# Math A: What was it?

For readers not from New York State, this must be a strange title. Indeed, Math A and Math B are the names of strange state exams. Let’s roll back the clock.

(This is a longish post. Headings are: Old Math Regents; What Are Regents; The 1980s; Who takes regents? The 1990’s and Math A and B; June 2003 Math A; Integrated Exams. There is a list of vocational regents at the very end)

**Old Math Regents**

**What are the Regents?**

Education in New York State is governed by a Board of Regents, a semi-political, semi-expert panel. The Regents Exams are State of NY high school exams. I believe they were used to earn ‘academic’ as opposed to general diplomas. Only a portion of high school graduates in NYS passed them. The oldest group of exams I see include vocational topics as well*. Different diplomas for different exams? and an exam-free general diploma?

**The 1980s**

New York State Education Department had a “Mathematics Bureau” or something like that. It was a well-staffed office run by math teachers who knew the subject. They made mistakes, but they got most things right. The existence of this office meant: most items looked good to start with, errors could be corrected (math trumped ego), and math teachers had confidence in the knowledge and expertise of the State.

(Unfortunately, this office was de-staffed and now there are one or two managers assigned math without the experience or expertise of the old guys, and who do not inspire any confidence.)

A weak point was the introduction of probability, stats, and logic. There is not agreement in the mathematics community about some of the associated names and techniques. We got one version that in some ways is idiosyncratic. But the math teacher community in NY had virtually no prior knowledge, so none of the odd or limited items were challenged. Worse, many teachers learned what they know of these topics by teaching Course I or Course II. This is a massive no-no.

**Who takes regents? The 1990’s and Math A and B**

At some point (late 80’s? early 90’s?) the Regents introduced Regents Competency Tests (RCTs), lower level, basic exams, and made them graduation requirements. The RCT in math had little word questions, some arithmetic, some fractions and percents. I can’t find links to actual exams: maybe they were restricted? Though I remember seeing copies floating around. Now everyone took tests: Regents for what was now called a ‘Regents Diploma’ and RCTs for a ‘local diploma.’

More change: in the late 1990’s NYSED decided to phase in regents diplomas for all, and phase out RCTs (with certain limited exceptions in special education). At the same time, Commissioner Mills changed the exams. They became, and forgive the obfuscatory language, it is not mine, standards-based rather than content-based. Hm. It means in English, Global History, US History, Earth Science, Biology, Foreign Languages, they got easier. It also meant name changes (eg, Living Environment instead of Biology, but as you scan the archives you can see that exam names change periodically. Nothing nefarious about that)

They also set up two tiers: Regents diplomas (Math A, 1 science, US History, Global History, an English) and Advanced Regents Diplomas (extra exams including Foreign Language, a second science, and Math B).

In math though, standards-based meant that we would not know what topics would be tested, that it was the application of mathematics rather than the learning of particular skills that mattered. In other words, they really did not have a clue. Also, all of high school math was divided into Math A and Math B, without much rhyme or reason for what went where. Schools scrambled to rework courses to put the right topics in the right places. Schools that had tinkered with A/G/T to make them fit Course I/II/III were now stuck with exams after a year and a half.

In June 2003 the Math A Regents, floating around for 3 years, had its first test. Regular (non-accelerated) kids for the first time had no Course I option. Across NY State everyone took Math A. And across NY State, not just in poor areas, kids failed. Massively. It was not a particularly hard test, but no one knew what was being tested.

The whole idea of a standards-based exam in mathematics made (and makes) no sense. Give us the skills, and we will teach them to the kids. Instead, the exam asked for kids to look at strange contexts and choose appropriate math. This is what we ask, sometimes, after mastery of content. Not instead of mastery of content.

The editorial pages denounced the exam, and the now non-expert SED math people defensively retreated, a fighting retreat, yielding as little as possible.They rescaled the exam (in the day, exams were 100 points. Your score was your score. Mills introduced scaled scoring. Math A had 85 ‘credits’ – earn X and your ‘score’ would be 50. When they rescaled, the score became 66) (I can’t find what X was, but credits and scores are not proportional). Now, they rescaled to pass more kids. But where did they say they goofed?

They set up a commission, which recommended setting up a panel… Long and short, (mostly long because they dragged it out for 2 years) both Math A and Math B are being phased out, but they maintain the fiction that they are only changing the names: to Integrated Algebra, Integrated Geometry, and Integrated Algebra II and Trigonometry. But we won’t see Algebra until this June, a decade after A and B were introduced. And B sticks around until 2010. Far, far too long for something that should have never existed.

They made all the rest of the Math A exams much easier. And they adjusted future scales to inflate scores. They never admitted to this, but the scales prevent most suburban kids from failing.

B, in the meantime, had its own problems. It got less attention, since it was not a graduation requirement. But man, those questions stunk. And got worse. Artificial context was both the order of the day, and ridiculous. Stats and probability involved issues of measurement and rounding that they repeatedly got wrong, or over-penalized kids for. Two full years of material, tons of topic, little depth turned parts of the exam into vocabulary bees and calculator procedure drills. Obscure NY State versions of mathematics became more prominent. More than one question had to be thrown out, including the famous ‘impossible circle‘. And the scale was not softened. Only the Physics Regents remained as difficult.

**Integrated Exams**

The new exams will be rolled out over the next three Junes. First comes “Algebra,” in just five months. It will likely have an easy scale, like Math A did. It covers fewer topics, and it may reduce, but not eliminate, the silly context. It is only about half algebra, the rest a grab-bag of applications of geometry, probability, etc etc.

Geometry scares the State. They tried to delay the new exams partly because of this one course (and just because they like playing things safe and have no confidence in their ability to repair anything). Geometry will be almost 100% geometry. It could be the ‘hardest’ of the exams. There will be some proof, but it will likely be limited.

June 2010 Algebra II comes out. This one will cover many too many topics, lots of them superficially. Along with algebra II and trig there will be tons of stats, regression, probability… The depth vs breadth problem hurts my students, so for our school I think this will be tougher than geometry.

*** Advanced Algebra, Agriculture, American History and World Backgrounds I and II, Art, Biology, Bookkeeping II, Business Arithmetic, Business Law, Chemistry, Citizenship Education, Earth Science, English 1, 3, 4, French 2, 3, German 2, 3, Hebrew 2, 3, Homemaking, Intermediate Algebra, Italian 2, 3, Latin 2, 3, Mathematics Preliminary, 10, 11, Music, Physics, Plane Geometry, Science – preliminary, Shorthand, Shorthand 2 and Transcription, Shorthand Typewriting and Transcription, Social Studies, Solid Geometry, Spanish 2, 3, Trigonometry, Typewriting, World History**

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I found the June04 test at this address …

but question #33 wasn’t an “impossible circle”. I think you wanted the B test …

Thanks for catching that. I’ve updated the link, mine went to an A exam.

The June 04 B #33 circle is in fact not impossible… but that tangent? It’s not tangent. And the calculations are far harder than they intended.

When we got the State to back down, they agreed to accept a wrong answer based on the ratio of the arcs, or a wrong answer based on the lengths of the tangent and secant (both assuming, as implied, but incorrectly, that the tangent is a tangent), but they refused to give credit to the (small number of) kids who realized that the segment could not be tangent to the circle with the numbers given.

I think the teachers ignored them and gave the more than deserved credit.

i thought da 2008 math a regents was way to ezz. i no i aced it. wid a 95 or above.

At least they release the exams …

Here in Vermont, we don’t have end of year state testing. Progress is determined by the NECAP test. Test questions are “secure” and many principals interpret that as “No teachers involved.” Additionally, no one knows which questions were missed by which students. For years, the only things we got were vague lists of skills that each administering person’s kids needed work on. “Pythagorean theorem” might be mentioned but not the actual problem and so you can’t make intelligent decisions about your courses. If the P.T. were listed as being a skill needed for the “#33 impossible circle” question, for instance, all of the students would appear to need to work with Pythagoras …

Results are reported as being one of 5 levels worth 0 50 100 300 or 500 points to the school’s AYP. How many questions were correct and which ones? Where is the cut line? No one knows.

Then you add the fact that the guidance officers at my school never actually handed out those report sheets to the faculty and you get a true mess.

Despite all that and despite all the other flaws mentioned, I would prefer having a Regents-style program in Vermont. I can’t see it ever happening, though. NY thought of it first and Vermonters have this thing about self-determination that prevents us from copying the good parts of a good idea.

Bleah.

Vermont would probably do better copying from MA than NY anyhow, if they wanted to copy. I don’t know that much about MA’s program, but it seems decent from what I hear.

The Mills I mention above is a Vermonter. (doesn’t mean anything, but thought I should throw that out).

I don’t believe we have the wrong test. I believe we have no idea what we want to test, or why. Are these high school exit exams? College readiness exams? Proficiency exams in one or another course?

The reason has been lost. And without that reason, none of us could assemble a good test.

I liked the old Regents. You knew what you had to learn, and you could practice with the old exams until you were pretty skilled. And they did seem pretty good at distinguishing the people who understood the material from the people who didn’t.

I think perhaps the idea of “content-based” is what defines tests that teachers don’t mind teaching to. Most teachers test the material they’ve taught — and if you can agree on the content of what’s taught, its not to hard to build a test that teachers are comfortable with. But many “standards” are way to fuzzy for that

Believe it or not, the Math A scaling has a mathematical basis. Professor Alan Singer, a psychometrician from SUNY Stonybrook, often gave workshops to explain the curving algorithm when the tests were first developed. However, as a cynical retiree with a jaudiced view of the State Education Department, I think that the scaling is bogus.

As for the old sequence – Algebra, plane geometry, eleventh year math – this all has to be redone because of the impact of the graphing calculator. For example, I remember teaching Des Cartes’ Rule of Signs to help graph a function. Today, with a graphing calculator, you can enter the equation, see the graph and the “table” feature will show you exactly where the signs change on the axes.

All I can say is “good riddance” to Math A and B with all the contrived questions that required very little mathematical knowledge.

By the way, the curriculum change is great news for publishers

The Math RCT is pretty much a mix of middle school math and elementary school arithmetic. There are 20 short answer questions and 40 multiple choice questions. Its level of difficulty is somewhere between those of the state’s 4th grade and 8th grade math tests. Probably the most difficult question involves adding fractions with different denominators. There are a number of simple “practical” problems involving percents. I believe that these days, only students who are classified as special education can take it.

As of June 2005, it became a “secure exam.” Every copy is numbered. It comes in a sealed envelope which only the student is supposed to open. Teachers aren’t even supposed to look at it (but since many classified students have a reader as a testing accommodation, teachers do get a look). I believe the older exams used to be online, but they are no longer available. Obviously, they’re trying to save money by reusing questions.

If you think the Math A and B Regents are ridiculous, consider the following points about the Math RCT. Many classified students have use of a calculator as a testing accommodation, yet the RCT asks students to add three 4-digit numbers. A TI-15 calculator even makes the “hard” arithmetic questions (fractions, rounding) easy. And if it’s supposed to test “competency,” why do they want students to know how to add fractions anyway? How many times do people need to do that in the real world?

Part of the problem here is that A (and Algebra) do double duty: exit exams (“commencement level” ) and course summative.

There is no way to write those exams that doesn’t end up ridiculous. Separating them would have been better. Maybe the RCT is lousy, but at least it has a clear purpose.