In this study we investigated the development of 245 kindergarteners' mathematics problem solving (MPS) at two time points within 7 months using a cognitive diagnostic test, which measured three cognitive components (mathematical knowledge and skills, semantic understanding, and quantitative reasoning) with eleven cognitive attributes. The effects of five influencing factors [language ability, mathematics application ability, calculation ability, approaches to learning (ATL) and socio-economic status (SES)] on the children's MPS ability at the two time points were examined. The results indicated that the 245 children's mastery of mathematical knowledge and skills was much better than their mastery of semantic understanding and quantitative reasoning. Furthermore, they achieved significant progress in set comparison and addition and subtraction within the range of natural numbers to ten (two of the three cognitive attributes of mathematical knowledge and skills), additive composition reasoning and one-to-many correspondence reasoning (two of the three cognitive attributes of quantitative reasoning). Only their mathematics application ability significantly predicted their mastery of the three cognitive components of MPS ability at the two-time points. Their language and calculation abilities predicted only their mastery of mathematical knowledge and skills at the two time points. Their ATL predicted their mastery of the three cognitive components of MPS only at the first time point, and their SES predicted only their mastery of semantic understanding 7 months later.