For me, at least, the difference between doing a calculation for homework and doing a calculation for research is how much you check your work. Where one might be happy to get the right integral form or the right combination of coefficients for an academic exercise, there’s no wiggle room for stray factors of pi or root two when you’re planning on publishing your result. One of the tasks of a collaborator is to cross check calculations and programming for such errors.
As I’m in the thick of this process, I’ve picked up on the following bit of wisdom:
When having a graduate student check a long calculation or a chunk of code, always include at least one intentional error. There are two reasons for this. First, it’s a way to check if the student is doing a good job. Secondly, it makes the student feel like they’ve `done something’ even if the thing they are checking is otherwise error-free.
Afterall, despite being a “blue-collar” task, checking work is an absolutely necessary part of research. Anyway, the topic of intentional errors reminded me of three brief anecdotes.
Rubbish students couldn’t catch a simple error
A well-liked math(s) professor I had as an undergrad told a [possibly apocryphal] story about a colleague who would always include intentional errors in his lectures so that his students could catch them and learn to think on the spot. He was quite fond of this pedagogical method and his students developed the habit of participating in course discussions.
During a visit to another university, he was invited by another colleague to give a guest lecture to a group of postgraduates. He accepted the offer, and began the talk by making what he thought was a very obvious error in the first line on the chalk board. After pausing for a bit and being met only with a classroom of quiet students, he went on to continue his calculation. He was sure that students would quickly interrupt him as he began deriving increasingly nonsensical results from his initial intentional error.
However, much to his dismay, the students only continued to listen politely without making any effort to interrupt him. Eventually the results on the board were so self-contradictory that the visiting professor decided that the students must be incredibly thick and were a waste of his time. He turned around and stormed out of the lecture hall. Later that day he made it a point to tell his colleague that his students were absolute rubbish.
The following day his colleague returned to the class and cautiously asked his students what they thought of the guest lecturer. After a bit of murmering, one student replied: “Professor, we know the guest lecturer is a very famous mathematician, but he’s terrible at preparing lectures. He made a very simple mistake at the beginning of the lecture and derived all sorts of incorrect results. Since he’s only here for one day we decided not to embarass him by pointing out his error.”
Three intentional mistakes
Perhaps the solution to the previous story is to tell students ahead of time that there would be errors. This reminded me of an actual event last year in Cambridge. On the first day of class, one of our lecturers made the note that he would make “three intentional errors every lecture. I expect you to point these out.” The course was scheduled at 9am, and it was reasonable for him to do something to encourage student participation. However, in retrospect, the statement was meant to be a tongue-in-cheek way of telling us to participate in class.
Unfortuantely, many of the students were international and had decided that it was cruel for a lecturer to do something like this. Some of the students may have even became frustrated when they weren’t able to pick up on the `intentional errors’ that weren’t really there.
I wonder if this had to do with the saying that “Part III is a tool to transfer information from the notes of the lecturer to those of the student without travelling through the brains of either.” Perhaps some students didn’t like the idea that there might be intentional mistakes planted in the notes that they felt they had to regurgitate for exams. For what it’s worth, I thought the lectures were quite enjoyable once I stopped double checking every sign and coefficient.
The trick to giving a good talk
One last anecdote is a bit of advice I got from my undergraduate adviser on giving a talk. The trick to making yourself look good at a talk, he claims, is to always leave out one very obvious point from the talk. This way you know exactly what your first question will be and you can prepare a very eloquent answer it in advance. From that point, you’ll either be buoyed by your self confidence or otherwise any questions that stump you will be forgiven since you’ve already demonstrated your uncanny ability to think on your feet.
(He also said one should always wipe the chalk board completely clean before you talk, and that the comfy chair in the room is always his.)
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