I struggled over this story, which has been picked up and bandied about this week in the edu-blogosphere. To summarize, the number and percentage of students at California colleges and universities who require remedial math is increasing; this despite the fact that everyone must now pass Algebra 1 to get a high school diploma and must have passed Algebra 2 to get into a university.
How do we explain this? Are teachers watering down course standards? Are students not taking the college math placement test seriously? Are we teaching material that's different from what's being tested? Is grade inflation so rampant that A students really don't know anything?
As with so many other problems in education, I was prepared to excuse my school. Overall we do very well, both in standardized test scores and in numbers of students who attend colleges and universities. Our school has a very strong, well-earned academic reputation.
But in my pre-calculus classes the last couple of days I've seen the problem firsthand. It's not pretty.
Here's what I've come up with so far. This week we've worked on inductive proofs, which often allow us to prove so many of the formulas that up until now we've taken for granted. I teach them to SHOW the formula you’re proving works for n=1, ASSUME it works for n=k, and PROVE it works for n=k+1. When students get down to the proving part, there can be plenty of algebra to work through. Here I have this class of very bright pre-calculus (trig and math analysis) students, and I can’t tell you how many were asking questions about what to do next. They didn’t see the algebra right in front of them. I could tell them and *then* they’d see and know how to do it, but they couldn’t see what to do without my initial nudge.
It’s almost like they’ve compartmentalized their knowledge. They might be thinking, “Oh, we’re not working on getting a common denominator, so I didn’t think to get a common denominator when adding these two rational expressions.” As soon as I said “common denominator”, though, they knew right what to do. Or they were unwilling to try something and see where it led them; if they could do the algebra, they wanted me to tell them what to do, step by step, so that they only had to do the computation instead of the thinking.
Remember, these are the good students at a good school. If the college/university entry level math test is no harder than the sample problems shown in the linked article, then students who fail that test deserve to be in remedial math. But if the test includes problems requiring a synthesis of a variety of math skills, then even the students at my own school have shown that they might be in for a challenge.
At Davis I've seen a mixture of grade inflation and people not taking the tests seriously causing people to have to take lower math courses. The main thing to look at though is most people don't view this as a bad thing, unless your in the bottom most math class you still get units and a grade to help boost your GPA, so only in the truly remedial classes do people lose on the deal. I think a lot of people who are in those classes didn't review for the placement tests or just wanted a refresher before their grade depended on them knowing anything. So a lower math class can either help you by boosting your grade, or help you prepare to do better when the grade actually counts. The most interesting part though is that higher math classes can have placement tests waived by AP tests meaning the person might actually have very little understanding of anything under Calculus and still be able to continue on, meaning they struggle whenever they hit something from pre-calc.
Doesn't this come up perennially? I can remember stories about the large percentage of freshman class budgets allocated to remedial classes several years ago.
> How do we explain this? Are teachers watering down course standards?
I think it's an example of a theme I've been pounding on for some time: that education is of tangential or incidental importance institutionally in the public school system.
Education may, or may not, be important to a teacher but it's largely immaterial to the school. The teacher's pride may impel them to insist that students learn (that's a "tough" teacher) but the school doesn't insist that the teacher teach. There's nothing in the public education system that necessitates a feedback loop that determines whether the teacher is teaching in the sense that there is a feedback loop in, say, the school's sports teams. Nobody knows what the school's education standing is but everyone knows what the football team's win/loss record is.
If nobody gave a damn what that football team's win/loss record was then over time what would happen? Would the team get better or worse? Would the performance bar be set higher or drift downward?
I think it's pretty tough to argue that the football team would get better if the outcome of games wasn't tallied and made public. Why should it be different for education and the school as a whole?
I'm sure EllenK will have something to say about football :-)
And here I am...but seriously, our state has initiated this mandate of four years of each of the four core subjects, which on the surface appears to be a good thing. However, this means that kids who struggle to pass Algebra II will be thrust into Pre-Cal. After a couple of years lingering in Pre-Cal, the end of course test will come up and they will either pass and graduate or not. Once again, on the surface this appears good and just, but when you begin to have average students opting to get GED's because they simply aren't math people the choices will be clear-either dumb down the higher level math classes or accept the fact that your schools AYP is going to sink like a stone. And let's not forget, AYP is what determines if a school is functioning. Add to that the mix of severely disabled students being pushed into mainstream classrooms and taking the regular tests, numerous students who can't read word problems for any of a number of reasons from stark illiteracy to lack of English and you have a situation where there will be at some point a great educational divide. You can apply this same situation to science, to English or to Social Studies, but the endgame is that the only thing that matters is the test. Right now, I see kids in my class that are in AP classes, but who have problems reading and responding to a critical article in art. They are being taught to respond to stimulus, but not to take the next step and reason. This is why just testing or just counting kids who take AP tests or any simplistic fix should not be the sole criteria upon which schools are judged.
And BTW, if we could get HALF the kids who attend football games and hang out under the stands to show up for voluntary tutoring before or after school, we would be a totally different society. But we can't combat the institutional support for athletics over sports. The Greeks valued athletics too, but the knew that education created a balanced citizen. We simply think athletes are favored citizens.
Ellen, your state mandate reminds me of an apocryphal story about communism that my father liked to tell:
Since nails are measured by the pound the central bureau responsible for the production of building supplies mandated that some certain number of pounds of nails must be made. Since it's approximately as difficult to make one one-pound nail as it is to make one one-ounce nail the nail factory supervisors switched over to making very large nails which allowed them to handily meet their quotas.
You can take the story as an example of the inevitable, cynical tricks people will pull to avoid doing more work then they have too and you'd be right but you also wouldn't be comprehensive. A similar outcome is possible even with the best of intentions on the part of all parties. In any complex set of requirements there's always room for honest misinterpretation.
But that may not be the worst aspect of centralized administration.
Look at the direction of the arrow of responsibility.
Rather then being responsible to the hero of the Great Patriotic War who strolls into the local hardware store to get a couple of pounds of nailskis to repair his honest, socialist chicken coop the nail factory is responsible to the central nail directorate. Maybe after a couple of years of proudly reporting that the state has a 200-year, and rising, supply of 18-inch drifts (those are really big nails) complaints from prospective chicken-coop repairers gets the nail directorate to revisit the nail production mandates.
Even with the best of intentions the structure of the organization, the top-down orientation, works against efficiency and efficacy. Without the best of intentions you get the Detroit Public Schools system with its 25% graduation rate.
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