•We studied the interplay of achievement and self-concept in primary education.•We used a longitudinal U.S. representative data set with math and verbal test-scores.•Within domains reciprocal relations between achievement and self-concept were found.•Across domains effects of achievement on subsequent self-concept were negative.•Overall, the findings strongly support the RI/EM for primary school students. The reciprocal internal/external frame of reference model (RI/EM) extends the internal/external frame of reference model (I/EM) over time and the reciprocal effects model (REM) across domains. The RI/EM postulates positive developmental relations between academic achievement and self-concept within a domain and negative relations across two non-matching domains (e.g., math and English). However, until now, empirical investigations of the RI/EM had only focused on secondary school students from specific countries. In the present study, we test whether the RI/EM also applies to primary school students and to students in the United States, by using a representative longitudinal data set: the Early Childhood Longitudinal Study-Kindergarten (ECLS-K: 1998–1999). We found positive reciprocal relations between academic self-concept and standardized test scores within a domain, whereas the effect of prior achievement on self-concept was much stronger (skill-development part) than the effect of self-concept on achievement (self-enhancement). Furthermore, we found negative effects of achievement on subsequent self-concepts across domains (I/E frame of references). Overall, the findings of the study strongly support the RI/EM for primary school students. Our results are compared to previous findings in the literature for secondary school students and are discussed with regard to self-concept formation in primary school.