# Passing Integrated Algebra apparently does not mean much

Dan Koretz (Harvard) and Jennifer Jennings (NYU) (f/k/a Eduwonkette) looked a little at kids who take New York State exams. Turns out, the exams don’t predict much, or at least don’t predict what some people thought they did.

Math A (now Integrated Algebra) are the graduation requirement in mathematics. And many kids passing the exam had to take remedial math when they got to college. Something’s not right.

Is the cut score too low? That’s the conclusion that’s being drawn across the media and the commentators.

“The bar was set too low,” Deputy Education Commissioner John King said at a Board of Regents meeting. “But we are changing that now,” he pledged.

He is wrong. The bar wasn’t set too low. The tests stink.

Almost all the kids (over 90%) who squeak by with a 65, 66, 67, 68, or 69 take remedial math in college. I guess that’s not a big surprise (though it’s really not right)

Over two thirds of the kids who score in the 70s take remedial math in college. Does that suggest that the passing score should be higher? Keep reading.

Just 10% of those taking the exam score above 80. So 80 is some sort of gold standard? Or maybe that’s where the passing score should be set. No and no. One quarter of those students take remedial math in college.

The NY State Math Regents measure the ability of a student to take and pass the NY State Math Regents. The exam is aligned with overly-broad standards. The exam is poorly written. The exam is poorly designed. It tests vocabulary skills and guessing skills. It tests test-taking skills.

The NY State Integrated Algebra regents exam does not measure knowledge or skill in algebra, or in any area of mathematics for that matter. It cannot be fixed. A student’s score on this exam will never correlate strongly to SAT scores or college placement.

It is time to admit that the New York State Education Department is no longer good enough to create mathematics exams.

Great post, J. I was trying to get those thoughts straight in my head – but you nailed it. These tests don’t tell us anything other than how well the students can do on the test.

WRT Integrated Algebra, SED’s position is (ought?) to be that the PIs conform to NCTM (sort of, yes), that the exam questions are written by high school math teachers (yes, but constrained to targeting PIs and, in at least some cases, heavily edited out of sight), and organized and structured by nationally prominent testing companies (yes, but read Todd Farley’s “Making the Grades” for a depressingly amusing viewpoint). Bottom line: “Not our fault.”

All this focuses on the manifestations rather than the causes: the PIs themselves. Why these specific PIs? What are the goals the PIs are supposed to target? What alternatives to theses specific PIs (or the entire PI “approach”) are there that point to the goals? I’ve asked a number of times in a number of appropriate forums and have never received an answer that reached beyond platitudes and saluting the flag. (One time I asked why we should even salute the NCTM flag and the look of bewilderment was priceless…and saddening.)

So, we have developed a not unreasonable test development system that is a classic GIGO (Garbage In, Garbage Out) machine. Lots of storm and fury, but signifying nothing. (Except, of course, a very defensible distractor from where the conversation should be taking us.)

Exactly. People think “raising the bar” will solve education problems. But if kids are failing, making most of them fail doesn’t encourage them to study – it does the exact opposite exact for those who already take it seriously and have well-developed skills from the past. What you need to do is change what you teach, so it’s relevant to them not just in math, but in other problem-solving areas.

The fact that teachers constantly try to find “motivations”, applications of PI skills, shows the standards are not good. We should teach problems and then investigate the mathematical concepts that would help us solve them more efficiently. Not the other way around.

I wish someone in the DOE would issue a Put-Up-or-Shut-Up ultimatum (even in jest) at these complaints because, frankly, I bet that a half-dozen posters on this blog (or any of a number of others) could brainstorm a better, more predictive test in one day of PD. (Probably less, but let’s try to get a whole day of it.)

pbp…

On another blog someone asks in response – “but don’t we need some standards?” – and I think that, in the current standards movement, there is nothing I want to save.

But let me toss it to you – if you wanted to specify what should be taught (let’s stick for the moment to high school math, sorry Steve), how would you do it? Name the course? The topics?

(I think the key moment is when we decide not to standard-test it).

But run with this a little. I’m curious where you go.

(the other blog, if you want to peek )

i agree completely jd. i have taught integrated algebra for the past three years, and the standards are just a mess. there are so many things that i have absolutely no idea why they are in the curriculum at all, and i struggle to make them relate to absolutely anything else in the curriculum.

my students have been wildly successful (this year i had 22 eighth graders take the test, the low score was a 78, the high a 96, and the average an 84), but i literally spend the day before reminding them about stupid things like relative error and bias.

(not to say that relative error isn’t a valid concept, but what the heck is it doing in an algebra course?)

then, i watched more than half of my extremely capable algebra students bomb the question about bias in the driving survey…but the reality is, i covered bias in one day in a four day flurry of statistics, which was completely disconnected to anything else.

i wish someone important would listen to your wise words!

Could it be that the officials who head up State Ed.’s assessment function have no professional-level training and coursework in testing/assessment, evaluation, statistics or any other relevant professional area of expertise?

Aha! The decision-makers are all ex-district superintendents. They do what they know how to do very well. Unfortunately, that entails keeping other sitting superintendents happy. That’s the sum and substance of the purpose of the NYS Ed. Dept.’s entire assessment program … and will continue to be until such time as NYSED is cleaned out and cleaned up.

Not in my lifetime … but a girl can dream.

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jd…

Let me start with this: I think there are four types of “learning math” through high school level.

1) Fluency in day-to-day arithmetic calculations, trade and practice type of calculations, and scale of numbers.

2) Comfort with abstraction as a tool to find underlying commonality between seemingly different things.

3) Knowledge and comfort with “modern reality” mathematics such as relative event probabilities, data display (and distortion), and statistical analyses and reporting.

4) Preparation for college-level mathematics for science, technology, and engineering.

What has happened is, as a society, number 4 has become the only “acceptable” output. So we’ve warped everything to target that goal (e.g. getting rid of “trade school” classes in high schools). To the point where preparation for taking (presumably AP) calculus in the senior year is considered “normal” pacing good for the vast majority of kids, and taking calculus as a junior is “accellerated.” (In the 1970s, when I was in HS (not NY), accellerated was calculus as a senior and normal was trigonometry…we didn’t have pre-calculus.) To achieve calculus as a normal senior course (especially if there is a pre-calculus in the sequence) means lots of prepatory stuff has to be shoved down the pipe. And in order to insure “success” (aka calculus in the senior year), we need to have tests showing that all students are making progress towards that goal. Etc.

So anyway, in my mind, we should begin the debate with what we expect to have come out of this intellectual pipe. Once we know what the product should be, then, as is one of the wonderful things about mathematics, the various processes for getting there can tested and the best performing ones adopted widely.

p.s. I am strongly opposed to heterogeniety of mathematics skills in the class room. The wider the skill spread, the lower the resulting overall learning. This opposition to heterogeniety is generally not approved of in our current social structure.

p.p.s. My belief is that the attempts to at least acknowledge the other three goals is a major part of why we end up with messes like Integrated Algebra Regents PIs and exams.

I’m working on change…

Well, this gives me much to think about. My kids who take the algebra regents may not have even passed the regular math test. Thanks for this.

Hi,

I am not a teacher. I am a student who has an idea.

This year, as an 8th grader, I took the Integrated Algebra Regents course and exam. I will say that I had to put in a good few hours of studying on certain topics (e.g. exponential functions, rational expressions), the course was overall not too bad. I do not have specifics for all of my class on the Regents; however, I do know that on our practice Regents, nobody failed, even students who had been consistently failing all year.

That’s the background. Here’s my idea.

I believe that the state should mandate Integrated Algebra for any 8th grade student who scored at a 3 or 4 on their 7th grade math exam (possibly even a 2.) They could take the Regents. Then, the state could change passing to 80 which, if you’ve been passing all year, is attainable. Students who score 80+ could move on to Geometry, and those who score below could retake the course in high school, undoubtedly doing much better with the background.

If this was implemented, the state could achieve many goals on many different levels. They could accelerate more 8th graders. They could achieve higher state test scores on both intermediate and high school levels. They could broaden students’ mathematical horizons. Maybe with this, students would be more prepared and motivated to take Precalculus and Calculus in high school.

Just a thought…

Not retaining basic Algebra but passing the basic Algebra class — not surprising, really. Some kids/people/students forget some things after graduating and need to learn some of it again, even if in a remedial class in college. Fortunately, for those who put in the full effort, they should learn much better when the course is repeated.

So the PARCC tests should bring some of the problems back out into the open. No more hiding behind a facade of passing Regent exams as being equivalent to subject and grade level skill proficiency (finally, but unfortunately too late for my child) and telling the parents that are fiercely advocating for better special and individualized instructional methods and more effective utilization of their time at school. This is obviously how all of the struggling middle schoolers seen to miraculously disappear and no longer are tracked and fall under the radar and graduate from high school while not achieving the grade level skill sets that their high school diplomas no longer guarantee!!!!