The internal-external frame of reference model describes a seemingly paradoxical pattern of relations between math and verbal self-concepts and corresponding measures of achievement (see Marsh, 1986, 1990c, 1993a; Marsh, Byrne, & Shavelson, 1988; Marsh & Hau, 2003; Marsh, Kong, & Hau, 2001) and why math and verbal self-concepts are almost uncorrelated, even though corresponding areas of academic achievement are substantially correlated (typically .5 to .8, depending on how achievement is measured). According to this model, academic self-concept in a particular school subject is formed in relation to two comparison processes or frames of reference. The first is the external (normative) reference in which students compare their self-perceived performances in a particular school subject with the perceived performances of other students in the same school subject. It predicts, not surprisingly, that good math skills lead to higher math self-concepts and that good verbal skills lead to higher verbal self-concepts. The second is an internal (ipsative-like) reference in which students compare their own performance in one particular school subject with their own performances in other school subjects. According to this process, good math skills should lead to lower verbal self-concepts (once the positive effects of good verbal skills are controlled) and good verbal skills should lead to lower math self-concept.
In a particularly strong test of the cross-cultural generalizability of predictions from this model, Marsh and Hau (2004) evaluated responses from nationally representative samples of 15-year-old students from 26 countries who completed common achievement tests and self-concept surveys. In support of a priori predictions, (a) math and verbal achievements were highly correlated, whereas math and verbal self-concepts were nearly uncorrelated; and (b) math and verbal achievements each had positive effects on the matching self-concept domain, but negative effects on nonmatching domains (e.g., verbal achievement had a positive effect on verbal self-concept but a negative effect on math self-concept). Very demanding tests of invariance that required all four path coefficients relating the two achievement test scores to the corresponding self-concept measures to be the same in each of the 26 countries provided a good fit to the data. Because there was such good support for predictions based on the internal-external frame of reference model and such good support for the generalizability of these results across the 26 countries, the results clearly supported the construct validity of the model and its cross-cultural generalizability.
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