1. Maher Abu-Hilal Sultan Qaboos University With Sahar Al-Abri
Internal/External Frame of Reference Model with Science and Math Self-Concepts and Achievement among Omani Eighth Graders
Maher Abu-Hilal
Sultan Qaboos University
With Sahar Al-Abri

2. SELF Eighth Biennial International Conference, Kiel, Germany
Objectives
The aim of the present study was to test the assumptions of internal/external frame of reference model using science scores and self-concept in place of language. Marsh, Kong and Hau (2001) suggest that internal comparisons should be a function of all school subjects; hence, this study is using science instead of language to test this claim.
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Method
Sample Three hundred twenty six eighth grade students in Al-Dhahra School District in Oman responded to a short version of SDQ-I. The sample was selected from those who took the TIMSS in 2011 (N=741).
SELF Eighth Biennial International Conference, Kiel, Germany

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Method
Analysis In this study, we tested two models, one with competence and affect were conflated and one with competence and affect were separated. Multiple samples were also employed as gender was the grouping variable.
SELF Eighth Biennial International Conference, Kiel, Germany

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Results
The conflated model produced indicators of good fit (c2 = , df=124, CFI =.960, RMSEA = .043). The model with competence and affect are separated also produced good fit to data (c2 = , df = 115, CFI = .977, RMSEA = .034).
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Results
In the conflated model, math achievement had significant positive effect on math SC (.47) and negative effect on science SC (-.21). Science achievement had significant positive effect on science SC (.67) but no effect on math SC.
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Fig. 1: I/E Model (Math and Science for the Total Sample of Omani 8th Graders
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Results
As for the model that separates SC into competence and affect, math achievement had significant positive effect on both competence (.56) and affect (.36) math SC and negative effect on science affect SC (-.26). Science achievement had significant effect on competence and affect science SC (.66). The study partially provides support to the I/E frame of reference model. It replicates previous findings among Arab students.
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.90
.17
.45
.22
.91
.25
Fig. 2: I/E Model (Math and Science for the Total Sample of Omani 8th Graders
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Results
The data from TIMSS produced weak relations between achievement and SC. Thus, the findings of this study confirmed that academic self-concept is more associated with teacher assessment than with standardized tests.
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Table 1: Regression weights, SE, CR, Probability and standardized weights b
S.E.
C.R. P
s.b.
Math Com
MATHSCORE
.034
.006
5.822
.000
.551
Math Aff
.021
3.469
.355
Science Com
-.007
.005
-1.540 NS
-.155
SCIENCESCORE
.009
.007
1.402
.142
6.225
.650
.004
.598
.055
Science Aff
-.011
-2.415
.016
-.260
.030
.654
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Table 2: Indices of Goodness of Fit of Different Models of I/E Frame of Reference in Oman across Gender
Model c2 DF P
CFI
RMSEA
c2/DF
Unconstrained
230
.000
.966
.044
1.624
Measurement weights
242
.963
.045
1.648
Measurement intercepts
258
.958
.046
1.683
Structural weights
266
.956
1.697
Structural means
268
.948
.050
1.813
Structural covariances
271
.946
.051
1.835
Structural residuals
281
.943
1.847
Measurement residuals
304
.931
.054
1.955
Saturated model
1.000
.194
Independence model
342
13.253
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13. Separated SC across Gender
Measurement invariance, structural invariance, and structural path invariance were examined across gender. A series of invariance tests were conducted and Table 1 shows the results.
Consistent with predictions and with the findings of previous research, science and math scores were highly correlated for girls (r = .88) and for boys (r = .84). The correlations between science and math self-concepts, however, were substantially lower than the correlations between science and math achievements.
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Discussion
As for the relationships among self-concept dimensions and academic achievement, the CFA as well as the SEM revealed that academic achievements were more strongly related to the cognitive (competence) components than to the affective components of self-concept. Similar results were reported by Arens et al. (2011) and Abu-Hilal and Abdelfattah et al. (2013).
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Discussion
Marsh, Kong and Hau (2001) suggest that internal comparisons should be a function of all school subjects. However, Dickhöuser, Reuter and Hilling (2005) failed to provide complete support to the assumptions about correlations between self-concept and achievement with biology and chemistry. Also, Chanal, Sarrazin, Guay and Boiche (2009) failed to find full support for the assumptions of the I/E frame of reference model with physical education included in the model.
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Discussion
Contrary to our conceptualization and that of Arens et al. (2011), Dickhöuser et al. (2005) and Chanal et al. (2009) who used the global conflated self-concept and did not separate self-concept into cognitive and affective components. Conflating cognitive and affective components may be the reason that self-concept-achievement relations across domains were inconsistent with the premises of the I/E frame of reference model.
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Implications
Probably the most important theoretical implication is that models and instruments developed in one culture can be justifiably employed in other different cultures. The results of the study also imply that counseling and intervention programs could be designed along domain-specific and components-specific lines, for example, to improve students' perception of competence and value in science and mathematics.
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