Developmental associations between adaptive number knowledge and routine mathematical knowledge

The development of adaptive expertise – the ability to flexibly apply knowledge to solve novel tasks – is a highly sought-after educational outcome. Adaptive number knowledge has been identified as one important manifestation of adaptive expertise in arithmetic. The present study is the first to examine the development of adaptive number knowledge and its relation to the development of routine mathematical knowledge. We examine 675 secondary school students’ adaptive number knowledge, along with their arithmetic fluency and their general curriculum-based mathematics achievement. We find bidirectional relations between adaptive number knowledge and the two measures of routine mathematical knowledge. Latent transition analysis revealed that prior arithmetic fluency and curriculum-based mathematics achievement were both predictors of students’ adaptive number knowledge development. These results suggest the mutually beneficial relation between how adaptive expertise in school mathematics may develop alongside more routine mathematical knowledge.