Frequently cited but seldomly actually measured: The mathematical cast of mind [Author Accepted Manuscript]

Understanding the sources of individual differences in mathematical abilities is considered essential by both researchers and society alike. Almost 50 years ago, the Russian psychologist V.A. Krutetskii proposed the concept of a mathematical cast of mind (MCOM), which he described as a predisposition to perceive the world through ‘mathematical eyes’. This MCOM should be particularly evident in gifted individuals, enabling them to acquire mathematical knowledge more rapidly and to achieve higher levels of mathematical performance. Although Krutetskii's concept is often referred to in models of mathematical giftedness, empirical attempts to measure it have been limited. The aim of this study is to identify specific tasks that capture aspects of the MCOM and to determine whether these tasks contribute to an MCOM factor that is associated with mathematical achievement above and beyond verbal and figural intelligence. To this end, 82 university students worked on tasks that measure the MCOM components of obtaining mathematical information, processing of mathematical information, and motivational tendencies. The results of an exploratory factor analysis showed a three-factor structure in line with theoretical components of MCOM but not a single factor of MCOM. From the three components, only motivational tendencies was a significant predictor of mathematical achievement. Obtaining mathematical information, in contrast, showed negative correlations with the other two factors and did not significantly predict individual differences in mathematical competence. These findings provide further insights into the concept of MCOM and if it can be measured reliably to eventually predict individual differences in mathematics.