To learn mathematical practices, students need opportunities to engage in them. But simply providing such opportunities may not be sufficient to support all students. Simultaneously, explicitly teaching mathematical practices could be problematic if instruction becomes prescriptive. This study investigated how teachers might make mathematical practices explicit in classroom discourse. Analyses of 26 discussions from 3 mathematics classes revealed that teachers made mathematical practices explicit primarily after students had participated in them. I present a framework of 8 types of teacher moves that made mathematical practices explicit and argue that they did so without turning practices into prescriptions or reducing students' opportunities to engage in them. This suggests a need to expand conceptions of explicitness to promote access to mathematical practices.
Jo Boaler and Sarah Kate Selling
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 longterm relationships with mathematics and different forms of mathematical expertise that are differentially useful in the 21st century (Hatano & Oura, 2003).
Erin E. Baldinger, Sarah Kate Selling, and Rajeev Virmani
Leading a whole-class mathematics discussion is complex work. The teacher must attend to and respond to student thinking while continually keeping the mathematical goals of the discussion in mind. This work is especially challenging for novice teachers who are just learning to facilitate classroom talk. We present a new sortingtask instructional activity designed to support novice secondary teachers in steering a discussion toward a mathematical point while eliciting and making use of student thinking. We describe our efforts to support novice teachers through learning about, rehearsing, enacting, and reflecting on this sorting task. We document the impact of these supports for the novice teachers, and share ways that other teacher educators can take up this structure.