College Basketball’s Numbers Game

This is a very interesting (and readable) article about the blending of mathematics and coaching college basketball:

The Math Behind Super Mario

Forbes magazine had a great piece that can be shared with students about how mathematics is used when programming video games:

Teaching Parents to Talk Math with Their Kids

From a recent article in the Boston Globe,

Researchers with a group called the DREME Network (which stands for Development and Research in Early Math Education) say it’s time for parents to begin to teach their preschool-age children basic math concepts with the same urgency that they encourage reading…

The concepts and skills that make a difference with kids ages 3 to 5 (which is where the DREME Network is focused) are so basic that any adult can handle them: counting objects and recognizing that the last number stated describes the total number of objects, talking about patterns, going on “shape hunts,” ordering sets from biggest to smallest.

“People think of math in a very narrow way, but block play, puzzles, spatial aspects of our cognition, these are also important to mathematics. We’re not advocating drilling kids,” says Susan Levine, a psychologist at the University of Chicago and DREME Network member.

The Running Nerd: The US Marathoner Who Is Also a Statistics Professor

I loved these articles about Jared Ward, an adjunct professor of statistics at BYU who also happens to be a genuine and certifiable jock… he finished the 2016 Olympic marathon in 6th place with a time of 2:11:30.

Ward started teaching at his alma mater after graduating from BYU with a master’s degree in statistics in April 2015…

Ward wrote his master’s thesis on the optimal pace strategy for the marathon. He analyzed data from the St. George Marathon, and compared the pace of runners who met the Boston Marathon qualifying time to those who did not.

The data showed that the successful runners had started the race conservatively, relative to their pace, and therefore had enough energy to take advantage of the downhill portions of the race.

Ward employs a similar pacing strategy, refusing to let his adrenaline trick him into running a faster pace than he can maintain.

And, in his own words,

[A]t BYU, on our cross-country field, on the guys side, there were maybe 20 guys on the team; half of them were statistics or econ majors. There was one year when we thought if we pooled together all of the runners from our statistics department, we could have a stab with just that group of guys at being a top-10 cross-country team in the nation…

To be a runner, it’s a very internally motivated sport. You’re out there running on the road, trying to run faster than you’ve ever run before, or longer than you’ve ever gone before. That leads to a lot of thinking and analyzing.We’re out there running, thinking about what we’re eating, what we need to eat, energy, weightlifting, how our body feels today, how it’s going to feel tomorrow with how much we run today. We’re gauging all of these efforts based on how we feel and trying to analyze how we feel and how we can best get ourselves ready for a race. As opposed to all the time on a soccer field, you’re listening to do a drill that your coach tells you to do, and then you go home.

I think we have a lot of time to think about what we are doing and how it impacts our performance. And statistics is the same way. It’s thinking about how numbers and data lead to answers to questions.

Yes, I think there’s probably some sort of connection there to nerds and runners.

Sources: and

Math Maps The Island of Utopia

Under the category of “Somebody Had To Figure It Out,” Dr. Andrew Simoson of King University (Bristol, Tennessee) used calculus to determine the shape of the island of Utopia in the 500-year-old book by Sir Thomas More based on the description of island given in the book’s introduction.

News article:

Paper by Dr. Simoson:

This Is Why There Are So Many Ties In Swimming

From the excellent article “This Is Why There Are So Many Ties In Swimming“, ties in swimming are allowed by the sport’s governing body because of the inevitability of roundoff error.

In 1972, Sweden’s Gunnar Larsson beat American Tim McKee in the 400m individual medley by 0.002 seconds. That finish led the governing body to eliminate timing by a significant digit. But why?

In a 50 meter Olympic pool, at the current men’s world record 50m pace, a thousandth-of-a-second constitutes 2.39 millimeters of travel. FINA pool dimension regulations allow a tolerance of 3 centimeters in each lane, more than ten times that amount. Could you time swimmers to a thousandth-of-a-second? Sure, but you couldn’t guarantee the winning swimmer didn’t have a thousandth-of-a-second-shorter course to swim. (Attempting to construct a concrete pool to any tighter a tolerance is nearly impossible; the effective length of a pool can change depending on the ambient temperature, the water temperature, and even whether or not there are people in the pool itself.)

You Can’t Trust What You Read About Nutrition

FiveThirtyEight recently had a terrific article about how difficult it is to apply statistical methods to nutrition studies. In a nutshell, the issues are confounding with observational studies, observer bias, and p-hacking. I recommend reading the whole thing:

Top 100 Math Blogs for Students and Teachers

Now this was an unexpected surprise. I recently received the following message:

Hi John,

My name is Anuj Agarwal. I’m Founder of Feedspot.

I would like to personally congratulate you as your blog Mean Green Math has been selected by our panelist as one of the Top 100 Math Blogs on the web.

I personally give you a high-five and want to thank you for your contribution to this world. This is the most comprehensive list of Top 100 Math Blog on the internet and I’m honored to have you as part of this!

Also, you have the honor of displaying the following badge on your blog. Use the below code to display this badge proudly on your blog.


I’m not gonna lie: it’s really, really flattering to see my blog listed on the same page (at #76) with some of the genuine heavy hitters out there in mathematical blogland.

This seems like as good an occasion as any to thank my former students — many of whom are now secondary teachers of mathematics somewhere in the Dallas-Fort Worth metroplex — for suggesting that I create this blog in the first place as a way of keeping touch with them after they graduated. I do hope that this blog has been a help.

Top 100

Katherine Johnson: NASA Pioneer and “Computer”

I recently stumbled on the article “This Black NASA Mathematician Was the Reason Many Astronauts Came Home — Their Life Depended on Her Calculations” featuring Katherine Johnson, one of the first African-Americans to work at NASA. The article features an interview with her; I recommend the whole thing highly.

Quantitative Literacy


March 1 saw the publication of the book The Math Myth: And Other STEM Delusions, by Andrew Hacker. MAA members are likely to recognize the author’s name from an opinion piece he published in the New York Times in 2012, with the arresting headline “Is Algebra Necessary?

On page 48, Hacker presents a question he took from an MCAT paper. It provides some technical data and asks what happens to the ratio of two inverse-square law forces between charges of given masses when the distance between them is halved. The context Hacker provides for this question is that medical professionals needs to be able to read and understand the mathematics used in technical papers. His claim is that this requirement does not extend to the physics of electrical and gravitational forces. In that, he is surely correct… What this question is asking for is, Do you understand what a ratio is? Surely that is something that any medical professional who will have to read and understand journal articles would need to know. Hacker completely misses this simple observation, and presents the question as an example of baroque mathematical testing run amok.

On page 70, he presents a question from an admissions test for selective high schools. A player throws two dice and the same number comes up on both. The question asks the student to choose the probability that the two dice sum to 9 from the list 0, 1/6, 2/9, 1/2, 1/3. Hacker’s problem is that the student is supposed to answer this in 90 seconds. Now, I share Hacker’s disdain for time-limited questions, but in this case the answer can only be 0. It’s not a probability question at all, and no computation is required. It just requires you to recognize that you can never get a sum of 9 when two dice show the same number. As with the MCAT question, the question is simply asking, Do you understand numbers? In this case, do you recognize that the sum of two equal numbers can never be odd…

You get the pattern surely? Hacker’s problem is he is unable to see through the surface gloss of a problem and recognize that in many cases it is just asking the student if she or he has a very basic grasp of number, quantity, and relationships. Yet these are precisely the kinds of abilities he argues elsewhere in the book are crucial in today’s world. He is, I suspect, a victim of the very kind of math teaching he rightly decries—one that concentrates on learning rules and mastering formal manipulations, with little attention to understanding.

My favorite response came from a very perceptive high school students in the New York Times’ letters to the editor (

In “Who Needs Math? Not Everybody” (Education Life, Feb. 7), Andrew Hacker, who teaches quantitative reasoning at Queens College, says that since only 5 percent of people use algebra and/or geometry in their jobs, students don’t need to learn these subjects.

As a high school student, I strongly disagree.

The point of learning is to understand the world. If the only point of learning is job preparation, why should students learn history, or read Shakespeare?

And while your job may never require you to know the difference between a postulate and a theorem, it will almost certainly require other math-based skills, like how to prove something or how to understand a graph. If nothing else, people need math to understand finance, which is a part of everyone’s life.

I also disagree with the logic that if people are failing algebra, then they shouldn’t take algebra. If people approach life that way, they will get nowhere.

Algebra and geometry have a place in the classroom. If students are failing, then the way math is taught may need to change. But what is taught needs no alteration.

Which is crying shame, because Hacker does have good ideas about what a quantitative literacy course should look like (again, from Devlin):

The tragedy of The Math Myth is that Hacker is actually arguing for exactly the kind of life-relevant mathematics education that I and many of my colleagues have been arguing for all our careers. (Our late colleague Lynn Steen comes to mind.) Unfortunately, and I suspect because Hacker himself did not have the benefit of a good math education, his understanding of mathematics is so far off base, he does not recognize that the examples he holds up as illustrations of bad education only seem so to him, because he misunderstands them.

The real myth in The Math Myth is the portrayal of mathematics that forms the basis of his analysis. It’s the same myth you see propagated in Facebook posts from frustrated parents about Common Core math homework their children bring home from school.