This article describes the A, E, I, O, U technique, designed to help teachers ensure that teaching and learning are not mutually exclusive in the classroom. Most teachers would agree that motivating average teenagers to communicate how they got an answer or justify their problem-solving strategies can be as difficult as teaching a dog to whistle. However, students must be given specific instructions and encouraged in their attempts if teachers are expected to assess accurately what has been learned. The A, E, I, O, U method, consisting of a simple mnemonic and accompanying rubric, serves to facilitate this process, thereby promoting mathematical discourse and improving both communication and assessment in the classroom. By associating necessary elements of good problem solving with each of the vowels, students are able to understand and easily remember what is expected of them. The technique's framework for structuring and evaluating mathematical work allows students to demonstrate what they know and allows teachers to evaluate their students' levels of understanding better. (Contains 6 figures.)