The present study aims to examine inter-individual differences in adaptive number
knowledge in secondary school students. Adaptive number knowledge is defined as a
well-connected network of knowledge of numerical characteristics and arithmetic relations.
Substantial and relevant qualitative differences in the strategies and expression
of adaptive number knowledge have been found in primary school students still in the
process of learning arithmetic. We present a study involving 879 seventh-grade students
that examines the structure of individual differences in adaptive number knowledge
with students who have completed one year of algebra instruction. Results of a latent
profile analysis reveal a model that is similar than was previously found in primary
school students. As well, arithmetic fluency and the development of arithmetic fluency
are strong predictors of adaptive number knowledge latent profile membership. These
results suggest that adaptive number knowledge may be characteristic of high-level
performance extending into secondary school, even after formal instruction with arithmetic
concludes.