Wednesday, December 23, 2015

Acceleration, math, and college standards

California has long had issues with matching up its public K-12 school system with its system of public universities. When I was out there a few years ago doing some reporting, I learned that a number of schools had (until recently, people were trying to change this) not offered the classes that were necessary to attend one of California's 4-year public universities. In other words, young people with perfectly good high school diplomas would find themselves needing to do lots of extra course work in order to enroll, not because they didn't stretch in high school, but because apparently no one was thinking that children from those high schools might wish to earn 4-year degrees from one of the major universities. Talk about low expectations.

Anyway, I was thinking of this as I read an article in EdSource about how districts are choosing to accelerate students. There's been a bit of a rethink about how many 8th graders are taking algebra as it's become clear that many haven't been prepared. If you have trouble with algebra, most higher level math is going to be tough to understand. This impulse brushes up with a different issue, though, which is that in order to attend one of the flagship universities, you really need to have followed a sequence that includes something like calculus your senior year. It's hard to get there without doing algebra in 8th grade.

So this leads to the question: who gets accelerated? Ideally, everyone would be free to work at his/her own pace with no judgements. But if not taking algebra in 8th grade means you're probably not going to have the right classes for a top university 4 years later, it becomes a bit more fraught. You potentially have people making the choice of who seems like college material and who doesn't, quite early.

So, broadly, how should acceleration decisions get made?

The Ed Source article details efforts to make sure the criteria are fair. I remember years ago taking the Iowa Algebra Aptitude Test to see if I was ready for algebra in 6th grade (fun story: the teacher administering it had such a heavy southern accent I thought for a long time that it was the "Owl" Algebra test). Of course, tests have their problems too. So there are other options. Teachers can recommend people who didn't quite get the right scores, though teachers can't recommend against someone who did get the right score. And parents can elect to accelerate children too.

There are arguments for or against these options. Good teachers naturally teach to the middle of a class. They are constantly checking for understanding, and if most of the class isn't getting something, they'll stay there. This means that if enough children who aren't quite ready for accelerated math are in a class, it can get watered down.

On the other hand, questions of who's in/who's out sometimes become so big and fraught that schools decide it's better to have everyone do the same thing. And that's not a win either. So in general I think that if people are willing to try more advanced classes, it's OK to let them, especially if classes are then benchmarked to state or national tests so there's a force against watering them down (a la AP Classes).

What math sequence did your children take? If they took classes post-calculus in high school, what were those?

Thursday, December 10, 2015

More kids take calculus in high school. Is this a good thing?

I took AP Calculus (AB) my sophomore year in high school, and then a semester of the BC version my junior year. While this was certainly considered "advanced," it's not particularly rare to take at least the AB version in high school anymore. According to this article in The Conversation, the proportion of students sitting for an AP Calculus exam has risen from about 5 percent in the 1980s to 15 percent now. Author Kevin Knudson posits that it's unlikely that the talent bench has gotten three times deeper in the intervening years. Instead, he claims that in the rush to stand out for college admissions, more students are pushing to take calculus. However, when they take college calculus classes, they find that they would have been better served by having a deeper understanding of algebra, geometry, and pre-calculus concepts.

I have mixed feelings on this. It is possible that having more students take AP Calculus classes could dilute the class. Experienced teachers have a good sense of what students are grasping and not grasping, and they naturally tend toward the mean. They move on when the majority of the class "gets it." This means the class would move slower if it contained a broad group of students vs. the most mathematically advanced students.

Knudson also points out that the rise of AP classes may be a result of schools failing to offer gifted education to high school students. Advanced classes seem like something, and since they're broadly perceived as a metric of a high school's quality, administrators are happy to offer them.

On the other hand, AP classes are that -- something -- and they're benchmarked for quality and understanding in a way that many other courses are not. If all a teacher's students score 4s and 5s on the AP exam, she is at least covering the required topics. If they score 1s and 2s, something isn't working. That's apparent, even if the students all get A's.

Likewise, one of the things that has always made gifted education easy to cut is that it's seemed aimed at just a few kids. AP classes that enroll 10-15 percent of students are harder to cut. That's a much bigger constituency.

What do you think? Is the expansion of AP classes a good thing, or is the situation more complicated?