This paper examines the contrast and distinction between divergent and convergent scientific creativity, and the paradoxical relationship of scientific creativity with cultural factors in elementary students. With a newly developed measure of potential for scientific creativity, EPoC Science (Lubart et al., in press), students produce ideas in response to scientific problems, and both divergent‐exploratory as well as convergent‐integrative processes involved in scientific creativity are analyzed. An empirical study (n = 118) was conducted in France with elementary school children (ages 7–10). The divergent‐exploratory task was scored for fluency and statistical uniqueness. For the convergent‐integrative task, the number of concepts that a student integrated and synthesized, and the originality of the synthesis were scored. Results showed that divergent and convergent task performances were weakly related to each other. This suggests that divergence and convergence are two relatively distinct processes for scientific creativity, and that the relation is more complex than commonly assumed. In terms of culture‐related variables, immigrant cultural background (number of family members born outside of France) was significantly and negatively correlated with the originality of divergent and convergent scientific creativity. Findings are discussed and educational implications are proposed.