Craig Jensen: A Dice Game for Engaging Teachers in Discourse
One of the challenges for me as a mathematician interested in professional development of teachers is finding or creating an engaging lesson that is in the high school curriculum and yet will challenge high school math teachers so that they engage in the mathematical practices at an authentic level. By authentic, I mean that teachers truly do not have an algorithm to apply to the problem and thus have to think deeply and share ideas with colleagues. As part of a Louisiana Systemic Initiative Program (LaSIP) mathematics grant for professional development of high school teachers that Yvelyne, Ivan, and I codirected, I shared a lesson on discovering the Sicherman dice which are two six-sided cubes, with the first labeled 1, 2, 2, 3, 3, 4, and the second labeled 1, 3, 4, 5, 6, 8. They are the only dice with positive integer labels having the same probability distribution for its sum as a pair of normal dice labeled 1 to 6. This lesson provided the type of challenge necessary for engaging the teachers in authentic discourse.