Why statistics professors should grade for craftsmanship

Like many mathematical topics, statistics can be persistently abstract and unintuitive. From dividing by n-1 instead of n, to proving results in infinite dimensional Hilbert spaces, statistics rarely goes down smooth on the first try. Most of the best statisticians take this challenge head on. They can quickly distill the intuition behind bafflingly abstract ideas, either to readers, students, or collaborators. Our community rewards this type of explanatory skill over the timespan of a career, but we put little value on it when grading students. Students are typically graded for correctness, completeness, and (sometimes) participation, but not for craftsmanship. That's a missed opportunity.

Over a career, statisticians who explain abstract concepts well will do better on the job market, be invited to give more talks, get better teaching reviews by students (all else equal), and will attract more students to do research with. Ultimately, they'll also get more scientists using their tools.

From the educational perspective, Jeremy Kun recently wrote a great piece on the habits of mathematical people, and why math education should be seen as a core tenant of training well-rounded adults. Knowing how an algorithm works does more than train us in how to use it, or how to “go under the hood” when it breaks down. Kun argues that it trains us to be conscious of our assumptions, to concretely define terms, and to admit when we're wrong. On top of this, working in a field that requires you to "spend almost all of your time understanding nothing" can hopefully imbue a kind of emotional resilience. To be successful, you have to be able to endure your own confusion until a blip of understanding seeps through. Gaurav Kulkarni argues that math and science teaches students to embrace the unintuitive, and to expect real life systems to be complex rather than tweetable. I would add on to this that, at its best, mathematics doesn't just train us to understand and explain abstract concepts correctly, it trains us to explain them artfully.

Perhaps we should better reflect this in how we evaluate statistics students. On homeworks and exams, correctness should take priority, but the craft of an argument's construction has value too.

One approach here is to treat craftsmanship in a similar way to class participation. Another partial solution could be to require a certain level of clarity and formatting polish in write-ups. While polish is certainly not the same as skillful explanation, it does focus more attention on the presentation and can be a push in the right direction.

Beyond this, balancing craftsmanship with correctness becomes a problem of limited time and resources, much like balancing the scope and depth of a course's topic load. From a student's perspective, improving a write-up's presentation cannot be done without sacrificing time or completeness. From an instructor's perspective though, prioritizing clarity, brevity and craftsmanship can increase resources by saving hours of grading time. Depending on the course, it may be helpful to put more focus on craftsmanship. Less topics would be covered, but it could also lead to more well-rounded students, and faster proliferation of statistical breakthroughs.

Author's note: I started thinking about this after a seminar session on the Julia programming language during this year's JSM conference. It was, by far, the most eloquent set of talks I saw. One highlight was a talk by Jiahao Chen, who referenced the Sapir-Whorf hypothesis that language shapes our cognition – with a more elegant language, we can write more elegant algorithms. It should not have been surprising that people who think about languages all day tend to also be darn good speakers.