Someone (not me) recently put two posters for “Mathematics Awareness Month” outside of my door. Here are the two posters:
I think that the first poster is good, but I think that the second poster is awful. The difference between the two is that, while both are applications of mathematics to sports, the first one (baseball) is reasonably authentic, and the second (basketball) is not authentic at all.
I could imagine the Colorado Rockies doing a mathematical analysis of the effect of humidity, and then making a decision about whether to humidify or not based on that analysis (I am assuming that the poster is about humidifying the baseballs, which they can carefully control, but the poster does not make this clear). On the other hand, I have shot as many jump shots as anyone reading this post, and I have never wondered about the chances of making a jump if the angle were 30 degrees. Moreover, I cannot pretend to come up with a reasonable estimate for my initial angle on a free throw—let alone a three-pointer or an 8-footer with a 6’4″ defender guarding me. Even if I did the analysis to determine the optimal angle, the angle would change according to my position on the court, the various talents and deficiencies of my defender, and my level of fatigue. For any given shot, I almost certainly would not have all of the data needed to describe the conditions of the shot—let alone do a detailed analysis of that particular shot—to help me increase my chances of making the jump shot.
This is another example of the scourge of “fake applications” in mathematics education. There are too many questions like, “the population of a certain type of fish is t^2, where t is time measured in years. Find the rate at which the population is changing when t=2.” Some amount of these fake applications may be useful in conveying how the mathematics would theoretically be used, but I think there is a greater harm: these types of problems (fish and jump shots) are pretty clearly not useful to anyone in the real world, yet they are clearly presented as an attempt to convince students that mathematics matters in real life. If I were a student, my reaction would be, “Really? Is that all you got? Jump shots?” I would leave feeling that the examples are contrived (which they are), and so there may not be real world applications.
As much as possible, I am for including authentic applications (my problem is that I do not know of many, since I am a pure mathematician who has been too lazy to find the authentic applications); I am going to include some coding theory and cryptography in my abstract algebra class this semester. I think that authentic applications have great value; contrived applications likely do more damage than good.