This project examines the nature of adaptive expertise in mathematics education, exploring relationships between this concept from cognitive psychology and effective middle school mathematics instruction. One goal of the project is to operationalize adaptive expertise in mathematics classroom using three dimensions: cognitive models of professional competence, instructional practices, and professional learning. Then, researchers seek to determine whether teachers who are more effective at raising student achievement are more or less adaptive. They use regression modeling to examine associations between teacher effectiveness and adaptive expertise, with teachers' mathematics knowledge for teaching as a mediating factor. They test a series of hypotheses in a one-factor correlational study with 60 veteran middle school mathematics teachers from the San Francisco Bay Area.