As education pundits often point out, the US is currently mid-range in its mathematics performance on international standardized tests. The TIMSS 2011 assessment shows us as being 9 out of 42, beat out by countries like Finland and Korea. In the battle for technological greatness in the 21st century, it is important to the United States to be shown as a leader in mathematical understanding. Therefore, this number is not a good one to show off.
Unfortunately, mathematics education in the US is not focusing on the correct content. The low performance on math tests across the country (including college entrance exams) points to a larger problem. In a recent research article in Educational Psychologist, the researchers point out that students are "apt to attempt procedures that are partially or incorrectly recalled without regard to the reasonableness of the solution" (p.190). Across the country, "the practices of American teachers often do not correspond at all well with the strategies [believed to] promote deep learning and acquisition of the conceptual structure of mathematics" (p. 190).
Stated succinctly: students think of math as a series of procedures and steps instead of the interconnected set of definitions and relations mentioned earlier.
The most recent example of this in Philadelphia is the Benchmark exam, a test crafted by CTB McGraw-Hill for use by teachers across the city. The exam consists of 25 multiple-choice and two open-ended questions for students to answer. While these questions are supposed to be modeled off the concepts in the Common Core Standards, they instead rely on much procedural reasoning in their implementation. Analysis of patterns was hardly a concept much focused on in this test.
If we as a country want to improve our understanding of mathematics on a deeper level we have to think about how to assess this information. Standardized tests are not the way to go - they are too simplified for this purpose. We need to deeply understand what it means to be mathematically knowledgable and assess comparably. Unfortunately, the fact that the Keystone test was administered last week does not matter to those in position of influence - we were just reminded of the upcoming benchmark assessments to be given in 2 week's time. I do not imagine they will be of much more use than the first set.