## Mathematics ("c")

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

- Elementary algebra or Algebra 1
- Advanced algebra or Algebra 2
- Two- and three-dimensional geometry

### Course guidance

The intent of the mathematics requirement is to enable students to develop the ability to think mathematically as well as to provide background and skills for classes and disciplines with specific mathematical content.

#### Goals of the mathematics requirement

The overarching goal of the subject requirement in mathematics is to ensure that freshmen are adequately prepared to undertake university-level study. 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 will follow the Algebra 1 – Geometry – Algebra 2 format outlined in the 1997 California Standards, other sequences may treat these topics in an integrated fashion. Combinations of integrated math, algebra, geometry and other courses 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 in either pathway that align with these standards.

More important than the topics covered, or even the skills used directly in class, are the more general abilities and attitudes that should be gained in the effort of mastering the content. These include fostering:

- A view that mathematics makes sense: it offers ways of understanding and thinking; it is not just a collection of definitions, algorithms and/or theorems to memorize and apply.
- 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, 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.
- A view that mathematics approximates reality and mathematical models can guide our 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. Mathematics is a language, fluency in it is a basic skill, and fluency in computation is one key component.

Approved “c” subject area courses must demonstrate how students acquire these competencies. A guide for the approaches and content expected in the “c” subject area courses is 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. Courses submitted to UC for “c” approval must demonstrate they include approaches discussed in Section 1 of the ICAS document – merely listing standards to be covered is not sufficient. Further perspectives can be found in the Common Core Standards for Mathematical Practice [PDF], in Understanding University Success (The Center for Educational Policy Research, 2003) and in Principals and Standards for School Mathematics, (National Council of Teachers of Mathematics, 2000).

#### Course requirements

Regardless of the course level, all approved courses are expected to satisfy these criteria:

- Courses should be consistent with the goals described above. Courses that incorporate the Common Core Standards for Mathematical Practice [PDF] will be taking a substantial step towards achieving these goals.
- The content for these courses will usually be drawn from the Common Core State Standards for Mathematics [PDF]. While these standards can be a useful guide, coverage of all items in the standards is not necessary for the specific purpose of meeting the “c” subject requirement. Likewise, simple coverage of all standards is not enough to assure course approval. For success in college, secondary mathematics teachers should help students learn to assimilate the major ideas and principles that encompass the standards rather than treating the standards as a check-off list. The ICAS Statement of Competencies in Mathematics can provide guidance in selecting topics that require in-depth study.
- One unit or yearlong course must either be a course in geometry or part of an integrated sequence that includes sufficient geometry.
- 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 utilizing this pattern, all grades awarded by the school are averaged in the GPA calculation. - Completion of advanced mathematics courses with a grade of C or higher can validate an earlier grade of D or F in the sequence provided that the material in the advanced course substantially builds upon the earlier course. Typically, Algebra II validates Algebra I, but not Geometry.
- Courses selecting topics from the 1997 California Standards as a base usually receive the following unit values: Algebra 1 (1.0 unit), Geometry (1.0 unit), Algebra 2 (1.0 unit), Trigonometry (0.5 units), Mathematical Analysis (1.0 unit), Linear Algebra (0.5 units), Probability and Statistics (0.5 units), Advanced Placement Probability and Statistics (1.0 unit) and Calculus (1.0 unit). Trigonometry is usually embedded in intermediate algebra, mathematical analysis or precalculus, and the preceding refers only to stand alone courses. Most courses titled precalculus are based on selected trigonometry and mathematical analysis standards and receive 1.0 unit. Each course in a rigorous integrated sequence (as indicated in Appendix A of the Common Core State Standards for Mathematics [PDF]) receives 1.0 unit.
- Courses that are based largely on repetition of material from a prerequisite or prior course (for example as test preparation or pre-college review) will not be approved.
- Other rigorous courses that use mathematical concepts, include a mathematics prerequisite, and that are intended for 11
^{th}and 12^{th}grade students, such as discrete mathematics or computer science may also satisfy the requirement. Such courses must deepen students’ understanding of mathematics by incorporating the depth implied by the Competencies statement [PDF].

### Sample courses

Samples of courses approved in the “c” subject area are available for reference as you prepare you own course for UC approval.

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

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