Baroody, A.J., & Wilkins, J.L.M. (2004). Inverting a Triangular Array: Involving Students in Mathematical Inquiry. Mathematics Teaching in the Middle School, 9(6), 306-313.
The Inverting a 36 Penny Triangular Array problem is a challenging activity that can immerse middle school, secondary school, college students, and in-service teachers in the processes of mathematical inquiry. Solving such problems can help students understand the importance of looking for patterns, evaluating conjectures generated by intuitive or inductive reasoning about the patterns, considering alternative conjectures, checking additional examples, and searching for counter examples. It can also help students understand that logical reasoning is only as reliable as the premises on which it is based and that even false starts can play an important role in mathematical inquiry.