I really don't mean to turn the whole blog over to all algebra, all the time, but Richard Cohen's idiocy has proved to be a good jumping-off point for a lot of interesting discussions (and a surprising number of comments, links, and TrackBacks...). The other ScienceBlogs comment on the whole thing that I'd like to address comes from Janet Stemwedel at Adventures in Ethics and Science, who asks about the student whose plight started this whole thing:

Were there just so many kids to get through, and so little in the way of support (on the extra-help/shifting to a different course/evaluating for learning disabilities axis) that even the most conscientious teacher couldn't have done more than recognize that Gabriela was in trouble and be sad for her?

'Cause, people? We can't keep calling these places "schools" if there's not some sort of mechanism for helping the kids who are going under. Even if Gabriela was a willing accomplice in her own failure the first time through algebra -- hardly ever coming to class or doing homework -- there should have been a mechanism for dealing with that.

It's a tough question, and something that everybody in the education business has to struggle with sooner or later. Whenever I teach a class in which some of the students are struggling (which is pretty much whenever I teach a class, given my discipline), I wind up wrestling with the question of how much effort I should go to to keep them from going under. It's always a tough call, because ultimately, it's not in my control.

(More after the cut.)

In the end, the student has to want to succeed. You can stage some sort of intervention, if you like ("Gabriela, we're worried about your inability to solve for x..."), and you can make extra help available, but you can't force anyone to **use** the extra help, or to do the work needed to succeed. You don't have any leverage ("If you don't stop failing, we'll, um... fail you."), and attempts to force a student to do extra work or attend extra sessions are likely to backfire-- they'll end up resenting the whole process.

(I'm assuming here that the real problem isn't an undiagnosed learning disability, and that there isn't another class available that satisfies the requirements for graduation. Failure to test for disabilities would be inexcusable, and if there were a different class available, I find it hard to believe that it wouldn't've been recommended after the third or fourth try at passing algebra.)

In the specific case of science and math classes, we're not helped by the fact that students are constantly being told (explicitly or implicitly) that math and science are really hard, and only total nerds do well in them. National columnists writing articles extolling the virtues of ignorance are an extreme example, but they're not alone. Students who struggle in math and science classes have a built-in excuse: "Math is hard." Failure isn't really their fault, it's just that the subject matter is alien and difficult.

The problem isn't just that people like Richard Cohen are telling students "You'll never need that..." The deeper problem is that Richard Cohen can cheerfully say in a column that he can't even deal with percentages, and not be laughed right the hell out of his job.

Ultimately, the responsibility for passing the class lies with the students themselves. I can and do try to make an effort to keep on top of the students who are struggling in my classes, but I very rarely end up failing people because they honestly can't understand the material (there are a few who get very bad grades, but if they've been doing the work and handing things in, they usually have enough points to get them a C-)-- the students who fail my classes do so because they don't do the work, even when I email them to say "You need to hand in the homework," and don't come to see me, even when I write "Please come see me if you have questions" on their papers, and don't seek out the student tutors, even when I mention to them after class that it might be a good idea to talk to the student tutors. There's only so much I can do **for** them-- I can't drag them into my office and force them to do the homework.

Now, the situations aren't identical-- I'm teaching at a fairly elite private college, not a public high school in Los Angeles. But the differences are of degree, not kind-- their students are somewhat less adult than mine, and they might have slightly more power to compel attendance, if not work. In the end, though, it's always up to the students-- if they don't want to put in the work, they won't put in the work, and there's very little we can do to force them.

(If you're really good, you can convince them that they want to do the work, but there aren't many real-world teachers with that kind of charisma...)

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In my experience when a student encounters such difficulties in one subject, it can be related to a lack of understanding in the subjects that came before and upon which that troublesome area is based. In this case, difficulties in algebra could probably be related to difficulties in understanding basic arithmetic. If you don't really understand what it means when we say 2+3=5, then you can't move on to the more symbolic: 2+x=y, solve for y=5. Without a solid foundation, its not possible to continue to build.

But I agree, you can't force students to learn.

It might have helped had she not missed 2/3 of her classes.

The "percentages" aside was what startled me, but it shouldn't have; I've heard plenty of stories about seemingly perfectly intelligent people who are so math-phobic that they're unable to grasp what a percent is. I know that my mother's told stories of being used as a neighborhood and office resource after it got around that she knew the occult arcana of percent.

Percentages and fractions seem to be common stumbling blocks for people who've gotten as far as being able to grind out integer arithmetic problems.

If you don't really understand what it means when we say 2+3=5, then you can't move on to the more symbolic: 2+x=y, solve for y=5. Without a solid foundation, its not possible to continue to build.How 2+x=5 can be a problem for

high-schoolstudents is beyond my comprehension. When I was in grammar school, public one, first grade -- we were seven year old kids then -- we solved such stuff and it was normal thing to do. This was not a "nerd class" -- I suppose a lot of the kids who learned such "symbolic" stuff went later to vocational schools and became carpenters or car mechanics.I think Chad is right: America has a cultural problem and it's name is "math is hard". No, it is not, at least not this kind of math. Probability calculus is hard. Integrals and differential equations are hard. But not 2+x=5. When you change the attitude prevalent in your culture, your kids will excel in math. They have one of the best countries in the world to live in, they can learn some basic algebra.

With rare exceptions: parents think and say math is hard (how many can help their kids with homework after middle school math?)and elementary school teachers think (and imply) math is hard (students get separate math teachers after 5th grade). So, kids get constant reinforcement of the idea that math is hard.

TV shows like Numb3rs might help buck the trend, though it's on at 10 on Fridays, not exactly prime time for kids.

Matt McIrvin:

The "percentages" aside was what startled me, but it shouldn't have; I've heard plenty of stories about seemingly perfectly intelligent people who are so math-phobic that they're unable to grasp what a percent is.Waiters must love him...

The really distressing thing about this is that his normal beat is op-ed writing about politics, which quite frequently involves budget math, often expressed in percentages. How can you make sensible judgements about issues relating to spending if you can't deal with percentages?

wheatdogg:

With rare exceptions: parents think and say math is hard (how many can help their kids with homework after middle school math?)and elementary school teachers think (and imply) math is hard (students get separate math teachers after 5th grade). So, kids get constant reinforcement of the idea that math is hard.What's more, we work very hard to make accomodations for people who don't like math, much harder than we work at making accomodations for people who can't read. Most colleges have programs in place that help students avoid anything remotely mathematical, but expect science nerds to take regular English classes.

TV shows like Numb3rs might help buck the trend, though it's on at 10 on Fridays, not exactly prime time for kids.Also, it's ridiculously dorky...

As a physics teacher in a better-than-average high school in Texas I can attest that one reason our students (here as well as nationwide) continue to perform poorly in algebra is that my colleagues in mathematics are forced to teach "How to use a graphing calculator," (no doubt in 10 easy steps!) rather than teaching Algebra. Combine this trend with the overbearing presence of "discovery learning" that is dominating and mandated within our curricula...well, I think the results speak for themselves. Don't get me wrong, graphing calculators and "discovery" approaches are great tools, especially when dealing with Gifted (thatâs a capital G) students, but they are neither substitutes for knowledge and practice, nor, as you point out, replacements for student motivation and self-discipline.

On an unrelated subject. I just started reading your blog about a week ago and I have enjoyed it a great deal.

I seem to recall enjoying math as a child, but at some point, early on in elementary school, I developed a very strong aversion to anything having to do with numbers. I distinctly remember sitting at the kitchen table after supper, and having the equivalent of hot flashes each time I attempted to solve a problem.

This anxiety followed me from grade to grade, though I always seemed to squeak by. When I was in the seventh grade, it seemed obvious to me that my math teacher's primary goal in life was to make me miserable.

In the ninth grade, a different math teacher staged a bit of an intervention on my behalf. He knew that I was doing well in my other subjects, and I generally responded well to him as a person, so he decided to help me, and for the duration of that year, I did very well. As I was preparing to select my courses for high school, I asked him if I should consider taking science math, and he genuinely seemed to believe that I could do it.

I honestly don't remember much of high school, but I managed to pass two years of science math by the skin of my teeth. It was during the third year that everything seemed to unravel and those old insecurities crept back into my immature brain. I failed by a single percentage point, and I decided to take arts math in summer school.

After high school, I avoided math like the plague. I chose to use plastic so I wouldn't have to deal with money, and I avoided jobs where I'd have to use a cash register. After I was accepted to university, I continued my anti-math progression, though by this point, I had also given up on the sciences.

At some point after university, my interest in science was rekindled, and I decided to face my math anxiety. In a very short period of time I managed to make my way through most of what I was taught in high school, but I must admit that I'm still rather confused about my ability to grasp concepts as an adult that gave me so many headaches as a teenager.