Answering this question has implications for preparing teacher candidates, designing professional development activities for classroom teachers, and focusing resources for grants to improve mathematics teaching. There are three domains for teacher preparation and improvement — knowledge of subject area content, special pedagogy, and general pedagogy.
I am most interested in the required knowledge and skills related to the mathematics content domains such as Algebra, Functions, Geometry, etc. Use the attached document related to the Function domain as a template for writing a standards document for a different content domain of the CCSS high school mathematics. Secondary Mathematics – Common Core Standards Functions
Teaching standards Washington state — secondary mathematics
Geometry domain
Overview:
Teachers need to be able to understand Euclidean geometry synthetically and analytically. Using transformations to introduce congruence, similarity, and symmetry, and logically formulated proofs as a result. Teachers might be able to define trigonometric ratios and know applications of trig. Especially as they direct to law of sines, law of cosines. Teachers need to know special right triangles and proportions. Teachers need to be able to connect and distinguish between the algebra of an equation and the geometry of the equation. Teaches need to be able to work with dynamic geometry environments, e.g manipulatives, and know how they promote learning.
Connections to equations:
Teachers need to be able to connect and distinguish between the algebra of an equation and the geometry of the equation.
Learning targets (indicators). Teacher candidates will be able to:
~understand Euclidean geometry – synthetically and analytically
~use transformations to demonstrate congruence, similarity and symmetry
~use deductive reasoning to prove geometric concepts
~understand how theorems, definitions and postulates are related
~understand right triangle trigonometry in the formulation of trig ratios
~use Pythagorean theorem to explore real-world situations
~demonstrate how PT can be extended to the formulation of law of cosines and law of sines
~connect and distinguish the role that geometry p lays in reinforcing algebra and vice versa
~use various tools and manipulatives to model and explore geometric concepts
Geoff La Brant & Aaron Brien