Disney World, math, and line logistics

(Cross-posted at Gifted Exchange) I’m recently 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. Score!

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.

Did you take calculus in high school? What’s your favorite real world application of math?

photo courtesy flickr user Tia Eliane Turismo e Intercambio

12 thoughts on “Disney World, math, and line logistics

  1. Another depressing thing: Among the majority-minority schools that do offer higher levels of math, many of them have teachers who don’t really know the math and textbooks that are falling apart. That’s according to my Upward Bound supervisor in college who said the school I was working at was not unique. (And why they loved having us math majors– the main focus of UB was getting students to teach themselves from the textbook… but they were pretty happy getting someone who could do actual math tutoring.)

    I use math all the time because it’s part of my job. But I think I agree with the woman on the plane who told me the reason they hire math majors at her company is because they think logically and systematically– they hire them to organize and manage, not to do actual math.

    At the grocery store, I’ve been having fun showing DC the cost-per-ounce info and explaining how to make cost/benefit comparisons based on the price and how much we prefer one brand to another. We don’t really need to do this anymore, but it will be a good skill for him to have when he’s starting out on a budget. Something my father taught me.

  2. Vacation planning, of course! I just did a rather complex multivariable optimization on the order in which to visit three different cities. As I was working through it all (by hand) I thought that I really should write software to do it. Maybe I will someday, but it might require more comp sci theory than I currently have.

  3. Edelman makes some good points. I’m optimistic that relatively soon, all high schools can offer a broad set of classes by letting motivated students take them online. (Unfortunately, I don’t think it will work well for unmotivated students.)

    I wish Edelman had broken out statistics for Asians separately (if racism is the root cause of the problem, why are teachers only racist against blacks and hispanics?) I would also like to see data on suspensions broken out by family status. I suspect that single parent vs. married parent families are a bigger factor than race. Teacher experience is probably a minor factor in student performance- if you swapped the teachers around, I don’t think it would change much in terms of overall student performance. The issue is student behavior. (My mom is a reading specialist who has worked with many disadvantaged kids in a community with lots of drug use.)

    1. David Figlio has an interesting paper looking at the effects of child’s names on behavioral outcomes.

      Additionally there’s a large literature in psychology on the effects of children’s names on grading for children who don’t actually exist. People grade low SES names worse than they grade high SES names. People grade white names better than they grade underrepresented minority names. Even when the papers are the same in randomized controlled trials and the children in question don’t actually exist.

      The education literature finds that the first two-three years of teaching experience is the number one predictor of outcomes. Nothing else about teachers seems to matter consistently across studies. After the third year the effect of experience flattens out. But there’s a lot of turnover in those first three years.

      Swapping teachers does have profound impacts on student performance. Kirabo Jackson has a very interesting new paper out on student-teacher matches that shows what kinds of teachers are most productive for what groups of students.

      1. I agree that teacher experience is probably the largest TEACHER effect. I just think that family background probably dwarfs it by a lot.

        Even poor families with involved parents don’t send their children to schools where lots of children have behavioral problems- they homeschool instead. I know several of these families and their children do well despite their income status. (Family income <$50k for families of 6+; perhaps <$40k)

        1. I’m sure homeschooling works really well for involved single moms.

          Also: 50K and 40K are really not low income. Even with families of 6+.

          And so what if family background is important. How is that ever the child’s fault? If someone’s parents cannot or will not move from an inner city to a suburb or pay for private school or home school, does that mean that child shouldn’t have a right to have access to a college prep curriculum? Really?

          1. I noted that I hoped the children could access college prep curricula online.

            I see little point in offering college prep curricula to students with elementary school reading and arithmetic skills, regardless of their age or background.

            For students with learning challenges, either parents pay (in time or money) for them to learn or most often they don’t reach a college prep level. Reading specialists like my mom only work with kids far below grade level. Grade level kids are only marginally successful in college, though many can be successful at vocational colleges.

  4. I’m generally amazed at the low standards public schools seem to have for what kids should know. Obviously there are a lot of kids with disadvantaged backgrounds who don’t get the support from home needed to do high level work, but even at the good schools I went to (public & Catholic), Calculus was offered only as an optional AP class. Not required. For that matter only 3 years of math was required.

    In contrast, my parents BOTH had to take Calculus when they were growing up in India. Made sense for my dad who was going into engineering, but even my mom who studied literature had to as well (they track kids pretty early into a study path there).

    It just seems to me like if we *expect* more of kids, they might actually be able to do it. Of course, maybe the 3 months off during the summer makes all that knowledge fall out of their heads, too 🙂

    1. I don’t know much about Indian schools, but everyone I went to graduate school with was upper class. What percentage of students reach the level of education at which your parents took calculus? An Indian engineer friend said she took calculus around age 13.

      1. That’s a good point, Twin Mom. I don’t know the answer to your question but I suspect that most poor students don’t do the extra last couple of years in high school, if they even make it that far.

        But if you compare apples to apples, ie middle/upper class students in the US to those in India, our kids are not learning as much math. (Except for the motivated/gifted ones.)

  5. Real world math? If an item is 40% off, you can multiply the price by .6 and get the final price. I am stunned by the number of people who balk and disagree when I suggest this.

    1. @Mary Witt- oh, there are whole books to be written on the many things about numbers that seem to elude people. Like if a stock falls 50%, it then has to rise 100% in value to reach the original price.

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