A colleague who does not teach in our Math Department was tutoring one of my students. Not being familiar with our mildly unusual Honors Geometry course, she found that she herself did not know how to do the last problem on his test. “But I figured it out,” she then reported. “Looking back at the earlier problems, I could see that they told a story, so I understood what the last problem must be all about.”
Naturally I loved the resolution of this difficulty. She was 100% correct, though that certainly wouldn’t have happened all the time. A test should tell a story. It should have a theme; a beginning, a middle, and an end; a conflict and resolution; and a plot that exhibits a well-defined arc. A test should tell a story, but all too often it doesn’t, whether it’s one that I wrote or one that someone else wrote. Occasionally I write a test that literally tells a story, one in which the student has to fill in some blanks and solve some problems along the way, but that distresses too many kids who are unaccustomed to that form for a math test. Most of the time the story can be discerned only by reading between the lines, but I hope it’s still there, at least on most tests.
Not only should a test tell a story, but a course should as well. A couple of years ago a colleague commented on an Algebra II course at another school by saying something like this: “It isn’t a course; it’s a collection of topics.” Unfortunately all too many Algebra II courses suffer from this failing, which is one of the many reasons why I tend to prefer precalculus over Algebra II. Precalculus, at least as I teach it at Weston, definitely tells a story, with all of the parts I outlined above: theme, beginning, middle, end, conflict, resolution, plot, and arc. Algebra II gets only halfway, though one of the attractions behind the decision to spend the fourth quarter on cryptography is that it truly helps to complete the story of Algebra II, with lots of attention to functions, inverses, matrices, exponents, representations, and of course real-world applications.