Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how the Erlangen program might be extended to mathematics in general, with specific examples from geometry, fractions, and algebra. By focusing on students' available ways of operating, we can empower students to construct mathematical objects for themselves, rather than learning about figures that are supposed to have a separate existence.