Plane Geometry - Bruce E. Shapiro

14 SECTION 3. CA STANDARDThe California Standards (1997)The California Board of Education sets forth 22 specific requirements forgeometry in secondary education. 2 These specifics are listed on pages 42-43 of Mathematics Content Standards for California Public Schools. TheMathematics Framework for California Public Schools expands on these 22requirements with specific examples (pages 85-89 of the Framework) anddiscuss specific considerations for high school geometry on pages 184-189of the Framework.California Framework1. Introduce students to the basic nature of logical reasoning.2. Use inductive reasoning and geometric constructions to build up a breadth ofknowledge from from a few basic axioms.3. Become proficient in proofs and learn the basic principles of plane geometry.4. Study the basic properties of triangles, quadrilaterals, circles, and parallel lines.5. Use the system built up to prove the Pythagorean theorem and from theredevelop and understanding of areas of differently shaped objects.6. Use coordinates and shapes as a natural jumping off into trigonometry.7. Show that the proofs of geometry can be repeated analytically using trigonometry.8. Develop the connection between geometry and algebra, introducing the conceptsof analytic geometry.According to the framework document, the main purpose of the geometrycurriculum is to develop geometric skills and concepts and the abilityto construct formal logical arguments and proofs in a geometric setting.“The geometry skills and concepts developed in this discipline are usefulto all students. Aside from learning these skills and concepts, studentswill develop their ability to construct formal, logical arguments and proofsin geometric settings and problems.” The curriculum is weighed towardsplane Euclidean geometry but allows (and encourages) some use on coordinatesystems and transformations. The “considerations” section (pages184-189 of the Framework) walk us through the standards and give us aperspective on how a geometry course might be structured.2 This material has been largely superseded by the adoption of the common core standardsby California in 2010.« CC BY-NC-ND 3.0. Revised: 18 Nov 2012