On the Frontline, and it Ain't Pretty
Two days ago, in the course of a test review, I was going over an exam that one of my "regular" (as opposed to "accelerated") chemistry classes took and did very poorly on. Very
poorly in this case means not a single person passed, in fact the highest grade was a 68. Bad, bad, bad ... On this day we were reviewing the test and any problems that anyone may have had with it. This test covered some very basic material, density being one of them. Many of you may remember mister density, which you obtain by dividing the mass of something by the volume it happens to occupy, which is mathematically represented as: D = M/V. On the test there were two density problems, and these were very straightforward ones by any measure of the term "straightforward". In both cases you're given the density and the mass, and asked to find the volume. So to do this you'd algebraically manipulate the density equation as such:
D = M/V, multiply both sides by V, therefore DV = M, and since you want to find V you need to then divide both sides by D, giving you V = M/D.
Simple, right? Well yeah, it is, but why was it that about a half dozen kids in the class came up with V = MD? What in the world is going on there? I would have understood this with one or two kids doing this, but six? What was more frightening was asking two of the kids to come up to the board to do the problem the way they understood it, i.e. starting with the density equation derive a formula that would give you a way to find volume. Neither could. Mind you I had two kids who were game enough to actually get up and try to do a problem on the chalkboard in front of the entire class, and both of them couldn't do it.
So I'm standing there in front of a classroom full of 18 kids and I'm sure I had the most befuddled expression on my face after I realized how incapable many of them were at doing what I consider to be a very, very rudimentary mathematical operation. First of all I had done at least six of these problems in front of them for homework review and no one questioned how I was coming by my answers. Then they also had the problems in the textbook to review and from all of that no one asked any questions nor were apparently put out by the fact that the book was arriving at an answer via means that somehow didn't jive with their particular mathematical worldview. I suppose I should be happy from a "better late than never" perspective that this came up as an issue during the test review; I mean in all actuality they could have been just as stoic about their problem with the test as they were about all else that they'd encountered so far, but this just flipped me out.
Upon realizing how poorly suited these kids were to the simple math required of them in this class, the next thing to go through my head was what math they had completed before getting into the course. The school's web site tells us that the math requirement for this course is as follows:
Pre-requisite: Algebra II taken previously or concurrently.
In fact they needed to have gotten through at least algebra 1 and technically should be in at least algebra 2 to be in this course, so they should have completed a year's worth of algebra,
preferably two years, or at least be in their second year of algebra. That's in fact true for some of these kids but a sizeable majority, which seemed to represent all of those who failed to get these questions right, were in something called IMP. I had to scout around a bit to find out what this was, and indeed I found a web site, Inside IMP which enlightens us with a number of things, not the least being the following:
The Interactive Mathematics Program (IMP) is an exciting new way for high
school students to learn mathematics. IMP's four-year program of problem-based mathematics replaces the traditional Algebra I-Geometry-Algebra I/Trigonometry-Precalculus sequence. This new curriculum meets college entrance requirements and prepares students to use problem-solving skills at school and on the job.
This program is intended to do away with all traditional math training but interestingly enough the only ones taking these courses are the kids considered to be on the "slower" track. My other students, by and large, take the traditional math courses and for all of that with those kids solving for "V" in a density problem doesn't seem to be a problem. Ok, so maybe who takes it isn't that much of an issue really, I mean if this is really a new and exciting way for kids to learn math, well darn, this is the group that you think would be sucking this stuff up, right? Well, yeah, you'd think, but at this point I'd have to say that the results are a tad short of anything to get excited about.
Yesterday I had to spend time with one of the school's guidance counselors when a student's mother asked for a meeting to discuss his place in accelerated chemistry. That went well and it was agreed that this young man should shift into the "regular" class, but before I got to leave the counselor's office she hit me with a request sheet for another student in the class alluded to at the start of today's entry. He pulled a 40 on the test and did nearly as bad on an open-booked quiz, and apparently had come to see her about getting out as he didn't really need the course and, given his other avenues for getting into college, he's right, he doesn't "need" the course. His specific stated problem with the class is the math, with his strongly expressing the feeling that he didn't think he'd be able to keep up with the math requirement. In his specific case he's been in the IMP pipeline for four years, he's a senior so this would be his last year in IMP. So he has three years of math under his belt and he can't do a 3 variable problem with 2 of the variables given - whoooooooooooa, for sure.
What I know is that I clearly have kids in a chemistry course who likely aren't mathematically prepared and that's a huge problem as what makes chemistry hard is NOT the whole idea of atoms and mixing things together. Mind you, I'm not saying the conceptual side of chemistry isn't difficult, it certainly is. In fact having to learn anything that exceeds the grasp of your day-to-day experience requires an exercise of imagination and, for lack of a better word, faith that for some can be quite taxing. But most people can make the necessary leap, they can handle it on the whole, but what kicks many of them in the gut when it comes to chemistry is the math. One of the things that makes chemistry "hard" is the applied math that's necessary to get through a wide range of different problems that comprise the curriculum. At the high school level we're not talking calculus or anything that requires higher-level math, we're talking about being able to manipulate a three-variable problem with some ease and fluidity, something that's at this point beyond the grasp of a significant number of students in this class.
I'm not sure where this is going to go, but I'm somewhat amazed that there's a math program that's in place to supplant the "traditional" math curriculum and there are no metrics being sustained to see if, indeed, the kids making it through the program are where they need to be as they move along. If kids who've had three years of math and are currently sitting in their fourth don't feel that they're qualified for a chemistry course I can only imagine their level of unpreparedness for when they step out into the world past high school. This pretty much seems to epitomize why so many people these days are wringing their hands over the inability of our kids to go out in the world to do math, or much of anything else that requires a skill level regardless of subject, because for whatever reason we seem to be increasingly less and less successful in imbuing those skills. Part of the problem, I'd surmise, is teachers or school administrators (I'm more and more convinced that it's not always teachers who are the culpable parties, but rather administrators looking to save money in some fashion) taking a fancy to new and aggressively marketed "innovative" teaching programs for which they're insufficiently trained and for which there are either no, or otherwise poor metrics with which to see if the program in question is indeed working. As I remind myself on a regular basis, "Welcome to the world of education."