The NBA Data Scientist

This is a nice feature from Bloomberg about Ivana Seric, a data scientist who uses statistical analysis for the Philadelphia 76ers.

What’s bigger: 1/3 pound burgers or 1/4 pound burgers?

I recently enjoyed reading about an unanticipated failed marketing campaign of the 1980s. Here’s the money quote:

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.

Here’s the article: https://gizmodo.com/whats-bigger-1-3-pound-burgers-or-1-4-pound-burgers-1611118517

 

Once upon a time in algebra class…

Side note: Yes, there’s only one true exponential curve on the graph. Yes, the spread of COVID-19 is best modeled with a logistic growth curve or an SEIR model. Nevertheless, this comic absolutely rings true.

Source: https://www.facebook.com/photo.php?fbid=10219301871391874&set=a.1147301637049&type=3&theater

Learning Math by Seeing It as a Story

I enjoyed this first-person piece about an English teacher who, by grim necessity, found herself thrust in the uncomfortable situation of co-teaching trigonometry and used her training as an English teacher to better engage her students.

Some quotes:

My students struggled with the calculations, thinking they just weren’t good at math. Like me, they hated it. What was the point in working and reworking these calculations? What were we trying to figure out anyway? And I originally agreed with them.

Yet trig slowly became my favorite class of the day. After spending years teaching English and reading, I was being challenged to move beyond what I had always been doing. When you’re new to something, you have a fresh perspective. You’re willing to take risks. You’re willing to try anything because you don’t know how something should be done.

And:

I brought in some books from Chris Ferrie’s Baby University series—books like General Relativity for Babies and Optical Physics for Babies. The idea is that you don’t fully know something unless you can break it down so simply that you can explain it to a young child.

That’s the task I gave my students. We started by reading Ferrie’s board books to see how simple language and illustrations could be used to explain complex subjects. Next, students chose a multistep equation they had initially struggled with. Working in pairs or small groups, they talked through their thinking and the steps needed to solve the equation. Their partners were encouraged to ask questions and get clarification so the ideas were explained at the simplest level.

And:

I used story problems as an opportunity to connect math to students’ lives by creating fictional math-based stories. First, students would work in small groups to go through the chapter in their math textbook and collect the story problems, writing them on index cards. Next, students would lay out the cards to see the questions as a whole: Out of 10 or more story problems in the chapter, were there five similar ones they could group together? What problem-solving skills were called for to work on these problems?

When they used creative writing skills to develop math story problems about things they were interested in, students became more engaged. They wanted to read the other groups’ stories and work on the math in them because they had a real investment in the outcome. The stories helped students find motivation because they created an answer to the question “Why do we need to learn this?”

 

Training Grad Students to Teach

This article from the Chronicle of Higher Education, What You Told Us About the Challenges of Training Grad Students to Teach, definitely gave me some food for thought about how we implement this in my own university.

 

How mathematicians are trying to make NFL schedules fairer

ESPN had a nice article about applied mathematicians at the University of Buffalo who are working with the NFL to create fairer schedules. A few quotes:

“This is a field I’ve worked in for 46 years, including 43 as a professor,” Karwan said by phone last week. “I’ve worked on very difficult problems that take more than 12 hours on the supercomputer to solve. And this is by far the hardest any of us have ever seen.”

And:

In developing the schedule, NFL assigns “penalty points” to outcomes such as three-game road trips, games between teams with disparate rest, and road trips following a Monday night road game. In their final proof of concept in 2017 before receiving the grant, Karwan and Steever took the 2016 schedule and lowered the penalty total by 20 percent…

The first step is based in both math and reality. Before creating the schedule, the NFL identifies a small number of games — usually between 40 and 50 — to lock in. The league refers to this as “seeding.” It helps accommodate expectations from television partners for key games in certain time slots, as well as about 200 annual requests from owners who prefer their stadiums not be used in a given week because of concerts, baseball games, marathons and other potential complications…

At that point, the NFL asks its computers to run schedule simulations until it finds one that has an acceptable penalty total. Usually that means juggling the 40 to 50 pre-seeded games. Karwan and Steever believe the key to improving the schedule is to better choose those pre-seeded games, allowing the computer to see stronger schedules that would otherwise be blocked by the initial choices through a process known as integer programming.

Not surprisingly, this research was publicized by the MIT Sloan Sports Analytics Conference, an annual conference dedicated to the integration (insert rim shot) of mathematics and sports.

Veteran teacher shows how achievement gaps in STEM classes can be eliminated

This press release from UC Santa Cruz definitely gave me food for thought about new things to try in my own classes. A few short snippets:

[Professor Tracy Larrabee] uses a three-pronged approach to support underrepresented students in her class.

“The first is that we have had a very diverse teaching staff,” she said. “We have one professor, four TAs and four MSI tutors, and during this time it just happened that of those people, half were female, we always had at least one African American, one Latinx, and one non-gender conforming tutor so that everyone could feel a connection to someone on the teaching staff.”

“Another technique I use is to emphasize failure as the appropriate path to learning,” she said. “Engineering is hard; it’s good to fail the first time you attempt a problem. People who fail at a problem the first time tend to retain things better than those who luck into the right answer.”

Her final tactic is to explicitly discuss stereotype threat. This is the risk that someone (i.e., from an underrepresented minority) might take routine negative experiences as confirmation that they are fundamentally unsuited for something like higher education.

“One of my African American MSI tutors—who are extremely high achieving students selected to provide supplemental tutoring to others—told me it was like having a light bulb go off for him,” Larrabee said. ”Until I discussed the issue in class, he felt like he didn’t belong in this major, but after we talked about stereotypes, he realized it wasn’t that he was unsuited for the material. It was hard for everyone!”

Article on John Urschel

I enjoyed reading this article about John Urschel, a former professional football player who is now pursuing a Ph.D. in mathematics at MIT.

https://hmmdaily.com/2018/09/28/john-urschel-goes-pro/

Why Should Physicists Study History?

I’ve always enjoyed reading about the history of both mathematics and physics, and so I really appreciated this perspective from Physics Today magazine about the importance of this field. One of many insightful paragraphs:

And a more human physics is a good thing. For starters, it makes physics more accessible, particularly for students. Many promising students drop out of the sciences because the material seems disembodied and disconnected from their lives. Science education researchers have found that those lost students “hungered—all of them—for information about how the various methods they were learning had come to be, why physicists and chemists understand nature the way they do, and what were the connections between what they were learning and the larger world.” Students can potentially lose the wonder and curiosity that drew them to science in the first place. Historical narratives naturally raise conceptual, philosophical, political, ethical, or social questions that show the importance of physics for the students’ own lives. A field in which people are acknowledged as people is much more appealing than one in which they are just calculating machines.

The whole article can be found here: https://physicstoday.scitation.org/doi/full/10.1063/PT.3.3235

Richard Feynman’s Integral Trick

“I had learned to do integrals by various methods shown in a book that my high school physics teacher Mr. Bader had given me. [It] showed how to differentiate parameters under the integral sign — it’s a certain operation. It turns out that’s not taught very much in the universities; they don’t emphasize it. But I caught on how to use that method, and I used that one damn tool again and again. [If] guys at MIT or Princeton had trouble doing a certain integral, [then] I come along and try differentiating under the integral sign, and often it worked. So I got a great reputation for doing integrals, only because my box of tools was different from everybody else’s, and they had tried all their tools on it before giving the problem to me.” (Surely you’re Joking, Mr. Feynman!)

I read Surely You’re Joking, Mr. Feynman! dozens of times when I was a teenager, and I was always curious about exactly what this integration technique actually was. So I enjoyed reading this article about the Leibniz Integration Rule: https://medium.com/dialogue-and-discourse/richard-feynmans-integral-trick-e7afae85e25c