Math SPIRAL students are enrolled in a 3-credit summer course at the University of Maryland. The course consists of two sub-courses that run in parallel. The first presents combinatorics and a strategic analysis of winning strategies for a variety of games. This is a very hands-on problem solving course. The second is a study of the core methods of mathematical reasoning and proof. We focus not only on solving problems but on accurately communicating those solutions both in writing and verbally. Formal public presentations of the academic and the research results are a key part of the SPIRAL program.