Gifted students' self-perceptions of ability in specific subject domains: factor structure and relationship with above-level test scores.

Self-concept can be defined as "a person's perceptions of him- or herself" (Marsh & Shavelson, 1985, p. 107). Current theories of self-concept suggest a multidimensional construct in which, particularly prior to late adolescence, domain-specific self-concepts contribute to global self-concept in a hierarchical fashion (e.g., Harter, 1982; Marsh, 1987; Marsh & Shavelson). The exact nature of the domain-specific self-concepts has been debated (Marsh & Shavelson), but some form of academic self-concept generally is included. Early models proposed a unitary academic construct (e.g., Hatter), but more recent research has suggested independent verbal and mathematical self-concepts (Marsh, 1987; Marsh, Byrne, & Shavelson, 1988; Marsh & Shavelson) or even more specific, subject-based self-concepts (Marsh, 1990, 1992). Most studies looking at academic self-concept in context (e.g., as affected by intervention programs or as experienced by certain groups of students) have considered either general academic self-concept or math and verbal self-concepts. Few have considered subject-based self-concepts, although Marsh (1990, 1992) found evidence that self-concepts in specific subjects can be distinguished from one another.

Marsh (1990, 1992) used six-item scales to look at each of nine subject-specific academic self-concepts. The nine scales consisted of identical items except for the school subject named (e.g., "Compared to others my age I am good at --"), and participants responded to each item on a six-point scale ranging from false to true. Factor analyses confirmed that the school subjects formed separate self-concept factors, with the exception of English language and English literature, which combined to form a single factor. Marsh (1992) then related the academic self-concept scores to students' school grades via path analysis, finding that relationships within subject areas were considerably stronger than those between subject areas, and little of the variance in serf-concept could be explained by a general academic factor.

Marsh's internal/external (I/E) frame of reference model (e.g., Marsh, 1986, 1992; Marsh, Byrne, & Shavelson, 1988) explains how a student might have poor self-concept in a particular academic area despite strong academic performance in that area. The model posits that self-concept is derived both from comparisons with others (external comparisons) and from comparisons within the self (internal comparisons). For an achieving gifted student, external comparisons are likely to strengthen self-concept, as the student's academic performance compares favorably to the performance of others. Internal comparisons, however, are expected to weaken self-concept in areas in which the student perceives himself or herself to be relatively weak. Therefore, for example, particularly strong performance in mathematics would be expected to relate positively to math self-concept (based on both internal and external comparisons) but negatively to verbal self-concept (based on internal comparisons, because of the relative weakness of performance in verbal areas).

Academic self-concept is important to understand because of its relationship to academic achievement and academic choices. Although achievement is often thought to inform academic self-concept, Marsh (1992) stated that the reverse also is true: "academic self-concept contributes, beyond what can be explained by prior achievement, to the prediction of subsequent achievement, subsequent coursework selection, subsequent educational aspirations, and eventually, university attendance" (p. 41). Such concerns may be particularly important with regard to gifted students, who may have more ability than most to succeed in challenging fields, but who may avoid those areas if their corresponding self-concept is poor.

In 2002, Olszewski-Kubilius and Turner considered gifted students' perceptions of their relative strengths and weaknesses in reading/English versus math/science, comparing student reports to their scores on the EXPLORE (American College Testing, 2001) test, which was administered to gifted students above-level (i.e., students in grades 4-6 took EXPLORE, which was designed for eighth graders). They reported that girls were more likely than boys to see themselves as better in reading/English than in math/science, whereas boys were more likely than girls to see themselves as better at math/science than at reading/English. They also noted that students' self-perceptions were related to their test scores, in that "the mean English and reading subscores for students who believed themselves to be better in reading/English subjects were significantly higher than the English and reading scores of those who believed themselves to be better in math/science subjects" (pp. 251-252) and vice versa. They reported no gender differences in the extent to which test score differentials matched self-perceptions of ability.

Interestingly, when the analyses were repeated with a sample that included third graders, replication was found for only the students in grades 4-6: "... among third graders and unlike fourth through sixth graders, there was no significant relationship between the students' perceptions of their subject area strengths ... and their performance on the corresponding subtests" (Olszewski-Kubilius & Turner, 2002, p. 258). It is unclear, however, whether the lack of relationship for third-graders was due to developmental differences or the small number of third graders in the sample (only 4% of the total sample were third graders).

Williams (1998) also compared self-perceptions to performance for high-ability students, but she focused on adolescents (i.e., ages 13-15) and adapted a general self-concept scale, the ME: Self Concept Scale for Gifted Children (Feldhusen & Kolloff, as cited in Williams, 1998), to reflect self-perceptions specific to English and mathematics. She found that self-concept was related to performance in both domains, although less than 30% of the variance in self-concept in any domain was explained by performance. She also noted that the majority of students in the sample demonstrated non-congruence between their self-concept and performance scores in that, when all scores were standardized, there was a discrepancy greater than .4 between English or math self-concept scores and English Total or Math Total achievement test scores, respectively. She did not, however, find the often-reported gender difference favoring boys' self-concepts in math and girls' self-concepts in English. Instead, she found that "there were non-significant differences between the numbers of female and male adolescents falling into the five discrepancy levels [i.e., overconfident, somewhat overconfident, somewhat underconfident, and underconfident] across the content areas" (p. 419).

The current study considered relationships between above-level EXPLORE scores and ability perceptions, and expanded upon previous research with gifted students by considering subject-specific ability perceptions as dependent variables and including grade level as an independent variable. As in the study by Olszewski-Kubilius and Turner (2002), participants were gifted students who took EXPLORE as an above-level test. At the beginning of the testing session, participants were asked how they believed they compared with other students their age in a variety of school subjects. Their responses were first correlated and factor analyzed to determine the extent to which their self-perceptions of ability were differentiated by subject. Because of the differences between third graders and more advanced students found by Olszewski-Kubilius and Turner, the third graders were considered separately from the rest of the sample unless their patterns were similar to those of older students. Next, students" self-perceptions were compared with their EXPLORE scores in Mathematics, Reading, Science Reasoning, and English and tested for differences according to gender, grade level, and school type (i.e., public vs. private).

Method

Participants

Third- through sixth-grade students (N=2,283) took EXPLORE, a test designed for eighth graders, as an above-level test by participating in the 2003 Carnegie Mellon Institute for Talented Elementary Students (C-MITES) Talent Search (see Table 1 for a breakdown by gender and grade level). Eligibility for the Talent Search required that students score at the 95th percentile or higher on at least one subtest of an in-grade standardized achievement test, administered as part of their school's regular testing program. Those who chose to participate in the Talent Search took EXPLORE at special testing sites near their homes, in the company of other Talent Search participants. Further details regarding qualification for and participation in the C-MITES Elementary Student Talent Search can be found in the registration brochure published by C-MITES (2003) or in previously published research (e.g., Lupkowski-Shoplik & Swiatek, 1999).

Instrumentation 

To register for the EXPLORE test, all Talent Search students completed a form that included basic demographic information. Information about participants' gender, grade level, and type of school (i.e., public, parochial, independent, homeschool) was used in this study.

On test day, prior to beginning the EXPLORE test, all Talent Search students were asked to complete 12 items to be used for research purposes. Items 4 through 9 are of interest in the current study. Each of these items listed a school subject and asked students to indicate how capable they felt in that subject compared to agemates:

A. I am much worse than most other students my age.

B. I am a little worse than most other students my age.

C. I am about as good as most other students my age.

D. I am a little better than most other students my age.

E. I am much better than most other students my age. The subjects listed (in order) were mathematics, science, social studies, reading, English, and spelling. Responses were coded from 1-5, such that higher scores indicated more positive self-perceptions.

Procedure

When students checked in at their test sites, they were provided with answer sheets that had been pre-gridded with the identification and demographic information they had provided on their registration forms. They were then seated in testing rooms and led through preparations for the test, which included verification of the information on the answer sheets. The 12 research items were then administered, with the room supervisor reading each item aloud to the group and answering questions as necessary. Immediately after completing the 12 research items, participants began the EXPLORE test.

Of the 2,283 participants, 1,744 (76.4%) responded to all six items and could be included in a factor analysis to determine whether self-perceptions of ability were subject-specific. This sample consisted of 797 (45.7%) girls and 945 (54.2%) boys, as well as 2 students who did not report their gender. Three hundred two (17.3%) of the students were in third grade: 594 (34.1%) were in fourth grade, 555 (31.8%) were in fifth grade, 291 (16.7%) were in sixth grade, and 2 students did not report their grade level. For all analyses other than the factor analysis, cases were excluded only if they were missing data relevant to a specific analysis.

Correlations were examined to assess the relationship between self-perception responses and EXPLORE scores. Then, following previous research on discrepancies between self-perception and performance (Hackett & Betz, 1989; Williams, 1994, 1998), self-perception responses and EXPLORE scores were standardized to z-scores (mean = 0, standard deviation = 1) and difference scores were calculated for each EXPLORE domain (i.e., mathematics, reading, science, and English) such that positive values indicated overconfidence (i.e., self-perception score higher than corresponding EXPLORE score) and negative values indicated underconfidence (i.e., EXPLORE score higher than corresponding self-perception score). Standardization of the variables was done separately by grade level to accommodate increases in mean EXPLORE scores from one grade level to the next. The congruence between self-perceptions and EXPLORE scores was examined for the participant group as a whole, and possible differences by gender, grade level, and school type were examined via analysis of variance (ANOVA).

Results

Means and standard deviations of participants' scores on the self-perception items and EXPLORE tests are displayed in Table 2.

Correlation and Factor Analysis of Self Perception Responses

Initial inspection of separate correlation matrices for third graders and fourth through sixth graders indicated that there were no consistent differences between these age groups. Therefore, the entire participant group was combined for the correlation analysis. The resulting correlation matrix is displayed in Table 3. Self-perception responses were significantly and positively correlated with one another, and no correlation was of a negligible effect size. Small (r [greater than or equal to] .10) and medium (r [greater than or equal to] .30) effect sizes were evident, although no effect sizes were large (r [greater than or equal to] .50; for the classification of effect sizes see Cohen, 1992).

The results of factor analyses, using principal-axis factoring, also were similar for third graders and fourth through sixth graders. Examination of the scree plot (see Figure 1) indicated that there was little differentiation among the solutions involving two through six factors. The best solution appeared to be a one-factor solution, which explained 45.0% of the variance in academic self-perception scores for the participant group as a whole.

Correlations Between Self-Perception Responses and EXPLORE Scores

Correlations between self-perception items and EXPLORE scores also did not differ consistently between third graders and fourth through sixth graders. The correlations between self-perception responses and EXPLORE scores for the entire participant group are presented in Table 4. All possible bivariate correlations between subject-specific self-perceptions are listed. This is a departure from Williams's (1998) work, in which only same-subject comparisons (e.g., math self-concepts with scores on standardized math tests) were considered. Further, due to the results of the factor analysis, self-perception responses were averaged across subjects to produce an overall academic sell-perception score, which also is included in Table 4. Internal consistency for the overall scale was acceptable (Cronbach's [alpha] = .75). The majority of correlations represented small effect sizes. Exceptions were one medium effect size (self-perception in mathematics with EXPLORE Math, r = .30) and five negligible effect sizes (self-perception in reading with EXPLORE Math, r = .05, and self-perception in spelling with: EXPLORE Math, r = .03; EXPLORE Science Reasoning, r = .06; EXPLORE Reading, r = .09; and EXPLORE Composite, r = .08).

Congruence Between Self-Perception Responses and EXPLORE Scores

In each EXPLORE domain and also for overall academic self-perception, standardized EXPLORE scale scores were subtracted from corresponding standardized self-perception ratings to create difference scores in which positive values reflected overconfidence and negative values reflected under-confidence. This procedure was carried out separately for students at each grade level to accommodate higher EXPLORE scores among more advanced students. Table 5 summarizes the numbers of students who were "underconfident" (difference scores below -0.8), "somewhat underconfident" (difference scores between 0.8 and -0.4), "congruent" (difference scores between -0.4 and +0.4), "somewhat overconfident" (difference scores between +0.4 and +0.8), and "overconfident" (difference scores above +0.8) for each EXPLORE domain (see Hackett & Betz, 1989; Williams 1994, 1998 for earlier uses of this classification system). Relatively few students were classified as congruent in any domain; the greatest proportion of congruent students was found for Mathematics (30.7%).

To create larger groups for comparisons by gender and school type. congruence scores were divided into three categories: overconfident (difference scores above 0.4), congruent (difference scores between 0.4 and -0.4). and underconfident (difference scores below -0.4). Also, because there were few students in the parochial, independent, and homeschool categories considered individually, parochial and independent schools were combined into one "private school" category (n = 659): homeschooled students (n = 10) were not included in the analysis. One 2 (gender) X 4 (grade level) X 2 (school type) ANOVA was performed on congruence in each of the four EXPLORE domains and on the overall (composite) scores, resulting in a total of five ANOVAs. The alpha level required for statistical significance was adjusted from .05 to .01 to counter the increased likelihood of Type I error created by the use of five separate ANOVAs.

No gender differences were found for mathematics, science, or overall confidence (composite). Significant gender differences favoring girls were found for both reading (boys' M = -.077, girls' M =.123, F= 17,994, p < .001, d= .23) and English (boys' M = -.064, girls' M = .083, F= 16.569, p < .005, d = .17), but the gender difference for English was of negligible effect size and will not be discussed further.

Grade level differences were found only for mathematics (F = 4.238, p < .01, [[eta].sup.2] = .006). Tukey post hoc tests indicated that sixth graders had higher math confidence scores (M = .1138) than both fourth graders (M = -.0842, p < .005) and fifth graders (M = -.0516, p < .05), but the effect sizes were negligible. Other grade levels were not significantly different from each other.

The most commonly found differences were between students from public and private (parochial and independent) schools. Significant differences by school type were found for confidence in every area except mathematics. In all areas, differences favored public school students: science (public school M = .009, private school M = -.108, F= 7.135, p < .01, d= .11), reading (public school M = .053, private school M = -.085, F = 9.347, p < .005, d = .16), English (public school M = .048, private school M = -.113, F = 16.569, p < .001, d = .18), and the composite (public school M = .050, private school M = -.086, F = 8.015, p < .01, d =. 16). In no case, however, did a difference by school type surpass a negligible effect size.

Discussion

The results of the current study were consistent with previous research in some ways but inconsistent with it in others. Where inconsistency was found, several possible reasons for it can be hypothesized.

The Structure of Academic Self-Concept

The correlations and the factor analysis both indicated that self-perception items were correlated with one another. Within the traditional academic areas, all but four of the correlations represented medium effect sizes. The scree plot in the factor analysis (see Figure 1) clearly indicated that a one-factor solution best represented the data. These findings are inconsistent with those reported by Marsh (1990, 1992), in which subject-specific self-concepts better explained the data than did more general academic self-concepts.

One possible reason for the one-factor solution in the present analysis is that the sample was comprised of such highly able students that they perceived themselves to be better than others their age in all subjects, scored at the ceiling of all self-perception items and, therefore, tailed to demonstrate differentiation in their self-concepts from one subject to another. If this were the case, however, the restricted range of their self-perception scores should have caused lower correlation coefficients in Table 3. Also, inspection of participants' scores on the self-perception items suggested that not all students' responses were at the ceiling of the measure (see Table 2), although the score distributions for most items were negatively skewed. Therefore, it appears that ceiling effects and resulting restriction of range do not fully explain the lack of distinct self-perception factors.

Differences in participant groups also may explain the difference between the current factor structure and that obtained by Marsh (1990, 1992). Participants in the present study were boys and girls in grades 3-6, whereas Marsh's 1990 study focused on separate participant groups of students in grades 5/6 and 7 through 10, and his 1992 study was of high school boys. The inclusion of younger students in the current sample may have influenced the results. The finding that data for third graders was not consistently different from that for fourth through sixth graders suggests, however, that this was not the case.

Perhaps the one-factor solution resulted from the use of one-item self-perception measures. The superior reliability of multiple-item measures may provide better data for factor analysis. It also is possible that students from a population as selective as that used in the current study (i.e., the top 5% in the nation in at least one academic area) do not distinguish among different types of academic self-concept as much as average-ability or more moderately gifted individuals do. It is premature to jump to this conclusion on the basis of the current study, however. Research using self-concept scales instead of self-concept items is necessary to address this possibility.

Congruence Between Self-Perceptions and Tested Ability

Because of the results of the factor analysis, overall academic self-perception scores (i.e., the mean score across all six self-perception items), as well as individual self-perception responses, were compared with corresponding EXPLORE scores. Given the lack of differentiation in the factor analysis, little differentiation was expected in the subject-specific correlations, but in fact the correlation between math self-perception and EXPLORE Math (r = .30) was noticeably larger than all other correlations. Interestingly, with the exception of this one correlation, there was little relationship between self-perception in a subject area and EXPLORE score in that same subject area. This finding is contrary to the results obtained by Williams (1998), who found larger correlations between self-perception and performance in mathematics and English in her sample of ninth-grade honors science students.

Given these results of the correlational analysis, it is not surprising that few students demonstrated congruence between their self-perceptions and their corresponding EXPLORE scores, or that the greatest proportion of congruent scores found was in math. It is interesting, however, that the amount of congruence found in the current study is similar to that found by Williams (1998) when she looked at scores on the Iowa Tests of Basic Skills (ITBS) and the ME: Self Concept Scale for Gifted Children. The current finding with regard to gender differences in congruence are similar to Williams's (1998) results among ninth-grade honors science students. Williams found no gender differences in any area. Here, there were no meaningful differences in any area except reading, in which a small difference favored girls. It may be that the loss of confidence that has been documented for both averageability and gifted girls relative to their male peers (American Association of University Women, 1991; Kerr, 1997; Sadker & Sadker, 1994; Silverman, 1993) has not yet surfaced among elementary students, but Williams's (1998) results with adolescents suggest that this trend might be weakening even for older students, at least among those who are high achieving. The present study extended Williams's (1998) work by also testing for differences according to grade level and school type, but none of the differences by grade level or school type surpassed a negligible effect size.

Conclusions and Directions for Future Research

The present results suggest that gifted elementary students may not distinguish among subject-specific academic self-concepts to the extent that other students do, but this is not a strong conclusion due to limitations in the measures available for the study. A more solid finding is that the majority of gifted elementary students were either overconfident or underconfident in their self-perceptions relative to their above-level test scores. Using above-level test scores for this type of research with gifted students is useful because the above-level test allows distinctions to be made among levels of ability (Lupkowski-Shoplik, Benbow, Assouline, & Brody, 2003). In other words, the above-level test provides a valid range of scores, which is required for meaningful data analysis.

The comparison between above-level test scores and self-perception items asking students to compare themselves to "most other students my age" raises unique issues, however. Students whose EXPLORE scores were at or near the mean for this sample were, in actuality, nowhere near the mean for the broad population of students their age (see Table 2). Rather, they were at or above the mean for eighth-grade students (i.e., students 2-5 years older than they). Therefore, even those students who demonstrated "congruence" between their serf-perceptions and their EXPLORE scores, per the definition used here, were actually underconfident. This is true even though the typical mean score for the self-perception items was approximately equivalent to "I am a little better than most other students my age," because a student 2-5 years advanced is more than "a little better" than his or her typical agemates. Similarly, students who were classified as "somewhat overconfident" (and maybe even "overconfident," at least at the lower end of the range within that classification) may have been those with the most true congruence between their self-perceptions and their tested abilities.

Further research is necessary to refine these findings. Most importantly, future studies should use multiple-item self-concept scales for each academic area of interest. Single-item measures are inherently unreliable; therefore, multipleitem self-concept scales would allow a stronger test of the generalization of Marsh's (1990, 1992) findings regarding subject-specific self-concepts to gifted elementary students. One feature of the current study that should be retained, however, is the comparison of self to a specific group in the self-perception measure. This type of comparison allows the researcher to determine whether students' self-perceptions are accurate. As noted above, if students with ability levels equivalent to individuals several years older than they believe themselves to be only "a little better than" the typical student their age, the self-perception is inaccurate even if it is "congruent" on the basis of standardized difference scores, such as those used here.

Table 1

Gender and grade level
of participants *

                 Boys        Girls

Grade level     n     %      n     %

Grade 3         228   65     124   35
Grade 4         425   52     389   48
Grade 5         384   56     303   44
Grade 6         189   51     179   49
Total         1,226   54   1,055   46

* Data were missing on gender and grade
level for 2 participants.

Table 2

Means and standard deviations for responses to
academic self-perception items and EXPLORE tests

                                             Standard
Measure                              Mean    deviation     n

Mathematics self-perception (a)       4.10       .80     2,098
Science self-perception (a)           3.80       .80     2,124
Social studies self-perception (a)    3.70       .83     2,170
Reading self-perception (a)           4.10       .89     2,161
English self-perception (a)           3.70       .84     2,167
Spelling self-perception (a)          4.10       .92     2,147
EXPLORE Mathematics (b)              50.96     27.83     2,282
EXPLORE Science Reasoning (b)        64.39     25.46     2,279
EXPLORE Reading (b)                  56.96     23.90     2,279
EXPLORE English (b)                  61.70     25.30     2,281
EXPLORE Composite (b)                59.10     25.47     2,278

(a) Likert-type scale from 1-5, with higher scores indicating
more positive self-perception

(b) Percentile scores based on an eighth-grade norm group

Table 3
Correlations among self-perception items. *

                Science  Social Studies  Reading  English  Spelling

Math             .306         .297        .217     .318      .265
Science                       .429        .252     .337      .241
Social Studies                            .331     .386      .299
Reading                                            .483      .369
English                                                      .429

* All correlations were significant at p < .01.

Table 4

Correlations between self-perception items
and EXPLORE scale scores. *

EXPLORE                              Self-Perception

                                               Social
                           Math     Science    Studies   Reading

Math                       .296       .123      .126      .053
Science Reasoning          .199       .179      .133      .168
Reading                    .162       .136      .144      .220
English                    .188       .127      .129      .195
Composite                  .246       .161      .154      .183

EXPLORE                         Self-Perception

                          English   Spelling   Overall

Math                       .106       .026      .172
Science Reasoning          .133       .058      .212
Reading                    .155       .090      .228
English                    .179       .108      .232
Composite                  .167       .084      .245

* All correlations were statistically significant at p < .001
except reading self-perception with EXPLORE Math (p < .05),
spelling self-perception with EXPLORE Science Reasoning
(p < .01), and spelling self-perception with EXPLORE Math
(not significant).

Table 5
Proportions of students in various congruence categories
for each EXPLORE domain.

Congruence Category          Mathematics            Science

                             n         %          n         %

Overconfident
(above 0.8)                 428       20.4       522      24.6

Somewhat overconfident
(from 0.4 to 0.8)           207        9.9       186       8.8

Congruent
(from -0.4 to +0.4)         643       30.7       502      23.7

Somewhat underconfident
(from -0.4 to -0.8)         242       11.6       284      13.4

Underconfident
(below -0.8)                575       27.5       624      29.5

Congruence Category            Reading              English

                             n         %          n         %

Overconfident
(above 0.8)                 548       25.4       556      25.7

Somewhat overconfident
(from 0.4 to 0.8)           238       11.0       203       9.4

Congruent
(from -0.4 to +0.4)         515       23.9       569      26.3

Somewhat underconfident
(from -0.4 to -0.8)         304       14.1       179       8.3

Underconfident
(below -0.8)                550       25.5       656      30.3

Congruence Category            Overall

                             n         %

Overconfident
(above 0.8)                 415       23.9

Somewhat overconfident
(from 0.4 to 0.8)           218       12.5

Congruent
(from -0.4 to +0.4)         440       25.3

Somewhat underconfident
(from -0.4 to -0.8)         190       10.9

Underconfident
(below -0.8)                476       27.4

REFERENCES

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Manuscript submitted December 5, 2003. Revision accepted March 23, 2004.

Mary Ann Swiatek, Ph.D., is the research specialist for the Carnegie Mellon Institute for Talented Elementary Students (C-MITES). She also is a Pennsylvania licensed psychologist and an adjunct faculty member in the psychology department at Lafayette College. Her research interests focus on psychosocial issues in the education of gifted students. E-mail: [e-mail]