Saturday, October 15, 2005

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."


Anonymous Anonymous said...

Hey James,
It is always a pleasure to read your thoughts, whether or not I have anything to add!
Your test experience almost exactly parallels that of my Dad, a Master Chief who retired after 33 years to teach High School ROTC in Patterson,N.J. He showed me the tests. Almost all were left blank, except for a few screwball answers attempting to be funny, but succeeding only in communicating a sort of dull anger.
My own theory is that Public Schools are subject to Public Pressure, and the fact is that the vast proletariat mob seem to value grades over actually learning anything. Try failing a kid who hasn't learned one measurable thing all year, and watch the Wrath and Fury descend. I tell you now, even though every administrator and colleague will agree with you in their heart, no one will back you up.
My conclusion: teaching is an easy Major, but a very difficult Career.

4:10 PM  
Blogger James said...


Thankfully I don't think I have it as bad as your father does. I also fully concur with your assessment that education is an easy major, but a very difficult career. In fact the statistics for the number of first time teachers who bail out of the profession would go a long way towards supporting that as well.

As for failures, etc., I'm making it so that if a kid fails the class they'll have to work at it. I'm sure a few will, but in the event that happens I'll have my butt covered. I'll see how the rest of the year unfolds.

9:52 PM  
Anonymous David C said...

Thats a shame, if they can't handle density I fear an even larger falling out in physics! This whole IMP situation seems short sided as you've mentioned, and whatever it's mission statement or whatnot, the math does not seem on par with other disciplinaries requirements such as your own. I do recall Chemistry being the most bothersome class of my four sciences, having since taken AP Physics and currently am in AP Biology, despite the latters more involving course work and two period requirement, chemistry during sophmore year seemed the most overwhelming. At the time I was taking Alegbra II, if you'd like any bearing, and found that the math didn't cause me to stumble as much as the concept. And dammit, I still loath significant digits.

Your class blog seems very appealing, and would be a great resourse to me if I were in your class. Its one of the most elaborate webpages for a teachers class that I've ever come across.

Have I mentioned to you that my AP Government teacher was Karl Rove's roomate? It's no joke.

1:43 AM  
Blogger she falters to rise said...

I have to sit down with graduate students all of the time and explain how to manipulate the equation
so that they can make their solutions.

How can you get this far and not know how to swap out values and move things around the equals sign?

These things start so early...

8:37 AM  
Blogger James said...

I'm amazed that graduate students wouldn't know how to do concentration problems. I'd like to think my accelerated kids could do a problem like this without much trouble, but ... I have no clue what happens when they get to college. A graduate student in biology should have taken at least 2 years of chemistry before getting into a graduate program and how it could be that they didn't have the knowledge and experience with working concentration problems, well that's just incredible.

David: Glad to see you still checking in now and again.

You're totally right about the physics debacle to follow if they don't get the chemistry. I'm still learning more about this IMP program and what I'm hearing doesn't exactly make me feel good about the program or what it's leading kids to believe about their ability to go on to anything in college. I'm amazed, which seems to be a common experience for me of late, that kids could be so far along in school but yet so fundamentally unprepared for what they're expected to be able to do with what I believe is very rudimentary math for HS juniors.

No, you never mentioned that your AP govt teacher was Rove's roommate. Frankly I'm not sure what to make of that given how much I have little nice to think about Rove. That said, I'm sure it makes for an interesting AP government experience, or at least it darn sure should.

3:25 PM  
Blogger GrrlScientist said...

I have people like this in my college anatomy and physiology class. every morning when i wake up, i lay in bed listening to NPR, surrounded by a cloud of depression, thinking IS THIS MY LIFE??? i did NOT get my PhD in science so i could attempt to teach science to students who are not prepared to be in college!


3:27 PM  
Anonymous Ivory said...

I see this at the college level all the time - their minds are wiped clean at the end of the semester like a reformatted disk. I teach microbiology to nurses and they have to have 2 semesters of college chem before they take my class. I give a pretest at the beginning of the class to see where the students are at and one of the questions asks them to explain how they would make 100ml of a 0.5M solution from a 5M solution. In my last class of 20 not a single student could answer the question. My question: what the heck were they doing in 2 semesters of chem if they didn't learn how to do a 1:10 dilution?

3:01 PM  
Anonymous Chemboi said...

I don't think this is a new problem, but it most certainly is a problem. It's not just math, but concepts as well. I remember taking a sophomore biology class at a large university *cough* years ago, and I was very popular because I was a chem major who could do a little math. I kept running into other students asking me to solve concentration problems, things like that. The final straw for me, though, was when I realized that, in a study group of 6, I was the only one who knew the difference between a protein and a proton. When I was asked that, I was so shocked I just sat in stunned silence. There's no excuse for getting into a college biology class lacking such fundamental knowledge.

4:39 PM  
Blogger James said...

Hedwig: I hear your pain, and feel it to a certain extent, but then I'm of the mind that I'm part of the problem - well, maybe not me per se, but it's somewhere at my level that we seem to push these kids on with some odd notion of having prepared them for college. Wrong, wrong, wrong ... they're told that IMP is going to prepare them and they can't do a simple three variable problem with two of the variables given - how did they get there? This whole thing is crazy, and causes me no small measure of head scratching, and I can't begin to imagine how much worse the feeling must be for someone who expects a semi-prepared student walking through the door and instead finds themselves dealing with something significantly less than that.

Ivory: You'd think after all that chemistry that they'd know how to use M1V1 = M2V2, I mean it doesn't get much simpler than that, but ... there you go. I'm looking forward (not really, but ...) to getting to concentrations with my kids to see where this goes. I'm wondering if I'll in someway be contributing to the problem, will I have to "pass" them, or ... I have no clue. But there are no surprises for me in that kids are unable to do what would be considered pretty rudimentary stuff.

Now all that said, maybe the curriculum has to be changed. Does there need to be a week or more spent on quantum chemistry, reduction/oxidation reactions, etc.? There's a lot that goes with traditional chemistry teaching that really has no practical use for a nursing student or much else, but there are many pratical applications to a great deal of a chemistry curriculum and maybe THOSE things should be focused on and reinforced such that these students know them in their sleep by the time they walk out the door. I don't care if they understand the Bohr atom, but I do if care that they know how to mix a problem solution and understand the difference between a milligram and a microgram.

Chemboi: You hit it on the head, there's no excuse, at all, for getting through much of biology without a good grounding in chemistry. But then as I share with Ivory above, there's a lot in a traditional chemistry class which is likely not very useful for a biology OR a nursing major, so why bother pushing it? We should have something akin to "vocational" chemistry where the basics are ground into the students' heads and they walk out with something that may have a semblance of a chance to actually stick when they need it to be there.

8:44 PM  
Anonymous David C said...

Woah. Proton v. Protien?? Here in highschool I don't think I've come across that. James, I don't know how the Science credit requirements work in your high school system, but here we are required 4. Perhpas I'm not being appreciative enough of sciences, but of my four years I've been able to donate 6 of 28 periods to it (That's like, 3/14!). In chronoligcal order, and the perferable order by our county, I've taken BIO I (9th), CHEMISTRY (10th), AP Physics (2 periods, 11th), and AP BIO (2 periods, 12th). Just in case anyone's wondering, as it seems to correlate with the subject at hand, I took Adv. Geometry (9th), Algebra II (10th), Pre-Calc (11th), AP Calc AB (12th).

I honestly sympathize for the teachers, who I feel are embarassed at my simple mistakes, if beyond my classes they run into the large problems you're addressing.

8:37 PM  
Blogger graycie said...

Some states or districts set up courses like IMP to (artificially) boost mandated standardized test scores. My school district has created Physics First for those freshmen who 'can't handle' Earth Science. Earth Science is a tested core course. Physics First is not. Boy, our city-wide scores jumped!

Educational bureaucrats somehow think that this solves the problem, when it simply removes groups of students from courses they CAN pass if appropriate measures (like smaller class size or team set-ups for freshmen) were implemented instead. Of course, that would cost money, and we can't have that, can we?

6:48 PM  
Blogger James said...


You're raising an issue that causes me to wonder. I can't say that our IMP students are excluded from the standardized testing, my "guess" is that they're not, but it's something I'm going to ask about this week. Of course that does make for a not so clever, and ultimately pretty cynical modus operandi.

As for your comment about saving money, and there are many guises for this I've come to find, it seems that this is the school administrator mantra every which way they go, and I'm still trying to figure out how they measure saving money over what's being done to students in the name of fiscal penury. It's clear to me that the students are not getting the training they need in some pretty fundamental skills, so how is it we're doing them a favor, and in the long run saving ANYONE any money, with the apparent result? I haven't a clue ... oh well.

3:22 PM  
Blogger graycie said...

Realistically, a good education entails a thirty-year payback. Most administrators only worry about this year and next, or maybe as many as the next five. There's no vision at all that encompasses the financial cost to the community -- certainly not on a long term basis.

I have no idea why this is so. I wish I did, and then maybe there could be something we could do to set things right.

7:05 PM  
Blogger BotanicalGirl said...

I'm late to the commenting, but I have extreme difficulties with math. Sure, I was in advanced math in middle and high school but it was a struggle every day. I got a 1 on the AP Calculus exam (the lowest score possible). I nearly failed semester 2 of calculus in college, except my roommate was a math major and helped me get a C.

While I can do basic MV=MV calculations, some dilutions really make my head hurt. I have to really work at it on paper, and then have someone double-check me. Sometimes it isn't the system that fails, but an inherent comprehension issue with the individual.

Also, I never could figure out synthesis questions for organic chemistry, no matter how well I had the reactions memorized.

2:13 AM  
Blogger James said...

BG, Glad you were able to stop by, especially given that you've laid something for me to think about in my brain.

I accept the fact that someone can be successful in some aspect of science without having a strong math backgroung, but it's also very difficult to do. Molarity/molality/normality problems are easy compared to some statistical tools that have to be brought to bear in the course of research, and without that you can't go but so far, or so it seems to me.

I also think that someone who's willing to muscle their way through it, especially if they're not shy about asking for help, can likely make it if they're dogged enough and secure enough in themselves. That's not always an easy combination.

Your observation that some people have a hard time "seeing it", or words to that effect, seem to be borne about by my observations. I've seen students trip themselves up over the simplest of formulas or mathematical progressions, and not be sure what the heck's going on that's causing this. On the whole it's likely that I can see something easily enough that they can't, and there's not much to do for it accept muscle one's way through and just keep trying. That we can't measure this in a concrete way, this difference in "seeing", I think does a disservice to students and the educational system in general for I'm confident that in many instances we're using the wrong tools for kids with these difficulties, and thereby increasing their frustration and that of their teachers.

8:48 PM  

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