So You Have to Take a Placement Test...

Many times, students (or soon-to-be students) have asked me what they need to do in order to study for an upcoming placement test, because they want to pass it. But this question misses the point.

What is the point of a placement test?

The point of a placement test, its purpose, is to determine how much you know and how well you know it. There is no "passing" or "failing" on a placement test. A placement test serves only to "place" you in one math class or another. It does not attempt to judge how "smart" you are (and never claims that you're "dumb"); it does not attempt to say how much you can accomplish in the future; it only judges, based on the experience of those writing the test, which math class would best serve your educational needs right now.

What does a placement test do?

The placement test does not try to "grade" your knowledge; instead, it tries to determine what your current knowledge is. The placement test isn't pass/fail; it's more a matter of "ah; now I see you!" And you want to be seen.

Maybe it's been twenty years since you graduated high school; maybe you're fine with fractions and percentages, but have forgotten "that math with all the letters in it". Ideally in that case, the placement test will measure your current skill set, determine that you do not need any remedial classes, and will place you in a pre-algebra or beginning algebra class. Or maybe you just graduated high school last fall; maybe you aced your AP Calculus course, and you still remember all of it. Then ideally the placement test will measure this, determine that you do not need algebra or pre-calculus, and will place you somewhere in the calculus series.

There is no "passing" or "failing" with a placement test; there is only "placing".

By way of illustration, I was wondering some years ago on what level my then-homeschooled son was reading. I found a website that had a reading test which was composed of a long list of groups of words. The instructions said that the child being tested was to read through the groups of words until he finally hadn't been able to read a certain number of words. From this stopping point, the current reading level could be determined.

The point of that test had not been to "pass" or to "fail" a young reader or to criticise his abilities or potential, but to measure (to "place") his current reading abilities. When my son ground to a halt midway down the table, he had not "failed" the test; quite to the contrary, he had done quite well for his age; but the real point of the test was that I then knew on what level he could read. Gaining or exceeding some "score" was not the point; getting the measurement was point.

Should I try to fool the placement test?

No, you really shouldn't. A placement test measures neither intelligence nor ability but experience, and there is no shame in lacking experience — but there can be real harm in pretending experience that you don't actually have. If you try to "cram" for a placement test and somehow manage (through lucky guesses on the multiple-choice questions, for instance) to fool the test into "scoring" you well, this could result in your being placed in a math class for which you are not properly prepared. And from sad experience I can tell you that this means that you will very likely flunk your first math class, probably many times over, because you will have entered the course lacking the necessary mathematical background to understand the material.

I took a placement test when I went back to college. It had been a few years since high school, and my education hadn't exactly been stellar, so I figured that I would need to start my renewed studies in some lower-level math course. I read the descriptions of the various courses in the catalog. Some of the courses described stuff that I knew how to do (so I could probably skip past those courses), and some other courses' descriptions used words I didn't even recognize (so I probably wasn't ready for them). But there was one course in the middle where I remembered some of the stuff from high school and didn't know the rest of the stuff. I figured that this class was probably where I would need to start.

What happened when you took a math placement test?

When I took the placement test, it came in two parts: a calculus part and a non-calculus part. I did the best I could on the non-calculus part, based on the experience I had and the material I could remember from five years previous when I'd graduated high school; I didn't even attempt to answer the questions on the calculus portion. The placement test put me right in the class I'd expected to start in. For the first half of that course, I was bored to tears. Then, about halfway through, the instructor reached material I'd never seen before, and the class started getting interesting.

The Purplemath Lady flunked her math placement test?!?

In a way, you could say that I'd flunked the placement test, because I couldn't even attempt the calculus half of it. But I'd passed the placement process with flying colors, because I'd honestly provided the information that the test needed in order to place me properly in the best course for my abilities at that point in time. Where did I start? In Intermediate Algebra, way before calculus — but just where I'd expected I'd probably need to begin. And here I am, writing a math site, so "flunking" the placement test certainly didn't mean I was "stupid".

What's the worst that could happen by fooling the test?

You could succeed. Then the placement test will misunderstand your current skill level, your adviser will sign you up for a math class for which you're not adequately prepared, and you'll almost certainly flunk. Possibly over and over. And over. You'll end up taking longer (and spending more money on) finishing your required courses, than if you'd just started where the test would otherwise have placed you.

I speak from repeated sad experience; I've seen this too many times. You do not want to fool the placement test and get locked into a first math course that is too advanced for you, only to end up banging your head against a wall, failing the same course over and over again. You really do want to start in the course that is right for you. So don't try to "cram" or study for the placement test; don't try to fool the test or to "pass" it. If you want to do a little review to brush up on what you already know, that's great. But the best thing you can do is just relax, do your best, and let the placement test do its job.

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