Testing the Internal/External Frame of Reference Model of Self-Concept
with Chinese High School Students in Talented and Nontalented Classes
Frances L. M. Lee, University of New South Wales,
Alexander Seeshing Yeung, University of Western Sydney, Macarthur,
Putai Jin, and Renae Low, University of New South Wales
Paper presented at the annual conference of the Australian Association
for Research in Education in Brisbane, Australia, 30 November to 4
December 1997
Abstract
This study examined the internal/external frame of reference (I/E)
model (Marsh, 1986) with Chinese students in "accelerated" talented (n
= 160) and "average" talented (n = 335) classes. Confirmatory factor
analyses showed support for the I/E model for students placed in
"accelerated" and "average" classes in a talented high school. Path
coefficients leading from Chinese achievement score to verbal
self-concept and from maths achievement score to maths self-concept
were positive and significant whereas paths relating nonmatching
domains were negative, although the sizes of the effects differed
across the two groups. The results support the multidimensionality and
content specificity of academic self-concept.
Recent research on self-concept has emphasised domain-specific and
multidimensional perspectives that are in contrast to traditional views
of a global composite self-concept that was assumed to explain
self-concepts in various areas (e.g., Byrne, 1984; Marsh, 1993; Marsh,
Byrne, & Shavelson, 1988; Marsh & Yeung, 1997). Shavelson, Hubner, and
Stanton (1976) proposed a hierarchical multidimensional model of
self-concept that posited a general (global) self-concept at the apex
under which were academic and nonacademic self-concepts which were
further divided into domain specific areas such as Verbal and Maths
self-concepts. However, further evaluations of this model found that
Verbal and Maths self-concepts were nearly uncorrelated (e.g., Marsh,
1986; Marsh, Byrne, & Shavelson, 1988); hence Verbal and Maths
self-concepts could not be combined to form a higher-order Academic
self-concept factor. Marsh (1986) further demonstrated that Verbal and
Maths self-concepts are distinct constructs. Thus a student having a
high self-concept in maths does not necessarily have a similarly high
verbal self-concept. In an attempt to explain these consistent
findings over several studies, Marsh (1986) developed the
internal/external frame of reference (I/E) model. Although some studies
have demonstrated the generalisability of the I/E model, less work has
been done to examine the applicability of the I/E model in an eastern
culture, and particularly to talented students. The present
investigation examines the applicability of the I/E model with
high-ability students in China.
According to the I/E model, Maths and Verbal self-concepts are
influenced both by external and internal comparisons. The external
frame of reference involves comparing the student's perceived academic
ability with the abilities of other students in a specific environment
(e.g., school, peer group). The internal frame of reference refers to
the student's comparison of perceived ability in one subject domain
with perceived ability in another subject domain. Thus a student whose
achievement in Maths is lower than most other students may have a low
Maths self-concept due to an external comparison with other students,
but may have a relatively higher Maths self-concept than, for example,
English self-concept if maths is the student's best among other
subjects. The joint effect of external and internal comparisons may
then result in a near-zero correlation between Maths and Verbal
self-concepts.
Using a confirmatory factor analysis (CFA) approach to test the I/E
model, Marsh (1986) demonstrated a positive effect of maths achievement
on Maths self-concept and a positive effect of verbal achievement on
Verbal self-concept, but a negative effect of maths achievement on
Verbal self-concept and a negative effect of verbal achievement on
Maths self-concept, and a substantially smaller correlation
(approaching zero) between Maths and Verbal self-concepts than the
typically large correlation between maths and verbal achievement.
Subsequent studies on the I/E model based on the English version of the
SDQ instruments have been very supportive of these findings (e.g.,
Byrne & Shavelson, 1987; Marsh, Byrne, & Shavelson, 1988). Furthermore,
apart from Marsh's Australian sample, studies of the I/E model
conducted in countries such as Norway (Skaalvik & Rankin, 1995), Spain
(Gonzalez-Pienda, Nunez-Perez, & Valle-Arias, 1992) and North America
(Tay, Licht, & Tate, 1995) also supported the generalisability of the
model.
Various studies have also demonstrated the generalisability of the I/E
model irrespective of the instrument used in the investigations. For
example, Marsh , Byrne, & Shavelson (1988) showed consistent support
for the I/E model when using different instruments such as the Self
Description Questionnaire, Affective Perception Inventory, Self-esteem
Scale, and the Self-concept of Ability Scale as well as the combined
self-concept scores. Using the Academic Perception Questionnaire, Tay,
Licht, and Tate (1995) found patterns that were highly consistent with
the I/E model. Similarly, the I/E model was also supported in the
Skaalvik and Rankin (1995) study in which measures of self-concept,
self-perceived aptitude, and self-perceived ability to learn were
combined into single maths and verbal latent traits.
To educational researchers the relationship between academic
achievement and academic self-concept has always been an important
concern. The I/E model explains, at least partly, the formation of
academic self-concept and the relationship between academic
self-concept and academic achievement from a multidimensional
perspective. Using a sample of 511 students from an "accelerated" class
and other "average" classes in a Chinese high school of talented
students, we hypothesise that the I/E model should be applicable across
abilities as well as across cultures.
In the field of talented education, most previous research
involved comparisons of means between gifted and nongifted samples.
Relatively little attention has been paid to the structure of
self-concept in gifted and talented children (Hoge & McShefrey, 1991).
More importantly, as most of the previous research on the self-concept
of talented children seemed to have suffered from methodological
problems (Hoge & Renzulli, 1993), findings have been inconsistent and
sometimes ambiguous (Kulik & Kulik , 1992). Also, the question of
whether a given instrument, such as the Self Description Questionnaire
II (SDQII) that is considered here, measures the same components of
self-concept with equal validity for talented and average-ability
students remained unanswered. Thus, in the present study, the
applicability of the Marsh (1986) I/E model to these talented students
is an important issue.
Method
Participants
The participants were 511 students (174 in Grade 7, 166 in Grade 8, and
171 in Grade 9) from a prestigious state high school in a province in
the southern part of China. In China, although gifted and talented
education is not officially emphasised, in some schools, special
programs have been set up to meet the needs of high academic achievers.
For example, students who participated in the present study were
strictly selected on the basis of academic performance. Upon admission
after keen competition, they had to attend a streaming test at the
beginning of Grade 7 for placement of the most talented in an
"accelerated" class (named experimental class). In the "accelerated"
class, students usually complete equivalent course work two to three
months in advance than the "average" classes. Then, some enrichment
programs and extensive courses were provided to these talented
students. For the present study, permission to participate in the
study was obtained from the students and their parents. Because of
absences and missing data, the following analyses used the responses of
495 students (160 in a "accelerated" class labelled as such and 335 in
"average" classes).
The SDQII Measures
The Verbal and Maths self-concept scales of the SDQII (Marsh, 1992)
were used in this study. Each SDQ item consisted of 10 items each
using a 6-point true-false response scale (1 = false to 6 = true). The
items were translated into Chinese by a professional two-way translator
and translated back into English by another translator to ensure
identical meanings were essentially conveyed by the original and
translated versions.
The Exam Scores
Exam scores of Chinese and maths were obtained about a month before the
administration of the SDQII instrument. The Grade 9 students had a
maximum possible score of 150 in math instead of the 100 for Grades 7
and 8; hence all exam scores are reported in percentages for ease of
comparison.
Statistical Analyses
Responses to all negatively worded items were reverse scored so that
higher scores reflected higher self-concept. Analyses were conducted
with item pair scores; hence the five item pairs for each of two SDQ
constructs (Verbal and Maths self-concepts) and achievements of two
subjects (Chinese and maths exam scores) yielded a 12 x 12 covariance
matrix for CFA. The approach of CFA and the use of item pairs have
been described elsewhere (e.g., Bollen, 1989; Byrne, 1989; Joreskog &
Sorbom, 1993; Marsh, 1994; Marsh & O'Neill, 1984; also see Pedhazur &
Schmelkin, 1991) and are not further detailed here.
Chinese
.36* Verbal
exam
self
-.11*
.35*
-.06
-.22*
Math
.51* Math
exam
self
Figure 1. Path model relating Chinese achievement and maths achievement
to Verbal self-concept and Maths self-concept. Path coefficients shown
here are based on solution of model C2 with factor loadings, path
coefficients, and residuals and correlated residuals constrained to be
equal across the "accelerated" and "average" groups.
Analyses were conducted with the SPSS version of LISREL (Joreskog &
Sorbom, 1988) to test the a priori path structure on the basis of the
Marsh (1986) I/E model (Figure 1). The goodness of fit of models is
evaluated based on suggestions of Marsh, Balla, and McDonald (1988) and
Marsh, Balla, and Hau (1996) with an emphasis on the Tucker-Lewis index
(TLI) as well as the chi-square test statistic and the relative
noncentrality index (RNI).
Results and Discussion
Preliminary Analysis
Reliability estimates for the SDQII Verbal and Maths self-concept
scales are good (alphas = .85 and .91, respectively.) Although not the
focus of the present study, students in the "accelerated" group had
generally higher maths self-concept (M = 4.69 and 4.29, respectively)
and also higher verbal self-concept though to a lesser extent for most
items (M = 3.90 and 3.80, respectively) than those in the "average"
group. Not surprisingly, both the Chinese and maths exam scores were
higher in the "accelerated" group (M = 81.02 and 83.11, respectively)
than in the "average" group (M = 76.42 and 78.59, respectively). Even
so, it is interesting to note that these mean exam scores are
remarkably high even in the "average" group for high school students,
reflecting the stringent selective criteria for high-ability students
in this particularly prestigious school in the province.
Model A: Using The Total Sample
The first model considered the total sample of students (N = 495).
Paths between latent variables were posited as shown in Figure 1 and
the pattern of paths applied to all of the following analyses, although
only the solution of a 2-group invariance model is presented at Table
2. A summary of the goodness of fit and path coefficients for each
model considered here is given at Table 1. The total-sample model
converged to a proper solution with a reasonably good fit (TLI = .952,
RNI = .964). Consistent with the I/E model (Marsh, 1986) the path
coefficient of the path from maths exam to Maths self-concept (.52) was
positive and significant whereas that from maths exam to Verbal
self-concept was negative and significant (-.22). Also, the path from
Chinese exam to Verbal self-concept (.37) was positive and significant
but the path from Chinese exam to Maths self concept, though negative
as expected, was not significant (-.08). The magnitude of positive
paths between matching academic domains tended to be greater than the
negative paths between nonmatching domains. More interestingly,
coefficients of the positive paths tended to be greater than those
typically found using the English version of the SDQ instruments (e.g.,
Byrne & Shavelson, 1986; Marsh, 1992).
Model B: The "accelerated " group. This model considered only students
in the "accelerated" group (n = 160). The model converged to a proper
solution with a reasonably good fit (TLI = .937, RNI = .952). The path
from maths exam to Maths self-concept (.25) was positive and
significant whereas that from maths exam to Verbal self-concept was
negative and significant (-.19). However, the paths from Chinese exam
to Verbal self-concept (.11) and from Chinese exam to Maths
self-concept were not significant (-.09) although the direction of the
signs was consistent with the I/E model. The path coefficients were
comparatively small in size in the "accelerated" group.
Model B: The "average" group. This model considered only students of
"average" group (n = 335). The model converged to a proper solution
with a reasonably good fit (TLI = .954, RNI = .965). Consistent with
the I/E model (Marsh, 1986) the paths from maths exam to Maths
self-concept (.66) and from Chinese exam to Verbal self-concept (.49)
were both positive and significant whereas paths from maths exam to
Verbal self-concept (-.29) and from Chinese to Maths self-concept
(-.19) were both negative and significant. The sizes of the positive
paths were greater than the negative paths, and the sizes of all paths
were greater than those in the "accelerated" group.
As stated in earlier review, the I/E model predicts that due to the
external frame of reference, students compare their academic
achievement in each domain with those of other students; thus Maths and
Verbal self-concepts should be substantially correlated as are the
academic achievements in these two subjects. Thus high ability in maths
would lead to higher Maths self-concept whereas high verbal achievement
would lead to higher Verbal self-concept. However, because of the
internal frame of reference, students compare their performance in one
area with their own performance in another area, and as a consequence,
good maths achievement would lead to lower Verbal self-concept and good
verbal achievement would lead to lower Maths self-concept. The results
of Models A and B provided support for this notion, although the paths
from achievement to non-matching self-concept domains in the
"accelerated" group were not significant, suggesting that the internal
reference (i.e., self-comparison of subject domains) may not be as
strong in the extremely talented group as in the "average" talented
students. Thus, we used the multiple-sample analyses to assess the
ability difference.
Model C. To test the factorial invariance between the "accelerated"
and "average" groups, we test a series of models with different
combinations of constraints to estimated parameters. Methods in testing
the factorial invariance are widely discussed are not further detailed
here (for more detailed discussion, see Bryne, Shavelson, & Muthen,
1989; Joreskog & Sorbom, 1988). Because our focus is on the invariance
of path coefficients across the "accelerated" and "average" groups, the
critical models to consider were those that imposed constraints on both
the factor loadings and the path coefficients in comparison to other
alternative models. The goodness of fit of models that converged to
proper solutions is shown in Table 1 (Model C). Models that did not
converge to proper solutions are likely to be problematic for
interpretations and are thus not reported.
The goodness of fit for Models C1 to C4 is all reasonable and close
(RNI ranging from .939 to .944 and TLI ranging from .933 to .937).
Because these models are nested, choice of the best fitting model can
be done statistically by comparing their (2 values and their df.
Typically the choice of a better model than another one requires
significant decrease in (2 value with reference to the decrease in df .
Otherwise the more parsimonious model (one with fewer estimated
parameters and hence larger df) is chosen. A comparison of the (2
values of the four models considered (section C of Table 1) resulted in
our choice of Model C2 as the best fitting model among others (a
decrease of (2 value of 22.90 per 10 df compared to Model C1, p < .05).
The CFA solution for Model C2 is thus presented in Table 2. However,
the choice of a best fitting model is not a critical concern in this
particular case because the focus is on the path coefficients and
incidentally all four models that resulted in proper solutions had the
path coefficients constrained to be equal across groups. Thus as long
as the models fitted the data, the magnitude and direction of the paths
are the critical concern.
In all these four models, the paths between matching domains, i.e.,
from maths exam score to Maths self-concept and from Chinese exam score
to Verbal self-concept, though lesser in magnitude, were positive and
significant. In contrast, paths between nonmatching domains, i.e.,
from maths exam score to Verbal self-concept and, to a lesser extent,
from Chinese to Maths self-concept, were negative and significant.
These results were consistent with the I/E model, and the invariance
models in section C (Table 1) showed that the pattern is reasonably
similar across the "accelerated" and "average" groups.
In sum, all the CFA models considered here supported the I/E model.
The patterns of path coefficients showed that achievement in a specific
academic domain had a significantly positive impact on self-concept in
the same academic area; but also had a significantly negative impact on
another academic area due to an internal comparison of abilities in
these academic areas.
Table 1
Goodness of Fit Summary for Alternative Models and Critical Path
Coefficients
Path Coefficients
From
Chin Maths Chin Maths
Model N (2 df RNI TLI GFI Description To
Vsc Msc Msc Vsc
A. All students
Null 495 3113.55 66
Total 495 159.91 50 .963 .951 .950 Total sample
.37* .52* -.08 -.22*
B. Separate groups
Null 160 868.60 66
"accelerated" 160 85.48 50 .952 .937 .920 "accelerated" class .11
.25* -.09 -.19*
Null 335 2314.94 66
"average" 335 128.31 50 .965 .954 .942 "average" class
.49* .66* -.19* -.29*
C. 2-group invariance
Null 160+335
C1. 160+335 311.22 128 .939 .937 .927 FL,PC,R,U inv
.36* .51* -.12* -.22*
C2. 160+335 288.32 118 .943 .937 .932 FL, PC, R inv
.36* .51* -.11* -.22*
C3. 160+335 299.20 120 .940 .934 .928 PC, U, R inv
.36* .51* -.12* -.22*
C4. 160+335 277.92 110 .944 .933 .933 PC, R inv
.36* .51* -.12* -.22*
Note. RNI = Relative noncentrality index. TLI = Tucker-Lewis index.
GFI = Goodness-of-fit index. RMSEA = Root mean square error of
approximation. FL = factor loadings. PC = path coefficients. U =
uniquenesses. R = residuals. inv = invariant. Models that did not
converge to a proper solution are not presented here. CFA solution for
Model C2 is presented at Table 2.
Table 2
CFA Solution for Model C2
Factor Loadings Uniq
Chin Maths MSELF VSELF
"accelerated" Group (n = 160)
1 Chin 1 0 0 0 0
2 Maths 0 1 0 0 0
3 MSELFP1 0 0 .82* 0 .39
4 MSELFP2 0 0 .73* 0 .34
5 MSELFP3 0 0 .84* 0 .39
6 MSELFP4 0 0 .83* 0 .35
7 MSELFP5 0 0 .89* 0 .17
8 VSELFP1 0 0 0 .79* .38
9 VSELFP2 0 0 0 .70* .59
10 VSELFP3 0 0 0 .78* .39
11 VSELFP4 0 0 0 .76* .54
12 VSELFP5 0 0 0 .66* .66
"average" Group (n = 335)
1 Chin 1 0 0 0 0
2 Maths 0 1 0 0 0
3 MSELFP1 0 0 .82* 0 .30
4 MSELFP2 0 0 .73* 0 .52
5 MSELFP3 0 0 .84* 0 .29
6 MSELFP4 0 0 .83* 0 .28
7 MSELFP5 0 0 .89* 0 .24
8 VSELFP1 0 0 0 .79* .39
9 VSELFP2 0 0 0 .70* .48
10 VSELFP3 0 0 0 .78* .39
11 VSELFP4 0 0 0 .76* .38
12 VSELFP5 0 0 0 .66* .51
Path Coefficients (identical for both groups)
to MSELF -.11* .51*
to VSELF .36* -.22*
Correlations between constructs (identical for both groups)
Chinese --
Maths .35* --
MSELF .07 .47* --
VSELF .28* -.09 -.14 --
Residuals and correlated residuals
Chinese 1
Maths .35* 1
MSELF 0 0 .77*
VSELF 0 0 -.06 .88*
Note. N = 495. The four constructs were Chinese achievement (Chin),
Maths achievement (Maths), Verbal Self-concept (VSELF), and Maths
Self-concept (VSELF) inferred from 5 item pairs (P1 to P5). Uniq =
uniqueness. Parameters with values of 0 or 1 were fixed in the
definition of the model. All parameters, except uniquenesses, across
the two groups were constrained to be equal. * p < .05
Summary and Limitations
The present study examines the applicability of the I/E model of
self-concept using a Chinese sample of talented students. The results
of this investigation clearly support predictions from the Marsh (1986)
I/E model for Maths and Verbal self-concept. Since most previous
studies of the I/E model were conducted in western countries, the
results of the present study show the strength of the I/E model across
cultures. In the present study, the path coefficient from maths exam to
Maths self-concept and Chinese exam to Verbal self-concept were
significant and positive whereas that from maths exam to Verbal
self-concept was negative and significant. However, in the total
sample, the path from Chinese exam to Maths self-concept was negative
but nonsignificant. When two groups were tested separately, all path
coefficients of the "average" group was consistent with the Marsh
(1986) findings. However, for the "accelerated" group, the paths from
Chinese exam to Verbal self-concept and Math self-concept were not
significant, although they were in the predicted direction. As some
researchers (e.g., Byrne & Gavin, 1996) have suggested, measures of
verbal achievement and Verbal self-concept are not always as stable as
assumed because language may involve a wide range of elements, such as
the study of literature, writing, reading skills and grammar, or the
combination of these. Nevertheless, an inspection of the models tested
in our analyses revealed that the particularly small sizes of negative
paths between nonmatching subject domains are found mainly in the
"accelerated" group in which the brightest students in the province, or
perhaps the highest achievers in the country, are placed. Another
limitation which is worthy to note here is that only one single
indicator for Chinese and maths achievement (Chinese exam score and
math exam score, respectively) was used . In a CFA solution, the
problem of using single indicators has been discussed elsewhere. As
summarised by Helmke & van Aken (1995), the use of single any
indicator does not allow proper tests of the reliability of the
indicator and corrections of relations between constructs for
unreliability. Nevertheless, in general, the findings of the present
study support the applicability of the I/E model with Chinese students,
except that for extraordinarily high achievers in both maths and verbal
domains, the external frame of reference seems to be more dominant than
the internal frame of reference.
To sum up, the present study found that the I/E model based on the
multidimensionality and domain-specificity of self-concept found in
Western samples can be generalised to Chinese students. Like other
students, talented students generally form their self-concept on the
basis of an internal/external frame of reference by comparing
themselves with other students in specific curriculum areas as well as
between their own performances in these curriculum areas, although the
internal frame of reference may not function as strongly as the
external frame of reference.
References
Bollen, K. A. (1989). Structural equations with latent variables. New
York: Wiley.
Byrne, B.M. (1989). Multigroup comparison and the assumptions of
equivalent construct validity across group: Multivariate Behavioral
Research, 23, 361-375.
Byrne, B.M. (1984) The general/academic self-concept nomological
network: A review of construct validation research. Review of
Educational Research, 54, 427-456.
Byrne, B. M., & Gavin, D. A. W. (1996). The Shavelson model revisited:
Testing for the structure of academic self-concept across pre-, early,
and late adolescents. Journal of Educational Psychology, 88, 215-228.
Byrne, B. M., & Shavelson, R. J. (1986). On the structure of
adolescent self-concept. Journal of Educational Psychology, 78,
474-481.
Byrne, B. M., & Shavelson, R. J. (1987). Adolescent self-concept:
The assumption of equivalent structure across gender. American
Educational Research Journal, 24, 365-385.
Gonzalez-Pienda, J. A., Nunez-Perez, J. C., Valle-Aries ,A.(1992).
Procesos de comparacion externa/interna, autoconcepto y rendimiento
academico. Revista-de-Psicologia-General-y-Aplicada,45, 73-81.
Helmke, A., & van Aken, M. A. G. (1995). The causal ordering of
academic achievement and self-concept of ability during elementary
school: A longitudinal study. Journal of Educational Psychology. 87,
624-637.
Hoge, R. D., & McShefrey, R. (1991). An investigation of
self-concept in gifted children. Exceptional Children ,57, 238-245.
Hoge, R. D., & Renzulli, J. S. (1993). Exploring the link between
giftedness and self-concept. Review of Educational Research , 63,
449-465.
Joreskog, K.G. & Sorbom, D. (1988). LISREL 7: a guide to the
program an application. Chicago: SPSS, Inc .
Joreskog, K. G., & Sorbom, D. (1993). LISREL 8: Structural equation
modeling with the SIMPLIS command language. Chicago: Scientific
Software International.
Kulik, J. A., & Kulik, C. C. (1992). Meta-analytic findings on
grouping programs. Gifted Child Quarterly, 36, 73-77.
Marsh, H. W. (1986). Verbal and Math self-concepts: An
internal/external frame of reference model. Educational Research
Journal, 23, 129-149.
Marsh, H. W. (1992). Self-Description Questionnaire II: Manual. New
South Wales, Australia: University of Western Sydney, Macarthur,
Faculty of Education, Publication Unit.
Marsh, H. W. (1993). Academic self-concept: Theory, measurement, and
research. In J. Suls (Ed.), Psychological perspectives on the self
(Vol. 4, pp. 59-88). Hillsdale, NJ: Erlbaum.
Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit
indices in confirmatory factor analyses: The effect of sample size.
Psychological Bulletin, 103, 391-410.
Marsh, H. W., Balla, J. R., & Hau, K. T. (1996). An
evaluation of incremental fit indices: A clarification of mathematical
and empirical processes. In G. A. Marcoulides & R. E. Schumacker
(Eds.), Advanced structural equation modeling techniques (pp. 315-353).
Hillsdale, NJ: Erlbaum.
Marsh, H. W., Byrne, B. M., & Shavelson, R. J. (1988). A multifaceted
academic self-concept: Its hierarchical structure and its relation to
academic achievement. Journal of Educational Psychology, 80, 366-380.
Marsh, H. W., & O'Neill, R. (1984). Self-Description Questionnaire III
(SDQIII): The construct validity of multidimensional self-concept
ratings by late-adolescents. Journal of Educational Measurement, 21,
153-174.
Marsh, H. W., & Shavelson, R. J. (1985). Self-concept: Its multifaceted
hierarchical structure. Educational Psychologist, 20, 107-125.
Marsh, H. W., & Yeung, A. S. (1997). Causal effects of academic
self-concept on academic achievement -- structural equation models of
longitudinal data. Journal of Educational Psychology, 89, 41-54.
Pedhazur, E. J., & Schmelkin, L. P. (1991). Measurement, design, and
analysis: An integrated approach. Hillsdale, NJ: Erlbaum.
Shavelson, R. J., Hubner, J. J., & Stanton, G. C. (1976).
Self-concept validation of construct interpretations. Review of
Educational Research, 46, 407-441.
Skaalvik, E. M. & Rankin, R. J. (1995). A test of the internal/external
frame of reference model at different levels of Math and Verbal
self-perception. American Educational Research Journal, 32, 161-184.
Tay, M. P., Licht, B. G., & Tate, R. L. (1995). The internal/external
frame of reference in adolescents' Math and verbal self-concepts: A
generalization study. Contemporary Educational Psychology, 20, 392-402.