This study purports to explore the degree of universality of the constructs involving self-beliefs, intrinsic motivation, and engagement in 58 countries. The study conducted a factor invariance analysis of six background questionnaires of the Trends in International Mathematics and Science Study (TIMMS) 2011 fourth-grade. The intrinsic motivation scales in mathematics and science were noted to exhibit a higher degree of cross-cultural equivalence, while the self-beliefs scale shows no degree of invariance. These results suggest that the motivation scale is the only one sufficiently invariant for making valid comparisons across countries. Different factors that could affect the cross-cultural invariance are addressed.