There is a general sense today that constructivist teaching is not up to the task of preparing students for high-stakes exams. In this article, the authors describe a highly effective constructivist approach used to teach students in a learning situation that takes the meaning of "high stakes" to another level. They talk about teachers of "cane travel," teachers who maintain a steadfast dedication to constructivism. Cane travel refers to a set of skills a person who is blind or who has low levels of vision uses to navigate the world independently. They discuss the concept of structured discovery, by considering a transcript of a travel lesson as an example of how the technique works. Among other things, the authors also describe lessons that can be drawn from structured discovery as it is practiced in teaching cane travel. (Contains 7 endnotes.)