Students’ manifestations of adaptive expertise in mathematics [Author Accepted Manuscript]

Mathematics is not only relevant in formal situations such as in a classroom, but students use mathematical knowledge and pay attention to mathematical features even in situations that are not explicitly mathematical. Adaptive expertise in mathematics is required to apply mathematical skills to novel and everyday problems. Situations in everyday life may also provide opportunities to develop adaptive expertise in mathematics. We suggest that Spontaneous Focusing On quantitative Relations (SFOR), Spontaneous Focusing on Numerosity (SFON), and Adaptive rational Number Knowledge (ArNK) are different manifestations of adaptive expertise in mathematics. Thus, we investigated how adaptive expertise in mathematics manifests in general upper secondary school students (n=106). We also examined whether these skills are related and differ if a student chooses an advanced or basic mathematics syllabus track. The results showed individual differences in how adaptive expertise in mathematics manifests in general upper secondary school students. Furthermore, ArNK was found to have a positive correlation with SFOR and SFON. However, there were task-based differences. In addition, students in the advanced mathematics syllabus track had a higher ArNK than those in the basic mathematics track, but there were no consistent differences in SFOR or SFON. This research furthers our understanding of individual differences in mathematics learning outcomes and adaptive expertise in mathematics at the start of upper secondary education.