California Mathematics Draft Framework

Wow! I’m genuinely impressed. California, which so often is a force for idiocy in education, is blazing trails towards a new (old?) mathematics curriculum.

http://www.cde.ca.gov/ci/ma/cf/index.asp

I’ll go over all the standards in more detail later, but for now I’ll make a few quick observations on the chapter on geometry.

• Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning
• Students construct, and judge the validity of, a logical argument and give counterexamples to disprove a statement.
• Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.
• Students write geometric proofs, including proofs by contradiction.
• Students prove basic theorems involving congruence and similarity.
• Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
• Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.
• Students prove theorems and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
• Students prove the Pythagorean theorem.
• Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle.
• Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.
• Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.

Sincere kudos to the drafters of this curriculum!