# (Math-MthEd) Survey of Geometry

(Math-MthEd) Survey of Geometry
Logical and historical development of Euclidean and non-Euclidean geometry, transformations and symmetry; relationships among axiomatic systems; use of software and other geometric models; proofs and Van Hiele levels.
MATH
362
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites MATH 290 Taught Fall, Winter, Spring Programs Containing MATH 362
Course Outcomes:

### 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.

### Multiple Geometries

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.