I was saddened to recently read of the passing of Harry Lucas, Jr., who was a great proponent and benefactor of inquiry-based learning (IBL). To remember his contributions to the mathematical community, I certainly won’t be able to surpass the eloquent words of Michael Starbird in the June-July issue of MAA Focus.
Instead, I’ll share a little bit about my own interactions with Mr. Lucas. My first administrative position at my university was the founding co-director of Teach North Texas, a UTeach replication of the pioneering program UTeach program at the University of Texas for preparing teachers of secondary mathematics and science. I first met Mr. Lucas at the annual UTeach conference, and I don’t remember how it came up, but he personally encouraged me to submit a proposal to the Educational Advancement Foundation for the funding of equipment typically found in physics labs to get our university’s new Functions and Modeling course off the ground. Thanks to his generosity, hundreds of UNT students have experienced IBL firsthand early in their mathematical studies, often giving them an eye-opening new perspective on the way that mathematics “should” be taught. At future conferences, Mr. Lucas always had a keen interest in how Teach North Texas was progressing and seemed delighted to hear of our successes.
In the words of Dr. Starbird, “Mr. Lucas is one of very few individuals whose personal vision, decisions, persistence, and encouragement have clearly improved the lives of thousands of students and teachers across the country.” Thank you, Mr. Lucas.
I enjoyed this opinion piece at phys.org about project-based instruction in mathematics. A sample quote:
Mathematician Jo Boaler from the Stanford Graduate School of Education says that a “wide gulf between real mathematics and school mathematics is at the heart of the math problems we face in school education.”
Of the subject of mathematics, Boaler notes that: “Students will typically say it is a subject of calculations, procedures, or rules. But when we ask mathematicians what math is, they will say it is the study of patterns that is an aesthetic, creative, and beautiful subject. Why are these descriptions so different?”
She points out the same gulf isn’t seen if people ask students and English-literature professors what literature is about.
In the process of constructing the RabbitMath curriculum, problems or activities are included when team members find them engaging and a challenge to their intellect and imagination. Following the analogy with literature, we call the models we are working with mathematical novels.
Despite its hopelessly flawed methodology, U.S. News & World Report continues to sell magazines with its lists of Top 25 or Top 100 universities in various categories. Some universities who don’t play along, like Reed College, have long suspected that their rankings are penalized. So I enjoyed this press release from Reed College about statistics students who reverse-engineered the rankings to measure the magnitude of this penalty. The results are startling: while Reed was officially ranked #90, the formula should have them at about #38. In one glaring example, the magazine underestimated the college’s financial resources by over 100 spots even though this information the magazine could have obtained this information from free government databases instead of their survey.
I was intrigued by this article in the Chronicle of Higher Education about professors who asked students to write their own exam questions, thus forming a test bank from which the actual exam would be constructed. I’m not sure if I’d try this myself, but it definitely gave me food for thought.
This is a nice feature from Bloomberg about Ivana Seric, a data scientist who uses statistical analysis for the Philadelphia 76ers.
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
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.
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.
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.
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.
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?”
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.
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.”
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.