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.