In a previous study of 2 schools in England that taught mathematics very differently, the first author found that a project-based mathematics approach resulted in higher achievement, greater understanding, and more appreciation of mathematics than a traditional approach. In this follow-up study, the first author contacted and interviewed a group of adults 8 years after they had left the 2 schools to investigate their knowledge use in life. This showed that the young adults who had experienced the 2 mathematics teaching approaches developed profoundly different relationships with mathematics knowledge that contributed towards the shaping of different identities as learners and users of mathematics (Boaler & Greeno, 2000). The adults from the project-based school had also moved into significantly more professional jobs, despite living in one of the lowest income areas of the country. In this article, we consider the different opportunities that the 2 school approaches offered for long-term relationships with mathematics and different forms of mathematical expertise that are differentially useful in the 21st century (Hatano & Oura, 2003).
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