In 1975, K. Patricia Cross mailed a questionnaire about teaching to faculty members at the University of Nebraska. She reports, “An amazing 94 percent rate themselves as above-average teachers, and 68 percent rank themselves in the top quarter on teaching performance.”
This finding is an amusing example of illusory superiority, but it raises the question of what it means for one teacher to be “better” than another. Exam scores, student evaluations, and peer observations only capture part of the short-term picture, much less the entire picture. Still, the complexity of approaches and goals doesn’t imply that nothing can be done; most Americans agree that the United States education system could be better.
So what does “better” really mean? The field of education is full of debates just about pedagogical practices alone, including the reading wars, math wars, and active learning vs. lecture. In this post, I’d like to humbly illustrate one potential reason that these debates continue to rage on: different teachers have different goals. A common one is raising the class average on the final exam, but there are many ways to do this, and there are many other goals.
Situation 1: John the Rawlsian
John is about to teach a class of 15 second graders. There’s going to be a standardized test at the end of the year, and John’s annual raise depends on his students’ scores on said test. In particular, his raise is proportional to the lowest score earned among the 15 students. Thus, he wants to maximize that minimum score, whatever value it winds up being.
Even without the raise, John’s goal would be the same. He teaches reading, a subject he loves and wants everyone else to love, so he’s intrinsically motivated to help his students, especially the ones who are experiencing greater difficulties. He believes that no child should be left behind.
On the first day of school, eager to get started, John asks every student to take a practice test. Then, he devotes all of his attention to the lowest-scoring student while everyone else does some activity. After an hour of private tutoring, he’s pretty sure that this student isn’t the lowest-scoring student anymore, so he turns his attention to the new lowest-scoring student. After tutoring that student for a while, he switches to someone else (possibly the first student), and so on, for the rest of the year.
Situation 2: Albert the Einsteinian
While John’s bouncing from one student to another, Albert is teaching a 1-credit graduate seminar. But his motivation is very different: Albert wants to hire someone to join his fancy physics lab. His research requires deep intuition about dark matter along with extraordinary mathematical brilliance. Albert’s goal is to get tenure!
Like John, Albert gives a test on the first day, but his test is completely open-ended, and none of the problems have definitive solutions. In fact, even the problem statements are so unclear that most of the students flounder, but Albert doesn’t care. He scans their submissions for what he considers signs of a potential superstar. He looks for something like “creativity,” and he feels no need to create a rubric (unless it becomes required for tenure).
After scanning, judging, and conducting a few interviews, Albert picks Nathan as his protégé. They talk about physics for twelve hours a week. During class, Albert and Nathan continue their discussions while the other students aimlessly scroll on their laptops. One student wishes that he had been chosen instead of Nathan, but otherwise, everyone’s happy with this arrangement.
Whose approach is “better”?
John and Albert each pay attention to one student at a time, but otherwise, their approaches are polar opposites: John’s maximizes the minimum according to a standardized test, while Albert’s maximizes the maximum according to his personal judgment. Their goals are so different that I don’t think it makes sense to say that one approach is “better” than the other. Both approaches (perhaps with less neglect of the non-lowest-scoring and non-Nathan students) make sense for their respective situations.
I am not a John, an Albert, or an education researcher. But based on what I’ve seen, most papers in education would be more convincing if they explicitly addressed, or at least acknowledged, the fact that different teachers are in different situations. There are too many goals, constraints, and personalities out there for a one-size-fits-all approach to be optimal for everyone.
Efforts at improvement might be more fruitful if reformists reduced their scope and worked more closely with individual teachers’ situations. My suspicion is that most faculty would be more convinced to try something new if they heard about a positive experience from a close colleague than if they stumbled upon a meta-analysis online.
Same averages, different distributions
John and Albert represent extreme cases, but even when two teachers set and achieve the same goal, the details can differ in important ways. For example, one way to raise the average exam score is to employ a pedagogical technique with all students. (This, understandably, seems to be the default approach in the education literature.) Another way is John’s approach of focusing on the lowest-scoring student. A third way, closer to Albert’s, is helping the high-scoring students achieve perfect scores.
The details of exactly how a technique raises exam scores are important, especially to a skeptical teacher who is considering adopting the technique but wants to see more data. If their mindset is more like John’s, but the proposed intervention is more like Albert’s, they’d be reluctant to try it out.
Anyway, I think this is starting to sound too technical—let’s just take a look at the figure below. Which is “better,” Section 1 (red) or 2 (blue)? Even though their averages are identical, John would prefer Section 1, while Albert would prefer Section 2. Their standard deviations are different, but my point is that reasonable people can disagree on which distribution is “better.”
Since both sections experienced significant improvement from the baseline, the distinction between their distributions might seem unimportant. But every decision made by the teacher nudges the distribution in some direction. For example, many courses have crowded office hours—should the policy be anything other than “first-come, first-served”? In response to this problem, Mark Guzdial, one of the most prominent researchers in computing education, explicitly suggests, “Teach to the bottom third of the distribution.”
In contrast, I’m not aware of anyone who explicitly advocates for teaching to the top third of the distribution. But as an undergraduate, I felt that some of my math instructors (implicitly) subscribed to that philosophy. They lectured at their own brisk pace, and everyone else’s job was to try to keep up. Many (perhaps most, including me) got lost, but maybe the top third (or less) learned a lot from those lectures.
Grades aren’t everything
All of this discussion about distributions is based on the assumption that we can capture the effect of a course on a student in a single number. But there are many objectives that, I suspect, a substantial number of people would like to (possibly implicitly) maximize:
Broad coverage of a large number of topics
In-depth coverage of a small number of topics
Amount of time spent on non-teaching activities
Exam scores, difficulty of exams
Student and/or peer evaluations
Job and/or graduate school placement rate
Students’ future incomes
Alumni donations to the school
Civic virtue (as difficult as it is to quantify), the joy of learning and discovery, self-actualization, etc.
These objectives often conflict, so teachers constantly face tradeoffs. For example, a friend once told me about a course they took that included a special project. The instructor had spent a lot of energy designing it, and student feedback was largely positive. Unfortunately, some students found parts of the project unappealing, especially since they were tangential to the core material.
So is it “better” for an instructor to do something if 90% of students love it but 10% of students hate it? It’s hard to say. The same goes for John the Rawlsian and Albert the Einsteinian—there’s no single right approach because there’s no single best objective. Most teachers might think they’re “better” than most other teachers, but often they’re simply aiming at different targets.