# In fuzzy math, 55 percent = 33 percent

New York City’s math tests produce fuzzy results, writes Andrew Wolf in the New York Sun.  For example, two thirds of last year’s fourth graders were on grade level in math, yet only 38.6 percent tested at grade level as fifth graders. What’s going on?

Wolf offers a story problem: There are 84 questions on the Math A regents exam; the passing grade is 55 percent. How many questions must a student answer correctly to pass?

You say 47? Wrong.

The state education department has decreed that answering just 28 questions correctly earns you a 55 and a passing grade, even though that is only a real score of 33.3% . . .

Sixty of the questions on the test are multiple choice. Merely making random guesses will earn the average student 15 of the 28 correct answers needed to pass. Another 13 right answers and it’s on to Math B. Basically,a student who is able to correctly answer 13 questions, just 15% of the test, and making random guesses on the balance, can pass the test.

Wolf suggests letting an independent board test students and determine the passing grade, taking the job away from the city and state education departments.

1. SRH says:

It seems that Andrew Wolf somewhat incorrectly summarized the structure of the Math A NYS Regents exam. (The exam and the grading key can both be found at: http://www.nysedregents.org/testing/mathre/regentmatha.html).

The exam consists of 39 questions worth a total of 84 points. There are 30 multiple choice questions worth two points each and nine free response questions worth between two and four points each. In order to pass with a scaled score of 55, a student must receive at least 28 of the 84 points on the exam. This is where the 33% comes in; passing the test requires receiving 33% of the points possible. (See http://www.emsc.nysed.gov/osa/june04cc/matha604cc.htm for the Regents’ conversion chart.)

A student who guesses randomly at the 30 multiple choice questions might get 7 or 8 of them correct, scoring 14-16 of the 28 points needed to pass. To earn the remaining 12-14 points, he or she would need to nail four of the highest value long answer questions or else get significant partial credit on the majority of the free-response questions. Looking at the exam and the scoring rubrics (full credit requires a completely correct response with correct work justifying every step), it seems unlikely that a student who couldn’t do better than chance on the multiple choice questions would be able to do much better on the long answer questions.

On the bright side, although a student (theoretically) needs to only answer 11 questions correctly in order to pass, 11 out of 39 is about 28%, which is pretty close to the 33% which defines passing — not the 15% suggested in your post.

(But, in any case, it’s still appalling.)

2. There may be items in the test that are intended to “raise the ceiling” of the exam. Basically put, some questions may be on a fifth, or sixth grade level. These items would be weighted differently from items that are intended for fourth, or even third grade students. In this instance, with items that are weighted differently, it could work out. But if a student can’t answer at least half of the questions correctly, they should not be answering those harder questions correctly.
So, I’m basically echoing SRH’s final point. It is appalling.

3. mike from oregon says:

Okay, I’m really confused, but that is the way that those who rule the school want me to be. I followed that various questions had various “values” assigned to them (some worth 2 points, some worth one, etc.). My question is WHY?

Why should there be questions that “raise the ceiling”? Isn’t the idea of the test (any test) to demonstrate that the child has mastered “X” amount of material? There should be a test that measures THAT – does the kid know what he is suppose to so he can be passed or not, so he can do it over again. Like I said, I’m confused.

4. SRH says:

Looking at the exam from this June, there don’t seem to be questions designed to “raise the ceiling.” The easiest multiple choice questions involve frequency tables and graph reading, but most of the questions require algebra or involve a multi-step solution.

A two-point problem would be a multiple choice question which asks: If 3x is one factor of 3x^2 – 9x, what is the other factor?

While a four-point problem would be a free-response (show all work) problem asking: Solve the following system of equations algebraically or graphically: x^2 + y^2 = 25 and 3y-4x=0. [I believe the students have scientific calculators but *not* graphing calculators.]

In my opinion, the vast majority of the questions are at the high school level, and the most heavily weighted problems require the most from the student.

My only quibble with the test is the editting; a few questions are phrased awkwardly. The test is not the problem here. It is on an appropriate level to assess whether a student knows the material from New York’s curriculum.

The problem here lies 100% with the officials who responded to the students’ poor performance by brazenly redefining passing. If it weren’t for their intervention, this test would be doing its job.

5. Michael says:

Anyone else what Kimberly Swygert to weigh in on this?

6. Mark says:

I haven’t paid a whole lot of attention to the Regent’s but there is no way x^2 + y^2 = 25 and 3y-4x=0 is high school level math, or at least it shouldn’t be. This is, at best, an example of what Mr. Jensen was teaching me in 7th grade 30 years ago.

If this is all that’s expected from high school graduates no wonder so many students need remediation when they get to college.

7. Michael says:

Mark, you’re wrong. That’s a classic example of freshman algebra. It does get taught in junior high, but it’s far more common in high school.

8. SRH says:

The question of what qualifies as “high school math” is certainly much thornier and more nuanced than the question of what score is needed to pass a specific exam. Whatever you might think of New York’s curriculum, at least it seems fairly consistent — questions similar to the ones on this year’s Math A exam have appeared on Regents exams going back to the 1950s. (See http://www.nysl.nysed.gov/regentsexams.htm for archived exams.)

But it hardly seems to matter which topics are in New York’s high school curriculum — as long as 33% is defined to be passing, it’s pretty clear that the students don’t know very much math.

9. There are two types of tests. You have your competancy tests, which is the more common type of test. It measures how much you know of something. Then you have your tests which measure how much you know in relation to everyone else (I forget the name at the moment). The SAT is an example of the latter. These tests need to be “normed” so that test designers can know which items are more difficult than others. This is the field of Psychometrics.

10. Dave says:

First of all, I had eighty of my students sit for this exam. Sixty nine passed with 55 or higher. Most were below average students. Not only did the test have relatively few questions of any reasonable degree of difficulty, having 33% scale to a 55 is absurd in extremus. No wonder employers say that kids coming right out of high school into the job force are ill prepared. The test is probably no more difficult that the exit math test in Massachusetts, but at least require a 65 based on 42 points out of 84 as a bare minimum.

They are required to have graphing calculators available for their use on the exam. Knowing how to use these calculators effectively can usually help them on at least 45/84 points on average based on our analysis of previous exams.

A grade of 55 qualifies for a “local” diploma. A student needs at least 65 on each of six regents exams (I believe) for a REgents diploma.

11. pmian says:

Dave,
A Regents Diploma requires passing 5 Regents examinations:
Math A

12. pmian says:

Dave,
A Regents Diploma requires passing 5 Regents examinations:
Math A
Global History
U.S. History
English Comprehensive (Given at the completion of three years)
Science, generally either Earth Science or Biology