In this chapter we identify strategies and task structures that have proved effective in prompting learners to construct mathematical objects. We draw on the various tasks used in previous chapters and on some further cases of classrooms, lessons, and other learning environments in which learners have been asked to construct LGEs for themselves. In each case we look for manifestation of the principles derived in chapter 3:

• Exemplification is individual and situational. • Perceptions of generality are individual. • Examples can be perceived or experienced as members of structured spaces. • Example spaces can be explored and extended by the learner, with or without external