Marina Vasilyeva

Understanding of the base-10 structure of multi-digit numbers is one of the critical aspects in early mathematics learning. It has been documented that children from different countries vary in their use of base-10 representations. Questions concerning potential sources of this variability have been debated for decades. One commonly posited explanation is that some languages provide explicit cues about the structure of multi-digit numbers, facilitating the development of base-10 representations. In the present study, we tested this view against an alternative view, positing that variability in children’s learning of numeric structure may reflect differences in their experiences with numbers. The study examined kindergartners and first-graders from four countries: Taiwan, South Korea, the USA, and Russia. Results showed that the use of base-10 representations by American first-graders increased dramatically over the last decades, following changes in curricular guidelines. First-graders across the four countries showed some differences in performance (however, not consistent with the language account), whereas kindergartners performed comparably despite the differences in their languages. The results suggest that the nature of early math instruction may be critical for children’s developing understanding of numeric structure.

The present study examined the extent to which college students’ academic mindsets predicted their persistence when solving challenging math problems. The study included an experimental manipulation, in which participants initially received either an easy or a difficult arithmetic task. Following the manipulation, all participants solved two target math problems: one that was solvable but very hard and another that was unsolvable.

Time spent attempting to solve each problem served as a measure of persistence. Results showed the predicted pattern for the solvable target problem, but not for the unsolvable problem. That is, for the solvable problem, the more of a fixed mindset participants had, the less persistent they were after completing a relatively difficult arithmetic task than after completing an easy task. The results suggest that, for certain types of math problems, students’ persistence may vary as a function of academic mindset and previous experiences of math success or failure.