This paper reports on 3-year case studies of 2 schools with alternative mathematical teaching approaches. One school used a traditional, textbook approach; the other used open-ended activities at all times. Using various forms of case study data, including observations, questionnaires, interviews, and quantitative assessments, I will show the ways in which the 2 approaches encouraged different forms of knowledge. Students who followed a traditional approach developed a procedural knowledge that was of limited use to them in unfamiliar situations. Students who learned mathematics in an open, project-based environment developed a conceptual understanding that provided them with advantages in a range of assessments and situations. The project students had been “apprenticed” into a system of thinking and using mathematics that helped them in both school and nonschool settings.
Jo Boaler, Lecturer, School of Education, King's College London, Cornwall House, Waterloo Road, London SE1 8WA, United Kingdom; firstname.lastname@example.org