Staff Resources
Proposed Mathematics Standards for California Public Schools - Grades Eight through Twelve - Introduction
The standards for grades 8 through 12 are organized differently than those for kindergarten through grade 7. Strands are not used for organizational purposes because, unlike in the earlier grades, in grades 8 through 12 the mathematics studied naturally falls under discipline headings: Algebra, Geometry, etc. Many schools teach this material in traditional courses, while others teach this material in an integrated fashion.In order to provide local educational agencies and teachers with flexibility, the grades 8 through 12 standards do not mandate a particular discipline to be initiated and completed in a single grade. Nevertheless, however it is taught, the core content of these subjects must be covered and all academic standards for achievement must be the same.
What follows are standards for: Algebra I, Geometry, Algebra II, Trigonometry, Mathematical Analysis, Linear Algebra, Statistics, Advanced Placement Statistics, and Calculus. It is recognized that many of the more advanced subjects are not taught in every middle or high school. Moreover, schools and districts have different ways of combining the subject matter in these various disciplines. For example, many schools combine some Trigonometry, Mathematical Analysis, and Linear Algebra to form a pre-Calculus course. Some districts prefer offering Trigonometry content with Algebra II.
The table below reflects typical grade level groupings of these disciplines in both integrated and traditional curricula.
Many other combinations of these advanced subjects into courses are possible. What is described here are standards for the academic content by discipline; it is not an endorsement of a particular choice of structure for courses or a particular method of teaching the mathematical content.
When students delve deeply into mathematics they gain not only conceptual understanding of mathematical principles but they also gain knowledge of and experience with pure reasoning. One of the most important goals of mathematics is to teach students logical reasoning. The logical reasoning inherent to the study of mathematics allows for applications to a broad range of situations where answers to practical problems can be found with accuracy.
By the eighth grade, students' mathematical sensitivity should be sharpened. Students need to start perceiving logical subtleties and appreciate the need for sound mathematical arguments before making conclusions. As students progress in the study of mathematics, they learn to: distinguish
between inductive and deductive reasoning; understand the meaning of logical implication; test general assertions; realize that one counter example is enough to show that a general assertion is false; conceptually understand that the truth of a general assertion in a few cases does not allow the conclusion that it is true in all cases; distinguish between something being proven and a mere plausibility argument; and identify logical errors in chains of reasoning.
Mathematical reasoning and conceptual understanding are not separate from content; they are intrinsic to the
