In IBL land a central idea is creating a sequence of problems, and letting students experience the learning process through guided discovery. The problems are spaced so that students have opportunities for authentic ownership of the mathematics and intellectual (and personal) growth. In the spirit of showing our kids learning to ride, here's an image of my son, Hutch, working on a lemma (i.e. riding a balance bike with no pedals). After he learned how to balance himself, he got on a bike and rode off. All he needed to learn was how to use the brakes. And you didn't need to tell him he got the right answer. Q.E.D.
