New York State Education Commissioner Richard Mills is under much pressure because of the high failure rate on the recent (June 17) New York Regents Math A exam. The latest and earlier instances of the exam and the associated scoring keys and conversion tables are posted on the Regents Examinations Web site, under the link to Mathematics A. Procedural information related to the exam is posted at the State Assessment site under High School General Information. I know of two reviews of the exam on the Web. There is my own Critique of the New York State Regents Mathematics A Exam, and there is an Analysis of the June, 2003, Administration of Physics and Math A Regents done by the New York State Council of School Supervisors (NYSCOSS).
In connection with the Math A flack the director of the testing division at the NYS Education Department was reassigned and chose to resign, but this is not presented as a cure for any problem. The State Assembly and Senate will hold hearings, according to a report in the Rochester Democrat and Chronicle:
[State Assemblyman Steven Sanders, D-Manhattan], who chairs the Assembly education committee, and Sen. Stephen M. Saland, R-Poughkeepsie, who chairs the Senate education committee, plan to hold public hearings for people to express their feelings about high-stakes testing in light of an estimated 37 percent passing rate on the June 17 Math A Regents exam. Those hearing dates have not yet been set, but Sanders said Rochester, Albany and New York City might be host cities.
Of course there are plenty of calls on editorial pages for the State to abandon its plan to require students to pass five Regents exams for graduation starting in 2004. However, according to an article in the Albany Times Union, Voided math test said to reveal systemic ills, the Regents and Commissioner Mills remain supportive of that plan.
Asked whether he and other Regents still stood behind Mills, board member Saul Cohen responded, "Sure," but added, "That doesn't mean we can't press him to do certain things as we did. We pressed him to nullify the results of the Math A, and I'm continuing to press him to re-examine the physics exam. But that doesn't mean we're not backing him."
A somewhat different take on the exam trouble is found in an article by Karen Arenson in the New York Times, Math Failures Are Raising Concerns About Curriculum.
But some explanations [of the high failure rate] touch on deeper issues, including whether the Math A curriculum is too broad, how much harder it is for students to solve problems than to manipulate equations, and whether unqualified teachers are even less likely to succeed in preparing students than they were with the old math curriculum.
[...] The shift from rote learning to a greater emphasis on mastery of concepts is welcomed by some college professors in math and science, who have been trying to accomplish the same shift. They say that although mastery of some facts is critical, students who focus on memorization may do well in a course but remember little of it six months later.
[...] Some educators say teaching students to be problem solvers takes more skill on the part of teachers, a challenge when there is a shortage of qualified math teachers.
"Teachers are not really prepared to prepare kids for this test properly," said Alfred S. Posamentier, dean of the School of Education, City College of New York, and the author of books on problem solving. "There is very little training for teachers in problem solving; it's assumed they will get it along the way."
My take on it is different. The low passing rate is a complicated affair in any case, and it isn't entirely clear from the data to what extent the exam was really more difficult than earlier instances. Students can take the exam three times per year over multiple years, in August, January, and June, and the character of the test taking population may vary greatly between the months. Many of last year's seniors may still have graduated on the basis of the easier Mathematics I exam. It is surprising that Commissioner Mills does not have the data to say anything more authoritative about the relative difficulty of the latest exam.
The main thing that can be learned from the low passing rate is that, in many cases, New York State high schools are failing to make up for the failures of elementary and middle school education. An eighth grader in a high performing country, say Singapore, or in a U.S. state that has high level content standards, say California, would be well placed to pass this exam. I find ony two kinds of questions that would probably be unfamiliar to such a student. One are the counting questions that require students to know something about permutations and combinations. The other are the very basic trigonometry questions: students must know the ratios in a right triangle that correspond to the sine, cosine, and tangent.
It does appear to me that the June, 2003, instance of the exam had a somewhat more difficult and less "standard" flavor than earlier instances, and in the open response section the June, 2003, exam tilts a bit more towards a test of aptitude rather than a test of school learning, relative to the previous two instances of the exam. This is not to say, however, that all the questions in August 2002 and January 2003 were of a standard and predictable form, and it is not to say that the June 2003 exam is plainly a test of aptitude and the earlier ones plainly a test of school learning.
The unintended shift in the character of the exam should be seen as a failure of the Regents testing division. In addition there are many mathematical flaws in the questions and dubious points in the scoring keys, as described in more detail in the Critique of the New York State Regents Mathematics A Exam and the Analysis of the June, 2003, Administration of Physics and Math A Regents, both mentioned earlier.