June 21, 2003

New York Regents Math A

The Regents Math A exam that was given on June 17, 2003, has received much negative press attention. For example: New York Daily News, Test Mess Threatens Diplomas. New York Newsday, Math Test Too Tough?. New York Post, Testy Teachers Blast 'Too Hard' Math Exam. New York Times, This Year's Math Regents Exam Is Too Difficult, Educators Say. Rochester Democrat and Chronicle, Huge Numbers Fail Math Test. Buffalo News, Many Seniors Fail Crucial Test. (The links will disappear, but the titles are clear enough.)

I don't know that there is any serious analysis of the exam to be found yet, so the following brief comments may be of interest.

The June, 2003, Math A exam is not yet posted on the NYSED Web site. The previous instance of the exam was in January, 2003, and that one is posted; follow the link to the Math A exams here. I have a FAX copy of the recent Math A exam, but not of the scoring rubrics.

The format of the test is identical between January and June. There are 20 multiple choice questions worth 2 points each, and 15 open response questions, 5 at 2 points each, 5 at 3 points each, and 5 at 4 points each, for a maximum score of 85.

Question 14 on the June exam is plainly faulty, and the scoring rubric has already been changed to allow two answers. The question asks: "If the expression 3-4^2+6/2 is evaluated, what would be done last?" Could be either addition or subtraction, but in the initial rubrics only addition was considered correct.

The wording of several other questions makes it plain that the exam was not proofread by people with adequate mathematical training. This was also the case with the January exam. Examples: Both the January exam and the June exam ask for the "inverse" of a statement of the form "if A then B". I am inclined to assume that this concept of the "inverse" of an implication exists in the curriculum guide, but I am sure that many professional mathematicians would have to guess what is meant. The given answers (multiple choice) make it clear that it is not the negation.

Another example of a poorly worded problem: January Question 7 and June Question 20. They are very similar and have the same flaw. June Q20 asks: "How many different five-member teams can be made from a group of eight students, if each student has an equal chance of being chosen?" The "equal chance" bit does not belong in the question.

There are some minor irritants. The tests (January as well as June) use "equivalent" where mathematicians would use "equal". June question 4 asks "Which of the following does *not* have rotational symmetry: trapezoid, regular pentagon, square, circle?" A mathematician would not be happy with this formulation, although it is clear which answer is intended. (The circle has complete rotational symmetry, the square and regular pentagon have symmetry with respect to rotations over a multiple of 90 or 72 degrees, and only the trapezoid has, in general, no rotational symmetry at all.) The data analysis questions, on the latest exam as well as on earlier instances, are a further source of mild irritation. Mathematicians tend not to care about the "mode" of a data set, but it is on the curriculum and students can learn what it is. Likewise for reading a stem-and-leaf display and reading a box-and-whisker plot.

Part 4 of the June test, especially, has several multi-stage questions that are probably as much a test of intelligence as of learning. (I don't mean this as criticism.) I have not made a careful item by item comparison between the January and the June tests, but it looks plausible to me that the June test is indeed more difficult. Without the scoring rubrics I wouldn't try to say more.

I am convinced that the Regents Math A should be a predictable exam of which the level of difficulty is carefully matched between instances. It is possible that the June, 2003, instance failed on that measure, and the State Superintendent should study that very quickly and decide if an adjustment of the passing score is in order. The press reports, however, give a wrong impression. The exam is, on its own, not unreasonable and not wholly out of line with earlier instances.

[Addendum, October 24, 2003. TheJune, 2003, and earlier instances of the exam 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 posted a Critique of the New York State Regents Mathematics A Exam on my Web pages, accompanied by a Detailed Critique of specific items on the June 2003, January 2003, and August 2002 exam instances. The New York State Council of School Supervisors produced an Analysis of the June, 2003, Administration of Physics and Math A Regents. I summarized the issues in a Blog entry Update on the Regents Math A. Commisioner Mills and the Regents appointed an independent panel to review the Mathematics A Regents exam. This panel provided a Report to the New York State Board of Regents and the New York State Commissioner of Education in October. At the same time the Association of Mathematics Teachers of New York State produced a Math A position paper for the New York Regents. Even before public release of the independent panel report commissioner Mills recommended and the Regents enacted changes in the future administration of the Math A exam. These changes are described in an October 2, 2003, press release (released October 9 or so): Four Policy Decisions on Assessment.]

Posted by Bas Braams at 08:46 PM