In this journal issue, the authors of the focus articles have provided a suite of very stimulating and thoughtful articles. The overarching purpose of this research is to explore the application of principles derived from the view of validity proposed by Kane (2004) to their research on issues related to the measurement of mathematical knowledge for teaching. The authors of this article have approached their commentary on their work as a conversation between a measurement theorist (Engelhard), and a mathematics educator (Sullivan). They each read the articles using their distinctive disciplinary lens, and then developed a set of questions that the articles generated for them regarding either the measurement issues related to validity or the substantive aspects of the construct being measured by the authors. Finally, the authors met to discuss the questions and answers, and this commentary reflects their discussion. The authors hope that their questions and answers will stimulate further conversations between measurement theorists, mathematics educators, and other researchers working in substantive areas to develop measurement tools for new constructs to improve education. The authors' questions and answers are organized by articles, although many of the points apply across articles. (Contains 1 figure.)