Halfway through my undergraduate career, I stopped reading course descriptions. Well, not quite; I was minoring in philosophy, so I read philosophy course descriptions. I stopped reading math course descriptions. There just wasn’t much point. I could generally tell from the title whether the course was something that interested me (”Topics in Geometry”, for example, did, while “Partial Differential Equations” did not), and the paragraph of text that followed the course title in the university calendar tended not to provide any additional information to anyone who hadn’t yet taken the class.
In Real Analysis I and II, I learned the Heine-Borel and Bolzano-Weierstrass Theorems, and I picked up some useful stuff on uniform convergence and L^p spaces. but a simple enumeration of those topics – which meant nothing to me until I was halfway through the course itself – was hardly enlightening. I was jealous of my peers in history and English, whose third-year course descriptions I had little trouble understanding.
I was a math major, mind you, so I wasn’t too vexed by this. My students, however, are taking precalculus and statistics as required courses, and I see no reason to throw a pile of disembodied terminology at them on the first day of class. Why lose them before it’s necessary? I feel particularly strongly about this in the case of the statistics course, which contains a good deal of material that is directly relevant to Real LifeTM; I don’t see why I shouldn’t summarize and motivate that material transparently on the course handout.
Here’s the course description, as it appeared in on the syllabus that one of the other faculty gave me:
An introduction to statistics which includes: organization and presentation of data, measures of central tendency and variation, probability and probability distributions, the normal distribution, central limit theorem, sampling and sampling distributions, estimations of means and proportions, choosing sample size, hypothesis testing, inferences from two samples, linear regression, correlation coefficient, curve fitting, goodness-of-fit, analusis of variance.
That’s not a course description; that’s a copy-paste job on the chapter headings from the textbook, mushed together into a run-on sentence.
Here’s my working course description:
How do we collect numerical information for a study, and how do we interpret it? These questions come up all the time – for instance, in assessing the effectiveness of a new drug, in determining the popularity of a national leader, and in comparing two companies’ customer service. In what ways can we usefully analyze large sets of numbers collected as part of a study? You’ve certainly seen one of the most common statistical quantities – the average – which your teachers may cite when they return your tests. Is there any way to get a good idea of how the grades were distributed – for instance, were they spread apart or bunched together? Were there a lot of high marks and a lot of low marks, or were most grades in the middle range? In this class, we’ll learn various methods of collecting, presenting, and interpreting numerical data.
Underneath I name the textbook, along with a list of the chapters we’ll be covering. The chapter names contain all of the terminology, which hopefully will make more sense to my pupils as the term progresses.
When I found out I was teaching this class, I knew immediately that I wanted to present it from the perspective of instilling a sense of media numeracy in my students. It’s a skill sorely lacking amongst people who read (and write) the newspaper, even as “media literacy” has become a buzzterm in recent years.
Today I read a journal post whose author expressed frustration with her ignorant peers for failing to interpret a certain work of art in keeping with her own enlightened, progressive politics; some time later in the same post, she mentioned in passing that she’d done poorly in high school math. One of her commenters proclaimed that What The World Needs These Days is fewer math classes, and more classes on media analysis and – wait for it – critical thinking in high schools.
(I’ve never heard anyone who doesn’t have an ideological axe to grind promote “critical thinking”, but that’s another matter.)
That the self-proclaimed purveyors of critical thought don’t see mathematical competence as another side of the media analysis coin is disturbing to me. And I’ve seen it the effects: socially conscious activists who can inflict a the latest trendy analysis on any news item at the drop of a hat, but who are rendered completely impotent as soon as numbers.
That cancer test with the 3% rate of false positives and the 3% rate of false negatives? Obviously correct 97% of the time. Arctic temperatures rising from 10 degrees to 12 degrees Fahrenheit? A whopping 20% increase. Unemployment – originally at 10% – falling an average of 0.5% per month? Keep that up for 200 months, and everyone’ll be gainfully employed. Yeah, we need to teach less math, so that people can analyze the news critically.
Rewriting the precalc description is more challenging; I’ve taken the “here’s some stuff you’ll need when you’re all grown up and taking calculus” approach, because I can’t come up with any compelling justification for learning how to factor quadratics or graph exponential functions. Last term I tried to emphasize what I thought were the most important skills: setting up equations in word problems, estimating answers, checking work. If I could have spent half the term just developing those skills, I would’ve; alas, the curriculum demanded otherwise.