Traditionally measured skills with arithmetic are not related to later
algebra success at levels that would be expected given the close
conceptual relation between arithmetic and algebra. However, adaptivity
with arithmetic may be one aspect of arithmetic competences that can
account for additional variation in algebra attainment. With this in
mind, the present study aims to present evidence for the existence and
relevance of a newly acknowledged component of adaptivity with
arithmetic, namely, adaptive number knowledge. In particular, we aim to
examine whether there are substantial individual differences in adaptive
number knowledge and to what extent these differences are related to
arithmetic and pre-algebra skills and knowledge. Adaptive number
knowledge is defined as the well-connected knowledge of numerical
characteristics and relations. A large sample of 1065 Finnish late
primary school students completed measures of adaptive number knowledge,
arithmetic conceptual knowledge, and arithmetic fluency. Three months
later they completed a measure of pre-algebra skills. Substantial
individual differences in adaptive number knowledge were identified
using latent profile analysis. The identified profiles were related to
concurrent arithmetic skills and knowledge. As well, adaptive number
knowledge was found to predict later pre-algebra skills, even after
taking into account arithmetic conceptual knowledge and arithmetic
fluency. These results suggest that adaptive number knowledge is a
relevant component of mathematical development, and may help account for
disparities in algebra development.