Experiencing Change: The Mathematics of Change in Multiple Environments

ed from their work. Instead, the boys engaged in a process of making each environment into a lived-in space for themselves and of developing family resemblances across their trips in these lived-in spaces, to create a family of trips that included the similarities among trips as well as the distinct identity of each trip. Of course it is sometimes important for a teacher and her or his students to step back from a diverse set of activities and ask what they have in common and to reflect on the general mathematical principles that describe the activities. However, we argue that these general principles become meaningful and relevant only to the extent that they are rooted in an ongoing background of experiences.