(Math-MthEd) Survey of Geometry
Knowing and Learning Geometry
Students understand central objects, concepts, relationships, definitions, and theorems of Euclidean geometry, how adolescents come to understand these, and the canonical examples and alternative approaches germane to teaching secondary school geometry.
Understanding What and Who Mathematics Privileges
Students describe the affordances and constraints of an axiomatic approach to doing mathematics and recognize that an axiomatic approach is just one way to do mathematics. Students understand that who counts as a mathematician is dependent on the ways in which mathematics is defined and recognize who has privileges associated with the status of "mathematician."
Communicating Geometric Ideas and Arguments
Students can communicate geometric ideas effectively using a variety of appropriate representations and can construct valid proofs of geometric theorems within a given axiom system.
Students understand and can describe the relationships among neutral, Euclidean, and non-Euclidean geometries in terms of fundamental geometric concepts, objects, and properties (particularly parallelism), and can use the fundamental properties of axiom systems and models to provide convincing arguments about these relationships.