We were driving from Billings to St. Mary, MT when we passed a sign that said “For Wind Information Tune to 1610 AM.” I excitedly reached for the radio, sure I was going to be getting a report on wind conditions around the state, only to be disappointed when I discovered that it was actually just a promotional station for the local energy utility and wind energy. I only listened for a minute, but it was long enough to here them comment that Montana is the fifth windiest state in the country. My disappointment was wiped away by a new sense of excitement and curiosity – was this really the fifth windiest state, and how do we know?
My wife/research assistant was up to the challenge and quickly found an article that listed Montana as fifth windiest. We then detoured into related trivia (“Guess which state is windiest/least windy/biggest/etc.”), but this fifth-place ranking kept bothering me. How was this ranking determined? Was it based on an average daily or hourly measurement of windspeed or on some continuous measurement? Where was the wind that was used to determine the rankings measured? How was the data collected? How were anomomlies like tornadoes and hurricanes factored in? If sampling was used, what was the confidence level, and how do you ensure a fair comparison when sampling from states of different sizes?
At this point, two things should be clear. First, Montana is a really big state, and driving across it gives one a lot of time to think. (As an aside, we later heard people refer to Montana as the “Texas of the north” because of both the landscape and the size, and it’s a pretty accurate description). Second, there’s a rich mathematical topic here, one that can be mined in many ways. I’ve already alluded to the various statistical issues involved, and the discrete/continuous question is a great one for both precalculus and calculus students to ponder. Beyond that, the very idea of ranking something can challenge students to apply even pretty elementary math (means, for example) in some pretty complex ways.
Suppose that I built part of a course around the question, “What is the best lunch the dining hall can serve to athletes on game days?” I’m pretty sure this meets Grant Wiggins’ definition of an Essential Question, and even if it falls short in some way it’s still a rich question that can be explored in multiple ways and is relevant to students’ lives. To answer the question, students would need to learn about and consider a variety of factors, including physiology, nutrition, sports psychology, and individual preferences. They would likely need to build some sort of metric for assessing and weighing the factors they identified, and they’d need to collect data and apply their metrics to it to come up with a ranking.
As I said, the math itself wouldn’t be terribly complicated in this example, but it would be a great project that pushed the students to more deeply understand the question and how to tackle it. I’m intrigued by the possiblity of finding questions like this that necessitate the exploration of various mathematical topics at all levels of the curriculum. What question might we ask that would let us get at logarithmic functions in a more interesting and engaging way?