The internal/external frame of reference (I/E) model and dimensional comparison theory posit paradoxical relations between achievement (ACH) and self-concept (SC) in mathematics (M) and verbal (V) domains; ACH in each domain positively affects SC in the matching domain (e.g., MACH to MSC) but negatively in the nonmatching domain (e.g., MACH to VSC). This substantive-methodological synergy based on latent variable models of Trends in International Mathematics and Science Study (TIMSS) data supports the generalizability of these predictions in relation to: mathematics and science domains, intrinsic motivation as well as self-concept, and age and nationality, based on nationally representative matched samples of fourth-and eighth-grade students from three Middle Eastern Islamic, five Western, and four Asian countries (N=117,321 students) with important theoretical, developmental, cross-cultural, and methodological implications.