We may need a complete redesign of the developmental math program in US two-year colleges.
My campus currently uses a placement test (Mathematics Diagnostic Test Project) to determine if students are ready for transfer level courses (math for elementary school teachers, stats, trig, precalculus, calculus) or what remedial course (arithmetic, prealgebra, elementary algebra, intermediate algebra) they should take.
But the Common Core State Standards for mathematics will have high school students studying mathematics organized in a fashion that does not align with our existing math courses.
California is one of the 45 states that have formally adopted the CCSS for mathematics, and I am on a recently appointed state committee whose charge is to align California’s math standards (a.k.a. the California Framework) with the CCSS.
One of the main reasons that I applied to be on the Mathematics Curriculum Framework and Evaluation Criteria Committee (MCFCC) was to better familiarize myself with what is to be taught in California's K-12 schools. (Another reason was to lose myself in abbreviations: SBE for State Board of Education, CDE for California Department of Education, IQC for Instructional Quality Commission, the body that forwarded my name to the SBE for approval to serve on the MFCC to align the CF with the CCSS.)
The CCSS specify a consensus of what math is required for students to be college or career ready. The standards are grouped into six conceptual categories: Number and Quantity, Algebra, Functions, Modeling, Geometry, and Statistics and Probability. (There are separately eight standards for mathematical practice that go across all grade levels.)
The CCSS differ significantly from what is typically required for graduation in most American high schools today. For example, the treatment of statistics and probability includes not only descriptive statistics but also conditional probability, inference, decisions based on probability, and rules of probability.
The CCSS include not only right-triangle trigonometry but also trig functions of a real variable, to be used in modeling periodic behavior. Thus trig spans the geometry, algebra, and function categories.
The CCSS gives math standards for high school without specifying courses or order of topics. But evidently the introduction of functions includes an emphasis on (linear and) exponential functions with domains restricted to a subset of the integers--sequences are explicitly studied as functions.
California community colleges do not require a high school diploma for admission. A student who masters the first CCSS high school math course will already have compared exponential functions with linear functions and solved equations both algebraically and graphically. The student will have had explicit instruction on descriptive statistics. The student may have worked with constructions and transformations in the plane and proved simple geometric theorems algebraically but not yet worked with polynomials (and specifically not with quadratic functions or quadratic equations).
How will our placement system advise this student?
One of the recommendations of California's Student SuccessTask Force is for better alignment between high school and college curricula. With the CCSS adopted across states, it looks as if most community colleges will need to make adjustments to their way of placing and educating their math students.