Tuesday, August 7, 2012

CCSS and Community College Math Programs

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.

Monday, August 6, 2012

MathFest 2012 and Common Core State Standards in Math

Andrew Hacker’s article "Is Algebra Necessary?" in the New York Times was a hot topic last week and mentioned by several presenters at the 2012 MathFest session "What Mathematics Should Every Citizen Know?".  The panelists, Bil lMcCallum, Lynn Steen, Hyman Bass, Joseph Malkevitch, and co-organizer Sol Garfunkel, were actually reacting to the Core Curriculum State Standards in mathematics.

Mathematicians and math educators agree that we are not  currently doing the best job of teaching algebra.  But unlike Hacker, the math community believes the appropriate strategy is to improve algebra instruction, not to abandon it to all but an elite few pupils.

On the other hand, the speakers on the panel, although quite civil with each other, clearly had disagreements about the best strategy to improve math education in the US.

McCallum, who was the lead mathematician in the development of the CCSS, emphasized the benefits of having commonality across states.  Having a set of standards that could be adopted by 45 of the 50 states (so far) required compromises, but the benefits accrue not only to pupils and teachers in our mobile society, but to all who do business with textbook publishers who currently provide materials for the multitude of different curricula.

Steen gave some numbers showing the dismal success of preparing US students for STEM, but argued that we should improve rather than remove algebra from the curriculum.  He favors a modeling-based approach and avoidance of common assessments.  When asked how to accomplish his recommendations, he cheerfully remarked that he doesn't need to worry about that now that he's retired.

Bass focused on pedagogy rather than curriculum as the key to improving math education.  Student learning is increased when the instructor employs appropriate classroom strategies.

Malkevitch promotes widening the curriculum.  He argued that we need to show many ways that mathematics impinges on daily lives.  He gave combinatorial graphs and fair choice algorithms as examples of mathematical topics that are new and accessible to very young children.

Garfunkel believes that the entire K-12 mathematics curriculum should be centered on modeling. He echoed Malkevitch's suggestions that the US curriculum needs to be widened, and said that Bill Schmidt had paid an advertising agency to create the phrase "a mile wide and an inch deep" that is used to characterize the US K-12 curriculum following the disappointing ranking of the US high school students in the Third International Mathematics and Science Study.