Explore the concept of radian measure in this 29-minute video lecture from the Insights into Mathematics series. Delve into the history, meaning, and logical structure of radians, examining their necessity in mathematics education. Investigate the distinction between applied mathematics used in technology and the theoretical constructs of pure mathematics. Analyze circular functions from a radian perspective and consider the challenges of justifying radian measure in high school curricula. Learn about the underlying theory of arc lengths and its connection to calculus. Gain insights into the ongoing debate surrounding the use of radians in mathematics education and the questions educators should be asking.