In a previous study of 2 schools in England that taught mathematics very differently, researchers 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, participants in the first study were contacted and interviewed 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. 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 longterm relationships with mathematics and different forms of mathematical expertise that are differentially useful in the 21st century.
The number of students who leave U.S. schools mathematically underprepared has prompted widespread concern. Low achieving students, many of whom have been turned off mathematics, are often placed in low tracks and given remedial, skills-oriented work. This study examines a different approach wherein heterogeneous groups of students were given responsibility and agency and asked to engage in a range of mathematical practices collaboratively. The teaching intervention, which was introduced in the first paper, took place as part of a summer class on algebra, and it gave students the opportunity to participate with mathematics in changed ways. This paper will report evidence that the vast majority responded with increased engagement, achievement, and enjoyment. The students chose collaboration and agency as critical to their improved relationships with mathematics.
Recent scientific evidence demonstrates both the incredible potential of the brain to grow and change and the powerful impact of growth mindset messages upon students’ attainment. Schooling practices, however, particularly in England, are based upon notions of fixed ability thinking which limits students’ attainment and increases inequality. This article reviews evidence for brain plasticity, the importance of mindset and the ways that mindset messages may be communicated through classroom and grouping practices.