Recent studies have concluded that children's development of private speech (private speech internalization) is related to and important for developing mathematical ability. In this article, we review a project consisting of studies exploring the cognitive factors that may underlie differences between the use of private speech by children with (MD) and without (MN) mathematical difficulties. The main issue of interest was whether private speech internalization is related to children's mathematical achievement, task-specific strategies, phonological awareness, and phonological memory, and whether any such relationships are modulated by age and mathematical achievement. The findings not only confirm that private speech internalization relate to mathematical achievement, they also highlight possible parallels between the contributions of strategies, phonological awareness, and phonological memory to subsequent mathematical achievement. Overall, the results seem to provide evidence for the hypothesis that mathematical achievement is causally related to phonological abilities -- which underpin the internalization of private speech -- rather than being directly related to the private speech internalization.