The interplay of g and mathematical abilities in large-scale assessments across grades

•We analyzed the interplay between mathematical ability, g, and Gf in six age cohorts.•We compared three different models of cognitive abilities for two LSA test types.•The two-correlated factors model and nested-factor models fitted the data best.•Across three grade levels, LSAs measured math-specific ability and g.•We related mathematical ability, g, and Gf to different student characteristics.

This study investigates the interplay between general cognitive abilities and domain-specific mathematical ability by applying three different models. The first model is a g factor model, the second model reflects two correlated factors, and the third model is a nested-factor model that comprises a g factor, a domain-specific mathematical factor and cognitive ability. Furthermore, we analyzed the relation between student characteristics such as self-concept in mathematics, gender, SES, and grade in mathematics. Using data from six different German LSAs of the three cohorts, Grade 5, 9 and 13 (sample sizes range from NGrade5 = 730 to NGrade9 = 3893), and two different frameworks (i.e., literacy and curricular), we confirmed that LSAs do test mathematical ability beyond g. The two cognitive factors correlated differently with the student characteristics considered; this calls for future longitudinal approaches to the issue.