The Teaching GeT working group continues to work on narratives to accompany the SLOs that we developed and at the same time is incorporating some changes into the SLOs.   

The SLOs deal with 10 broad categories:

1. Proofs Derive and explain geometric arguments and proofs in written and oral form. 
2. Proof Verification Decide whether or not geometric arguments given by others are correct.
3. Secondary Geometry Understanding Understand the ideas underlying the typical secondary geometry curriculum well enough to explain them to students and use them to inform teaching practice and pedagogy.
4. Axioms, Theorems, and Models Understand and explain the relationship between axioms, theorems, and geometric models in which they hold (such as the plane, the sphere, the hyperbolic plane, etc.).
5. Definitions Understand the role of definitions in mathematical discourse. 
6. Technologies Effectively use technologies such as dynamic geometry software to explore geometry.
7. Euclid’s Elements Demonstrate knowledge of Euclidean Geometry, including the history and basics of Euclid’s Elements, and its influence on math as a discipline.
8. Straightedge and Compass Constructions Be able to perform basic Euclidean straightedge and compass constructions and be able to provide justification for why the procedure is correct.
9. non-Euclidean Geometries Compare Euclidean geometry to other geometries such as hyperbolic or spherical geometry.
10.  NCTM Standards Apply the following NCTM Geometry Standards: (a) analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships; (b) apply transformations and use symmetry to analyze mathematical situations; and (c) use visualization, spatial reasoning, and geometric modeling to solve problems.

In addition to the SLOs, we included a statement that in addition to teaching these content standards, all Geometry courses for future teachers should give students many chances to experience and develop their abilities with the mathematical process skills of problem solving, reasoning and proof writing, oral and written communication of mathematical ideas, and productive collaboration within groups.  They should also get a chance to engage with the progression of exploration followed by making conjectures and trying to prove their conjectures.

So far, the working group has written narratives for SLOs 3, 4, 5, and 9.  Several of these narratives are included elsewhere in this newsletter.  We are continuing to work on narratives for the other SLOs, with different subgroups spearheading our efforts for each remaining SLO. We will continue to meet Thursdays at 10 AM Eastern every other week throughout the summer and would welcome others to join us.