The best way to make a difference?

Between exams, confusion over the start of the semester and, finally, an ill-timed "wind chill" day, I've only been in a few times this semester. Still, I've reached a dilemma -- how can I best use my time at Ypsi High to positively influence my students? Do I attempt to inspire or enrich as many students as possible by dividing my attentions over the whole class, or do I focus on bringing a small, struggling subset up to par? How can I balance these priorities?

I initially gave presentations on technical topics, trying to bridge the gap between contrived textbook examples and the students' or my own experiences. This can lead to some nice eureka moments ("You mean somebody actually uses this stuff?", or, "Wow, that's cool", sneakily making math cool by association), at least in the classes of older students, but it sometimes spreads thin on a class of 25 freshmen, over half of whom are failing basic algebra. It begs the question -- is my time better spent coming up with entertaining uses of math designed to appeal to a broad audience, but having little measurable effect, or else in concentrating on those few struggling students who would most benefit from extra attention?

This dilemma became acute in the leadup to semester exams. After observing so many students struggling with solving basic algebraic equations for lines, slopes and intercepts, presenting some bit of engineering entertainment seemed... irrelevant. Instead, with George's help I picked out a few borderline students in each class, kids on the knife-edge of passage or failure, that I hoped could make the leap with some extra time in a small group. We looked for a profile of students struggling to pass but still caring enough to put in an effort -- the kind of student who would benefit from a couple of days of tutoring, one-on-one or in a small group -- and I cleared my schedule to come in the Thursday and Friday before exams. We ended up with four students, three in a group and one by himself spread over two hours, and without the distractions of twenty other kids I walked them through as much material as we could manage, guided only by the areas that they found most confusing. While the group of three only included one student who fit both criteria -- one girl was doing well enough to pass (though struggling with recent material), and another just didn't want to be left out of going with her friends -- I figured I could handle three as well as one.

Despite the weather holiday that Friday depriving me of half my teaching time, one of my borderline students passed (I have yet to hear the result from the other). A small victory, to be sure, but a victory nevertheless. Still, while the imminent exam made this victory clear, it's less clear how effective my prior efforts were. Will someone who enjoyed one of my science talks and passed last semester discover a subject they might once have thought dull and dry? Where is the balance between lifting up the struggling students and helping the gifted ones soar?

For now, I'll enjoy my small victory. But next semester we return to square one, teaching those students who failed Algebra I and must repeat the course. I hope a few of them will soar, too.