Competencies in Mathematics 

Statement on Competencies in Mathematics Expected of Entering College Students

Revised 2013

The 2010 document has been revised to include the Common Core State Standards (CCSS) for Mathematics that were adopted by the California Legislature shortly after publication and release of the original version. A section on Mathematical practices has been added (see Part 3 on page 6), and Appendix B was rewritten to map the CCSS to the expectations of ICAS. 

The goal of this Statement on Competencies in Mathematics Expected of Entering College Students is to provide a clear and coherent message about the mathematics that students need to know and to be able to do to be successful in college. While parts of this Statement were written with certain audiences in mind, the document as a whole should be useful for anyone who is concerned about the preparation of California’s students for college. This represents an effort to be realistic about the skills, approaches, experiences, and subject matter that make up an appropriate mathematical background for entering college students.

“Entering College Students” in general refers to students who enter a California postsecondary institution with the goal of receiving a bachelor’s degree. However, it is important that students who plan to enter a California community college be aware that a wide variety of courses exist to help them transition from lower mathematical skill levels to the competencies described in this document. Most community colleges offer a wide range of mathematics courses including some as elementary as arithmetic.

The first section describes some characteristics that identify the student who is properly prepared for college courses that are quantitative in their approach. The second section describes the subject matter that is an essential part of the background for all entering college students, as well as describing what is the essential background for students intending quantitative majors. Among the descriptions of subject matter there are sample problems. These are intended to clarify the descriptions of subject matter and to be representative of the appropriate level of understanding. The sample problems do not cover all of the mathematical topics identified.

No section of this Statement should be ignored. Students need the approaches, attitudes, and perspectives on mathematics described in the first section. Students also need extensive skills and knowledge in the subject matter areas described in the second section. Inadequate attention to either of these components is apt to disadvantage the student in ways that impose a serious impediment to success in college. Nothing less than a balance among these components is acceptable for California’s students.

The discussion in this document of the mathematical competencies expected of entering college students is predicated on the following basic recommendation:

For proper preparation for baccalaureate level course work, all students should be enrolled in a mathematics course in every semester of high school. It is particularly important that students take mathematics courses in their senior year of high school, even if they have completed three years of college preparatory mathematics by the end of their junior year. Experience has shown that students who take a hiatus from the study of mathematics in high school are very often unprepared for courses of a quantitative nature in college and are unable to continue in these courses without remediation in mathematics.

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Previous Versions

October 1997 (PDF)