Stat 305. Engineering StatisticsSpring 2013
GPU Computing Seminar SeriesFall 2013
People understand the world through experience. Consciously or unconsciously, every abstract concept is inextricably linked in our minds to a good example. Consider Simpson's Paradox, a statistical phenomenon in which a trend in a sample reverses when the sample is divided into groups. Simpson's paradox is conceptually difficult, but I grasp it because my mind automatically goes to a toy example. I imagine that a field biologist catches several fish and measures their lengths and their blood pollutant concentrations. I mentally construct plots of hypothetical data like the ones below.
The plot on the left suggests that pollutgant levels are lower on average for heavier fish. But as the right-hand plot shows, this trend reverses for each species individually: heavier salmon have higher blood toxicity, and the same is true for trout. This example is inseparable from my understanding of Simpson's Paradox.
When it comes to teaching, I aspire to an example-based strategy. My students build difficult concepts from simple examples. When I explain Simpson's Paradox, I use the example above. When I make the case that statistics is important to engineering, I tell the story of the Challenger disaster, where incomplete data and misuse of statistics contributed to the crash. When I teach conditional probability, I use the Monty Hall problem to show that probabilities can depend on hidden sets of conditions. With the right example, hidden misconceptions clarify, understanding forms, and the subject comes to life.
The best examples generate curiosity. When I can, I attempt to learn what my students find interesting and use it in the classroom. In one of my classes, for example, some students liked the analogy between hypothesis testing and court cases, and we discussed it for twenty minutes longer than I had originally intended. The extra time was well spent. Because they were engaged, they learned more in those twenty minutes than in a typical hour of routine lecture.
Students are most curious and engaged when they feel included and when they share ownership of the class, so I regularly solicit student feedback. The last question on each weekly assignment invites students to voice confusion about the subject matter and general course concerns. This practice gives students a convenient time, place, and excuse to address important issues. The responses are extremely useful, and I routinely use them to change course logistics and improve how I present the subject.
Immediate feedback helps students feel included and in control. To compensate for the inevitable delay of written feedback on homework and tests, I give frequent in-class exercises. I stop the class for ten or twenty minutes at a time to let students work through example problems, and I go through the solutions immediately afterwards. In addition, students exit my exams with solution sets in hand so they can check their work while the test questions are still fresh.
I am still growing as a teacher, and I am open to trying new things. In future courses, I will begin to implement Team Based Learning. This method not only involves regular hands-on activities, immediate feedback, and a high level of cohesiveness among students, but also transfers ownership to the students and turns the class into inherently social activity.