## Mathematics ("c")

** Three units** (equivalent to three years or six semesters) of college-preparatory mathematics are required (four units are strongly recommended) including or integrating topics covered in:

- Elementary algebra
- Advanced algebra
- Two- and three-dimensional geometry

Also acceptable are courses that address the above content areas, and include or integrate:

- Trigonometry
- Statistics

### Goals of the requirement

High school mathematics courses should prepare students to undertake freshman-level university study. In these courses, students should acquire not only the specific skills needed to master this subject’s content, but also the general abilities – in the case of mathematics, proficiency in quantitative thinking and analysis – to engage with coursework in other disciplines.

Courses in the “c” subject area recognize the hierarchical nature of mathematics, and advanced courses should demonstrate growth in depth and complexity, both in mathematical maturity as well as in topical organization. Although many schools may follow the traditional Algebra 1 – Geometry – Algebra 2 format (e.g., as outlined in Appendix A of the Common Core State Standards in Mathematics [PDF]), other sequences may treat these topics in an integrated fashion. Combinations of some integrated courses, algebra, geometry and other courses that integrate the Common Core Standards for Mathematical Practice [PDF] for high school, including courses that rigorously apply these standards in the development of career-related skills, can also satisfy the “c” subject requirement. Appendix A of the Common Core State Standards in Mathematics [PDF] offers a starting point for developing courses that align with these standards.

All approved mathematics courses should be designed to give students the following competencies and should demonstrate how students will acquire them (merely listing standards to be covered is not sufficient):

- A view that mathematics is not just a collection of definitions, algorithms and/or theorems to memorize and apply, but rather is a coherent and tightly organized body of knowledge that provides a way to think about and understand a broad array of phenomena.

- A proclivity to put time and thought into using mathematics to grasp and solve unfamiliar problems that may not match examples the student has seen before. Students should find patterns of reasoning, make and test conjectures, try multiple representations (e.g., symbolic, geometric, graphical) and approaches (e.g., deduction, mathematical induction, linking to known results), analyze simple examples, make abstractions and generalizations, and verify that solutions are correct, approximate or reasonable, as appropriate. Students should also be encouraged to see the
*purpose*behind each concept and skill. For example, why take up the concept of rational exponents? Why prove the angle-angle criterion for triangle similarity?

- A view that mathematics models reality and students should have the capacity to use mathematical models to guide their understanding of the world around us.

- An awareness of special goals of mathematics, such as clarity and brevity (e.g., via symbols and precise definitions), parsimony (removing irrelevant detail), universality (claims must be true in all possible cases, not just most or all known cases) and objectivity (students should ask “Why?” and accept answers based on reason, not authority).

- Confidence and fluency in handling formulas and computational algorithms: understanding their motivation and design, predicting approximate outcomes and computing them – mentally, on paper or with technology, as appropriate. Among its many functions, mathematics is also a language; fluency in it is a basic skill, and fluency in computation is one key component.

Perspectives regarding the nature of how students may acquire the above competencies can be found in the Common Core Standards for Mathematical Practice [PDF]. Additional guidance can be found in the Statement on Competencies in Mathematics Expected of Entering College Students [PDF], from ICAS, the Intersegmental Committee of the Academic Senates of the California Community Colleges, the California State University and the University of California.

### Course criteria & guidance

- Regardless of the course level, all approved “c” subject area courses are expected to be consistent with the goals described above as well as in the Common Core Standards for Mathematical Practice [PDF].

- Most courses receive full 1.0 unit value with a few exceptions. A course covering only trigonometry, for example, would be 0.5 units, but a single course covering trigonometry with significant integration of other advanced math content related to pre-calculus could receive a full 1.0-unit value.

- One-year mathematics courses taken over three or four semesters are acceptable to meet the mathematics (“c”) subject requirement, but credit will be granted for only one year (or two semesters) of work. For students using this pattern, all grades awarded by the school are averaged in the GPA calculation.

- One yearlong course (1.0 unit value) must be either a course in geometry or part of an integrated sequence that includes sufficient geometry.

- Other rigorous courses that use mathematical concepts, include a mathematics prerequisite, and are intended for 11th and 12th grade levels, may also satisfy the requirement. Such courses may incorporate math in an applied form in conjunction with science, career technical education or other rigorous content, or may consist of pure mathematics. They must deepen students’ understanding of mathematics by incorporating the depth described in the ICAS Statement on Competencies in Mathematics Expected of Entering College Students [PDF]. Examples of such courses include, but are not limited to, trigonometry, linear algebra, pre-calculus (analytic geometry and mathematical analysis), calculus, discrete math, probability and statistics, and computer science. For instance, a computer science course with primary focus on coding methods alone would not fulfill the mathematics requirement, whereas one with substantial mathematical content (e.g., mathematical induction, proof techniques or other topics from discrete mathematics) could satisfy the requirement.

- Courses that are based largely on repetition of material from a prerequisite or prior course (e.g., as test preparation or pre-college review) will not be approved.

### Tools & resources

### Other options for satisfying the “c” subject requirement

Completion of higher-level math coursework with a grade of C or higher may validate D or F grades earned in lower-level courses or when a lower-level course is skipped. A complete description and matrix of the math validation rules is available for download.

College courses or satisfactory scores on SAT Subject, AP or IB exams can also be used to fulfill the mathematics subject requirement.