The (California version of the) Common Core State Standards in mathematics purport to be what all students need to be
college and career ready.

The quantifier
"all" in this context indicates that the math content should be the
intersection (over all students) of math a student needs to be ready to begin
college (or begin a career). Critics of the CCSSM who decry that the standards
are not enough to prepare a student for an elite university such as Stanford
are missing the point. The intent of the CCSS was never to include the union
(over all students) of the math that a student needs to succeed in college.
(And if the CCSS could provide all the math and English Language Arts that
Stanford students need, then Stanford would not deserve its status as an elite
school.)

And what do all
students need? In 2013, the National Center on Education and the Economy
released a study What Does It Really Mean to Be College and Work Ready?, reporting on both mathematics and English
literacy. The report says, "Mastery of Algebra II is widely thought to be
a prerequisite for success in college and careers. Our research shows that that
is not so... Based on our data, one cannot make the case that high school
graduates must be proficient in Algebra II to be ready for college and
careers."

California's
Intersegmental Committee of the Academic Senates (ICAS) represents the faculty
academic senates of the three CA systems of higher education: the University of
California (UC), the California State University (CSU), and the California
Community College (CCC) system. The ICAS Statement on Competencies in Mathematics Expected of Entering College Students,
revised in 2013, describes a number of mathematical topics that are or could be
taught in high schools.

The ICAS competency
statement describes mathematical subject matter in four categories: Part 1:
Essential areas of focus for all entering college students, Part 2: Desirable
areas of focus for all entering college students, Part 3: Essential areas of
focus for students in quantitative majors, and Part 4: Desirable areas of focus
for students in quantitative majors.

The mathematics that
the CCSSM describe as what all students need should presumably match with what
the ICAS statement describes as "essential" and lists in Part 1. But although the UC
Board of Admissions and Relations with Schools (BOARS) states there is "close
alignment" between the CCSS and the ICAS statement, the ICAS statement
makes clear that there are many CCSS that are not "essential" but
rather merely desirable or for only some students. Appendix B of the ICAS
statement explicitly shows where Part 2, 3, and 4 areas of math are found in the
CCSS (and NCTM standards).

And the Interim Environmental Scan Report to The Common Assessment Initiative Steering Committee has in Appendix B a Table that shows a number of CCSS that do not
occur at all in the ICAS statement.

Here are examples of
CCSSM topics that might surprise some community college math faculty,
especially those who believe that intermediate algebra as currently taught
will be sufficient to cover all the CCSSM.

- Probability: sample spaces, independent events, conditional probability, permutations and combinations; analyzing decisions and strategies using probability
- Statistics: assessing the fit of a function by plotting and analyzing residuals; interpreting the correlation coefficient of a linear model in context; normal distributions, random samples, estimating population parameters, simulations, using probability to make decisions
- Transformational geometry: congruence defined in terms of rigid motion; similarity defined in terms of dilations and rigid motions
- Trigonometry: trig ratios, special angles, 6 trig functions of real numbers; modeling periodic phenomena, proof and use of the Pythagorean trig identity \( \cos^2 \theta + \sin^2 \theta = 1 \)