for Chinese education, that is, Confucianism, offers an explanation. The Confucian view of intellectual giftedness, according to Chen, Seitz, and Cheng (1991), can be stated as follows:

   The essence of Confucianism is to provide all the people
   with an education that includes both basic knowledge
   and moral precepts so that all individuals can
   develop their own capabilities to their utmost and
   become leaders in society. (p.316)

Stevenson (1998) further commented that in Chinese culture there is no elite group whose status or privileges are defined in terms of intellectual superiority. In fact, according to Analects, Confucius never spoke of prodigies (Waley, 1989). Therefore, it is not surprising that the preservice Chinese teachers in this research did not perceive the rarity criterion as a necessary condition for being gifted.

However, it should be noted that the present study controlled such variables as participants' age, gender, socioeconomic status, and self-rated abilities, whereas no such control was done in the previous studies of American and Hong Kong participants. Therefore, the different results obtained from the different studies render them suggestive rather than conclusive. Further research needs to be conducted to verify cross-cultural differences in people's conceptions of giftedness.

Implications

This study investigated the implicit theory of giftedness of preservice teachers in China. Because these preservice teachers will become part of the in-service teacher workforce in the near future, the research participants' views of giftedness may have important implications for education in China. We discuss four of these implications.

First, participants' responses to the pentagonal inventory and their rating of the 6 types of tests and 6 types of products consistently showed that these preservice teachers did take more than just excellence into account when they made judgments about giftedness. This suggests that these preservice teachers value all kinds of talents. This information can inspire confidence in a number of constituencies involved with schools, especially children's parents. Parents are normally socialized to believe that almost nothing but good test scores can lead their children to a bright future, and therefore they tend to discourage their children from participating in anything that does not help their children to achieve good test scores. The current finding may encourage parents to support their children in participating in activities that are not directly related to the "excellence" criterion.

Two different implications can be generated from the finding that the rarity criterion was not taken into account in the participants' judgments of giftedness. On the one hand, this finding implies that these preservice teachers put more emphasis on equity than on excellence, which is more in line with the criterion-referenced paradigm that encourages students to cooperate with, rather than, compete with one another. This helps explain why gifted education is not popular in China. Chinese educators may prefer to keep the "gifted students" in the mainstream classrooms so that these students do not feel segregated from their peers. Segregation from their peers may inhibit the socialization of the identified gifted students. Socialization is one of the two major goals for schooling in mainland China (see Stevenson, 1998). This finding, thus, points to the future direction of gifted education in mainland China. It was mentioned at the beginning of this article that gifted education in China is still very limited. Given that no emphasis was put on the rarity criterion by preservice teachers (who will become in-service teachers and potentially policy makers) in the present study, it is very likely the extent of gifted education will continue at its present level, rather than experience large expansion. The focus will be on mainstream education in which all students will be helped to reach their full potentials. This prediction seems to coincide with that of Stevenson.

On the other hand, this finding implies that an inequity will be created out of this apparent equity. That is, those students with high potential will be deprived of the opportunity to receive the special education that they need. Benbow and Stanley (1996) have referred to this phenomenon in education as that of "inequity in equity." This problem of "inequity in equity" must be addressed by a change in the foundations of education in China. Education in China should, as Benbow and Stanley have suggested, emphasize excellence of all and be responsive to individual differences, including the individual needs of students with high potential.

The fourth implication is derived from the finding that the demonstrability criterion was not taken into account in the participants' judgment about giftedness. This tendency of not taking demonstrability into account, as has been pointed out earlier, seems to be a common problem across cultures. It is a clear warning that some test users might be using tests without considering test validity. This finding is, indeed, a piece of bad news. The indifference shown by preservice teachers about test validity may reduce people's confidence in schooling. For example, parents may wonder what kind of education their children are getting by attending schools. Higher educational institutions and employers may not be willing to trust schools' recommendations of students for either pursuing a higher education or entering the world of work, for they do not have full confidence in the criteria used by schools for identification. Therefore, this finding should be perceived as suggesting that knowledge about test validity should be built into curricula for teacher training programs in China.

Table 1
Results from t-test/ANOVA (Dependent
Variable: Mean Rating on 30 cases)

                  t/F value         Sig.                df
Group           School   Self  School  Self     School        Self

Age               .70    2.2    .62    .06      (5,170)      (5,171)
Gender            .01     .05   .99    .96   (183,144.55)  (184,132.86)
Family Income    2.19     .96   .06    .45      (5,178)      (5,179)
Analytical        .84     .16   .54    .99      (6,176)      (6,177)
Creative         1.26    1.63   .27    .12      (8,174)      (8,175)
Practical        1.09    1.08   .37    .38      (7,175)      (7,176)

Note: Analytical = self-rated analytical ability
Creative = self-rated creative ability
Practical = self-rated practical ability

Table 2
Summary of Multiple-Regression Analyses

                             [beta] (Standardized regression
                                     coefficient)
Rating (statement)      Girls-School   Girls-Self   Boys-School

Yale Student Sample
Excellence (1)             .32 ***       .73 ***       .28 ***
Rarity (2)                 .45 ***       .38 ***       .25 ***
Productivity (5)           .37 ***       .22 ***       .44 ***
Demonstrability (3)        .00           .13 **        .03
Value (4)                  .49 ***       .26 ***       .50 ***
Value (6)                  .26 ***       .10 *         .28 ***
[R.sup.2]                  .78 ***       .91 ***       .68 ***
Root-mean-square-error     .46           .33           .60
(Yale student sample: N = 24 students evaluating 12 girls and 12 boys)

Yale Parent Sample
Excellence (1)             .33 ***       .53 ***       .34 ***
Rarity (2)                 .29 ***       .35 ***       .24 **
Productivity (5)           .34 ***       .50 ***       .44 ***
Demonstrability (3)        .02           .25 ***       .00
Value (4)                  .50 ***       .28 ***       .43 ***
Value (6)                  .44 ***       .20 ***       .35 ***
[R.sup.2]                  .76 ***       .90 ***       .68 ***
Root-mean-square-error     .49           .24           .66
(Yale parent sample: N = 39 parents evaluating 21 girls and 18 boys)

Hong Kong Sample
Excellence (1)             .32 **        .34 **        .47 ***
Rarity (2)                 .30 **        .46 ***       .25 *
Productivity (5)           .11           .24           .26 *
Demonstrability (3)        .10           .25 *         .04
Value (4)                  .56 ***       .33 **        .39 ***
Value (6)                  .33 ***       .20           .41 ***
[R.sup.2]                  .79 ***       .73 ***       .79 ***
Root-mean-square-error     .26           .25           .30
(Hong Kong sample: N = 72 students evaluating 35 girls and 37 boys)

Mainland Sample
Excellence (1)             .53 ***       .76 ***       .54 ***
Productivity (5)           .35 **        .52 ***       .30 **
Value (4)                  .37 ***       .24 ***       .37 ***
Value (6)                  .38 ***       .27 ***       .45 ***
[R.sup.2]                  .72 ***       .90 ***       .77 ***
Root-mean-square-error     .40           .17           .36
(Mainland sample: N = 189 Preservice teachers evaluating 96 girls and
  93 boys)

                          [beta] (Standardized
                         regression coefficient)
Flating (statement)            Boys-Self

Yale Student Sample
Excellence (1)                  .55 ***
Rarity (2)                      .23 ***
Productivity (5)                .58 ***
Demonstrability (3)             .28 ***
Value (4)                       .19 ***
Value (6)                       .07
[R.sup.2]                       .87 ***
Root-mean-square-error          .38
(Yale student sample: N = 24 students evaluating 12 girls and 12 boys)

Yale Parent Sample
Excellence (1)                  .49 ***
Rarity (2)                      .37 ***
Productivity (5)                .67 ***
Demonstrability (3)             .11 **
Value (4)                       .18 ***
Value (6)                       .13 **
[R.sup.2]                       .91 ***
Root-mean-square-error          .26
(Yale parent sample: N = 39 parents evaluating 21 girls and 18 boys)

Hong Kong Sample
Excellence (1)                  .60 ***
Rarity (2)                      .29 **
Productivity (5)                .34 ***
Demonstrability (3)             .26 ***
Value (4)                       .27 ***
Value (6)                       .27 **
[R.sup.2]                       .84 ***
Root-mean-square-error          .25
(Hong Kong sample: N = 72 students evaluating 35 girls and 37 boys)

Mainland Sample
Excellence (1)                  .65 ***
Productivity (5)                .52 ***
Value (4)                       .28 ***
Value (6)                       .30 ***
[R.sup.2]                       .83 ***
Root-mean-square-error          .24
(Mainland sample: N = 189 Preservice teachers evaluating 96 girls and
  93 boys)

* p < .05, ** p < .01, *** p < .001

Table 1
Means for Groups in Homogeneous Subtests

                                     Subset for alpha = .05
Test                  N      1      2      3      4      5     6     7

Athletic prizes      184   2.53
Performing arts
  prizes             184          2.93
Achievement tests    184          3.11   3.11
Social skills
  tests              182          3.14   3.14
Art projects         183                 3.38   3.38
Debating prizes      180                 3.38   3.38
Motivation tests     183                        3.63   3.63
Essays               182                        3.68   3.68
Intelligence tests   184                               3.84
Curiosity tests      184                                     4.17
Science projects     184                                     4.44
Creativity tests     184                                           4.80

Manuscript submitted May, 2001.

Revision accepted September, 2001.

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Authors' Note

Research for this project was supported by the Committee on Research and Conference Grants as administered by The University of Hong Kong. Our sincere thanks go to Mr. Deng Meng for his kind assistance in the data collection and to all those anonymous preservice teachers whose participation is indispensable to this research.

Dr. Li-fang Zhang is an associate professor in the Department of Education at The University of Hong Kong. She has published widely in the areas of approaches to learning, cognitive development, giftedness, and thinking styles. Mr. Sammy King-fai Hui is a research officer in the Department of Education, The University of Hong Kong. His field is research methodology and evaluation, and experiential learning.