### Mathematics

### Course Criteria & Guidance

All courses approved for the mathematics (C) subject requirement 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 proficiency in quantitative thinking and analysis to engage with coursework in other disciplines.

### Course Content Guidelines

- Regardless of the course level, courses will be consistent with the Common Core Standards for Mathematical Practice [PDF] for high school. Appendix A of the Common Core State Standards in Mathematics [PDF] offers a starting point for developing courses that align with these standards.
- Courses will also 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.
- Courses may be part of a traditional sequence (Algebra 1, Geometry, Algebra 2) or an integrated sequence (Mathematics I, II, and III). In addition, acceptable courses may be combinations of algebra, geometry, probability, statistics, trigonometry or other topics that address the Common Core Standards for Mathematical Practice [PDF], including courses that apply these standards in the development of career-related skills.
- Courses that use mathematical concepts, include a mathematics prerequisite, substantially align with Common Core (+) standards (see chapters on
*Higher Mathematics Courses: Advanced Mathematics*and*Higher Mathematics Standards by Conceptual Category*in Common Core Standards for Mathematical Practice [PDF]), and are intended for 11th and/or 12th grade levels are also eligible for approval and may satisfy the required third year or recommended fourth year of the subject requirement if approved as an advanced mathematics course. - Such courses may consist of pure mathematics or incorporate math in an applied form in conjunction with science or career technical education. 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, applied mathematics, calculus, computer science, data science, discrete mathematics, linear algebra, pre-calculus (analytic geometry and mathematical analysis), probability, statistics and trigonometry.
- For instance, a computer science course with substantial mathematical content (e.g., mathematical induction, proof techniques, or other topics from discrete mathematics) could be approved, but a course with primary focus on coding methods alone would not qualify for approval.
- Similarly, a data science course that includes the development and application of statistical models and mathematics concepts to interpret, visualize, and operate on data would be acceptable, whereas a course that addresses only data gathering or computer programming would not.
- 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.
- Most approved courses will satisfy a single year of the subject requirement, with a few exceptions:

- A course covering only trigonometry, for example, would fulfill only half a year, but a single course covering trigonometry with significant integration of other advanced math content related to pre-calculus could fulfill one year of the requirement.
- Mathematics courses taken over multiple terms that go beyond one year (e.g., three or four semesters) are acceptable but the course will be approved to satisfy only one year (or two semesters) of study.

Three years of college-preparatory mathematics required (four years are strongly recommended), including or integrating topics covered in: elementary algebra, two-and three-dimensional geometry, advanced algebra.

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

For information on how a student can fulfill UC A-G admissions requirements, please visit the UC Admissions website.

### Skills Guidelines

Courses that satisfy this subject requirement will support students to:

- Apply mathematical knowledge in a way that allows them to analyze and understand a broad array of phenomena (i.e., math is more than just rote memorization of definitions, algorithms, and/or theorems).
- Use mathematics to grasp and persevere in solving unfamiliar problems, and justify their solutions to those problems based on understanding the purpose behind each concept and skill they apply.
- Find and use patterns of reasoning or structure, make and test conjectures, try multiple representations (e.g., symbolic, geometric, graphical) and approaches (e.g., deduction, mathematical induction, linking to known results).
- Make abstractions and generalizations and verify that solutions are correct, approximate, or reasonable.
- Use mathematical models to guide their understanding of the world around us.

### Honors Course Criteria & Guidance

Honors-level mathematics (C) courses will be demonstrably more challenging than non-honors courses, and will fulfill the following criteria:

- General A-G honors-level course criteria.
- Have at least three years of college-preparatory mathematics (C) as prerequisite work.
- Integrate, deepen and support further development of core mathematical competencies.
- Address primarily the (+) standards of Common Core-aligned advanced mathematics (e.g., discrete mathematics, calculus, pre-calculus or statistics).
- This could also include trigonometric, logarithmic, and exponential functions.
- Be at the mathematical analysis (pre-calculus) level or above.
- Honors-level courses in mathematics can be designed as differentiation within heterogeneous classrooms, as long as they include sufficiently advanced depth of instruction and assessment.
**Calculus**qualifies as an honors-level course if it includes a substantial focus on limits and continuity, differentiation (derivatives and higher-order derivatives), and differential equations.**Statistics**qualifies as an honors-level course if it includes a substantial focus on data analysis, chance variation, an integration of probability to discern patterns in data, data collection, theory, and/or simulation based statistical inference.

### Core Competencies

Courses in the mathematics (C) subject area should be designed to give students the following competencies and should demonstrate how students will acquire them:

- Ability to recognize when and how mathematics can be used to solve or frame problems.
- 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.

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.