Monday, April 23, 2012

Disney World, and access to calculus and advanced math

I'm back from a week-long vacation at Disney World with my three small children. It was a lot of fun (if not exactly relaxing). My inner geek was on display, though, as I kept pondering the logistics of line management. Disney has huge crowds for the popular rides. In a keen bit of psychological insight, Disney understands that people tolerate waits better if there's transparency on time. The powers that be also know that some people detest lines enough that they will give something up (like complete flexibility) in order to be guaranteed a short wait. So all popular rides have two options: a stand-by line, with a posted wait time, and a "Fast Pass" option. To get a Fast Pass ticket, you go to a machine by the ride and insert your park pass. The ticket gives you an appointed window to show up in order to bypass the line. The catch is that there are only a certain number of Fast Pass tickets per day, and they are given out in chronological order. If you show up at 9am, you might get a fast pass time of 10am-11am. Show up at 1pm and your time window might be 8pm-9pm, with the downside that you probably can't get another fast pass ticket until you return yours to the ride in question. So you're shut out of other popular rides for the day, unless you wait in the 60-plus minute standby line.

Making best use of all this information involves optimizing various variables: how much you dislike lines, how long the lines actually are (often a function of time of day and day of week), and how much you care about this particular ride in comparison to other rides. For example, "Soarin'" is by far the best ride at Epcot. Our first day at Epcot, we got Fast Pass tickets for the ride for a roughly 8pm return. That was fine, because there weren't very many other popular rides at Epcot. Once we learned that Jasper really liked that ride, though, we showed up the next day when Epcot opened. He and I made a beeline for Soarin' and got on the first run. Meanwhile, my husband got us all Fast Passes for the 9:45-10:45 window. So we got to go on the ride twice with no wait. By the time we got on for the second time, the standby line was up at 30 minutes, and it hit 60 very shortly. Fast Passes sold out by afternoon.

Optimizing in a world of multiple variables is, of course, a real world application of math. Amusement parks are one thing, but many other fields make use of this knowledge as well: economics (and business forecasting in general), engineering, logistics. Not having a background in advanced math would make getting jobs in any of these fields rather difficult. That's why I was quite disturbed to read (in Marian Wright Edelman's Huffington Post column) about the results of the Department of Education's Office of Civil Rights survey of public schools in America. Edelman has her own opinions on tracking and funding that I don't share. But regardless, these are some disturbing statistics: "Fifty-five percent of the low-minority high schools surveyed offer calculus but only 29 percent of high-minority high schools do. Similarly, 82 percent of low-minority schools offer Algebra II compared to 65 percent of the high-minority schools."

While some enterprising students might take Algebra II or Calculus during the summer or petition the school for an online course (or do Khan Academy on their own), a school's course offerings pretty much set the tone for what a student is expected to know. That such a low percentage of high schools offer calculus -- and an appallingly low percentage of schools serving mostly minority kids -- does not bode well for a mathematically promising future. That's a far worse outcome than a 75-minute wait in the line for Space Mountain.


Bostonian said...

In some of the high-minority high schools, there may be few students qualified to take calculus, which requires proficiency in algebra and trigonometry. Before asserting that the educational system is discriminating against minorities in course offerings, regress the probability of offering calculus on the average math SAT score of the school and on the fraction of minority students. I bet the coefficient on the minority students variable becomes much smaller when average SAT score is controlled for.

Anonymous said...

As a projectionist, I used to start movies for which no tickets had been sold, just in case someone came late. If I were to leave the film on the platter and start it when the latecomer showed up, there wouldn't be enough time for the movie to finish before the next showing was scheduled. If I didn't start the movie at the regularly scheduled time, the theater would have to turn away the business of any latecomers.

Schools aren't movie theaters. They don't start movies for which no tickets have been sold.

Anonymous said...

Did this survey look at the availability of the course, or just whether it was offered at the school. There are often other options such as dual enrollment or travel or video class with a school that offers the classes.

It's not just math. Some schools offer a full menu of science classes, APs, etc while others don't. We should provide access, but we shouldn't waste teacher time on classes that have no students.

I can see it now, the big scandal of teachers who are paid to teach classes that don't exist.

Anonymous said...

Wow- can't believe these comments. How would you feel if your kid went to a school where their options were so limited? Presumably, if you are commenting on this blog, you have the resources and the wherewithal to ensure that your child would be able to access the material elsewhere. What about those kids who don't have such advantages?

Anonymous said...

I suspect such attitudes are why there is such mistrust and dislike of gifted programs, and the impression that they are elitist. When attitudes like those posted above prevail, the consequence is the weakening (and often abandonment) of gifted education programs everywhere.

Laura Vanderkam said...

I was a little surprised by some of the comments, too. Obviously, you don't just stick calculus in a school overnight. But the same school mindset that doesn't think it needs to be offered is likely the same mindset that has underwhelming math options in earlier grades too. I think most students look at the coursebook to decide what they're going to take. If a school consistently offered it, eventually there would be people in it. And even if it was undersubscribed, I was glad that the Indiana Academy offered some advanced math classes with 4 students in them. It's a question of priorities.

nicoleandmaggie said...

I'm not surprised by the comment. Consider the source.

Such commentary is a major driving force for keeping working women and underrepresented minorities off the davidson gifted forum. They're not welcome there.

Bostonian inspired this post from us on stereotype threat:

Bostonian said...

Why does nicoleandmaggie think "working women" have left the Davidson Gifted forum? Most posters there are mothers, and my impression is that most are not SAHMs.

Readers can look at the post she linked to and my posts on Davidson Gifted Forum and judge who makes more reasonable arguments and who is sexist. I for one don't speculate about the physique of other internet posters.

Anonymous said...

Did the survey take into account school size? A large school is more likely to offer a large variety of class levels than one with a low enrollment. And though I do agree that "minority" and "low-income" go hand-in-hand in much of the country, perhaps the problem of schools with low-income children (regardless of race). Smaller schools and schools with limited financial resources can't afford to staff a class for a small number of students, no matter their skin color.

My public high school was in an upper-middle class suburban (98% white) area. Yet my graduating class was the first in the district offered the option to take Calculus. Not because of money, but because of class size. My class was the largest ever seen at that high school and had only 200 students.

And the groundwork for that Calculus offering had to be set before any of us walked in the doors our Freshman year--starting with my year they re-organized the math curriculum so that we could complete all of the algebra, geometry, trig, etc and still have calculus.

My husband and I go back and forth on the issue of ideal school size for our children. I believe bigger is better because of the variety offered. He had the benefit of a tiny school where the faculty were willing to provide more individual attention (and could give select students advanced coursework). I fear that his experience is too rare to count on. (And of course we are raising our family in a completely different metropolitan area than where either of us is from).

Anonymous said...

"a school's course offerings pretty much set the tone for what a student is expected to know"

Cart. Horse.

Anonymous said...

I went to a top-ranked public school with several AP Calculus classes, as well as honors calculus classes from which students would often get 4s or even 5s on the AP exam anyway. I think everyone outside of special ed had a 4-digit SAT score (out of 1600). (More to the point, perhaps, is that I know this.)

Amazing what the rest of the country looks like. Half of schools don't offer calculus? One in five doesn't offer Algebra II? My jaw drops; my bubble pops.

Anonymous said...

I am offended by this post and the terms of divisive terms used.

Minority, has nothing to do with it, my child is a minority and I would say most of the gifted children I have met in the past 3 years are of African heritage, in Germany, many of the African kids, are extremely talented in math. When I visit Africa, I am amazed at the 3 and 4 year old that help their mothers in the market place and calculate and faster than you can use a calculator, in their heads. I visit schools and universities in Africa and I am appalled by this term "high minority schools", if you check the schools with the highest minority rates, with minority teachers have the highest scores. Why is there only a gap here in the US.

lgm said...

Minority has nothing to do with it. It is the quality of the teaching and the preparation of the students. If the majority are coming in to preK not having acquired preschool math skills such as 1:1 correspondence, then they will not have the time to get to Calculus by 12th grade, especially if the school is full inclusion, one daily lesson fits all. There is no royal road. There is also the fraction guantlet...did the school manage to hire enough proficient Gr. 3-5 teachers such that all unclassified children learn the math for those years? State test scores say 'no'.

That said, I'm in a district that offers calculus, but only through community college. Not good enough for kids going on to engineering - they need theory. Neighboring high schools of similar size have a different philosophy and offer Calc BC as well as honors math. Some have more minorities than ours.What is offered is up to the politicians.